 
Last updated on September 10, 2021. This conference program is tentative and subject to change
Technical Program for Wednesday September 29, 2021

WA21 
Tactic A 
New Developments in TimeDelay Systems 
Invited session 
Chair: Zhou, Bin  Harbin Institute of Technology 
CoChair: Wu, AiGuo  Harbin Institute of Technology Shenzhen Graduate School 
Organizer: Zhou, Bin  Harbin Institute of Technology 
Organizer: Yang, Xuefei  Harbin Institute of Technology 

14:4515:05, Paper WA21.1  
Adaptive Fuzzy Control for Uncertain Switched Nonlinear TimeDelay Systems with State Constraints (I) 

Yongchao, Liu  Harbin Engineering University 
Qidan, Zhu  Harbin Engineering University 
Keywords: Approximation techniques and numerical methods, Control of nonlinear systems
Abstract: In this paper, an adaptive fuzzy control strategy is proposed for uncertain switched nonlinear timedelay systems with state constraints. All system states are guaranteed to maintain the prescribed regions whereby barrier Lyapunov function (BLF). By choosing appropriate LyapunovKrasovskii functionals, the influence of timedelay is effectively counteracted. The fuzzy logic systems are explored to approximate the unknown dynamics. Combining the Lyapunov theory with average dwell time (ADT) method, it is shown that all states of the entire closedloop systems are bounded under switching signals and the predefined constraints are not violated. Finally, simulation results are given to show the validity of the designed scheme.


15:0515:25, Paper WA21.2  
Reachable Set Synthesis for DiscreteTime Markovian Jump Systems with TimeVarying Delay by Partially Asynchronous Control (I) 

Feng, Bo  Harbin Engineering University 
Feng, Zhiguang  Harbin Engineering University 
Zhang, Huayang  Harbin Engineering University 
Keywords: Control of linear systems, Numerical simulation, Lyapunov functionals and Lyapunov matrices
Abstract: The problem of reachable set synthesis for discretetime Markovian jump systems(MJSs) with timevarying delay is researched. Different from the traditional controller, a kind of partially asynchronous controller is proposed. The normal system mode and the asynchronous mode are fully considered in the desired control law including delay state and delayfree state that happen asynchronously. Moreover, Bernoulli random variables are applied to represent the probability distribution of above two kinds of states. On these foundations, by employing Lyapunov theory and linear matrix inequalities(LMIs), a sufficient condition of the reachable set synthesis for MJSs under partially asynchronous control is given. Finally, a numerical example is provided to show the effectiveness of the proposed methods.


15:2515:45, Paper WA21.3  
H_{infty} StateFeedback Control for Coupled DifferentialDifference TS Fuzzy Systems with Input Saturation (I) 

Xia, Tiantian  Nanjing University of Science and Technology 
Zhang, Baoyong  Nanjing University of Science and Technology 
Li, Yongmin  Huzhou Teachers College 
Dai, Mingcheng  Nanjing University of Science and Technology 
Keywords: Control of nonlinear systems, Stability
Abstract: This paper studies the H_{infty} fuzzy control for a class of coupled differentialdifference nonlinear systems with input saturation, bounded disturbance and timevarying delays. The purpose is to design a statefeedback fuzzy controller such that the resulting closedloop system is locally stable and satisfies a regional H_{infty} performance. Delaydependent sufficient conditions ensuring the existence of the desired controllers are obtained based on the fuzzyweighting dependent LyapunovKrasovskii functional approach and the linear matrix inequality (LMI) technique. Finally, a numerical example is used to illustrate the effectiveness of the proposed design method.


15:4516:05, Paper WA21.4  
Controller Design for Nonlinear Uncertain Systems with Time Delays Via Backstepping Method (I) 

Li, Wenjie  Qufu Normal University 
Zhang, Zhengqiang  Qufu Normal University 
Keywords: Control of nonlinear systems, Stability, Observer design
Abstract: For a class of nonlinear systems, a novel memoryless controller is designed by using the observerbased backstepping method. An observer is proposed to estimate the unmeasurable state of the system. The proposed controller solves the signal boundedness problem of the system under the appropriate design parameters. In the backstepping process, we construct novel LyapunovKrasovkii functional and appropriate control gain function in each step to solve the unknown time delays which exist in each system state. Finally, we apply the new control method to a twostage chemical reactor system with delayed recycle streams, and the effectiveness of this method is illustrated in the simulation results.


16:0516:25, Paper WA21.5  
Global Exponential Stability Analysis for a Class of Coupled Cyclic Genetic Regulatory Networks with Multiple TimeVarying Delays (I) 

Yu, Tingting  Heilongjiang University 
Zhang, Xian  Heilongjiang University 
Wang, Xin  Heilongjiang University 
Keywords: Nonlinear dynamics, Stability, Biology
Abstract: The coupled repressilators, as a special case of cyclic genetic regulatory networks, can be used to adjust scillations at the cellular level, and hence it have received extensive attention from many scholars. This paper addresses the problem of global exponential stability analysis for nonnegative equilibrium points of a class of coupled repressilator models with multiple timevarying delays. Sufficient conditions are investigated to guarantee that the considered model has a unique nonnegative equilibrium point which is globally exponentially stable. The obtained criteria are composed of several simple linear inequalities that are only related to the model parameters, so they can be easily verified by using the standard software tools. The results of two illustrative examples present the effectiveness of the proposed approach.


16:2516:45, Paper WA21.6  
PredictorBased Disturbance Attenuation Control of a Class of ContinuousTime Linear Systems with Input Delay (I) 

Wang, Yu  Harbin Institute of Technology (Shenzhen) 
Wu, AiGuo  Harbin Institute of Technology Shenzhen Graduate School 
Huang, Jing  Shanghai Aerospace Control Technology Institute 
Cao, Heyang  Shanghai Aerospace Control Technology Institute 
Keywords: Prediction based control, Control of linear systems
Abstract: In this paper, the problem of disturbance attenuation based on predictors is investigated for a class of continuoustime linear systems with input delay. First, a new predictor is constructed by taking account of the information of the unknown disturbance signal. In order to obtain this new predictor, the unknown disturbance is estimated by the error between a certain variable and the standard predictor. Under the transformation defined by the proposed predictor, the original system with input delay is converted into a delayfree system. Then, the disturbance attenuation performance for the predictors is analyzed in terms of the transformed delayfree system. A numerical example is presented to verify the effectiveness of the proposed predictor.


WB2T1 
Tactic 1 
Applications 
Regular Session 
Chair: Vyhlidal, Tomas  Czech Technical Univ in Prague, Faculty of Mechanical Engineering 
CoChair: Sipahi, Rifat  Northeastern University 

14:4515:05, Paper WB2T1.1  
A TimeDelay Approach to Vibrational Control with Square Wave Dithers 

Zhang, Jin  Tel Aviv University 
Fridman, Emilia  TelAviv Univ 
Keywords: Vibration control, Control of linear systems, Stability
Abstract: This paper studies stabilization of secondorder systems by fastvarying square wave dithers depending on a small parameter eps>0, which is inverse of the dither frequency. We first employ the known in vibrational control coordinate transformation that allows to cancel {1over eps} multiplying the square wave dithers, and then present a timedelay approach to periodic averaging of the system in new coordinates. The timedelay approach leads to a model where the delay length is equal to eps. The resulting timedelay system is a perturbation of the averaged system in new coordinates which is assumed to be exponentially stable. The stability of the timedelay system guarantees the stability of the original system. We construct an appropriate Lyapunov functional for finding sufficient stability conditions in the form of linear matrix inequalities (LMIs). The upper bound on eps that preserves the exponential stability is found from LMIs. Two numerical examples illustrate the efficiency of the method.


15:0515:25, Paper WB2T1.2  
Time Delay Model of the Turbine Pressure Water Conduit: Application to the OffTheGrid Regime Control 

Fiser, Jaromir  Czech Technical Univ in Prague 
Zitek, Pavel  Czech Technical University 
Kuchar, Michal  Czech Technical University in Prague 
Peichl, Adam  Czech Technical University in Prague 
Kucera, Milan  ZAT A.s 
Kulik, Pavel  ZAT A.s 
Vyhlidal, Tomas  Czech Technical Univ in Prague, Faculty of Mechanical Engineerin 
Keywords: Infinite dimensional systems, Neutral and advanced equations, Spectrum computation and optimization
Abstract: The paper presents modeling the hydroturbine governing system with delay in application to the turbomachinery control. The delay originates from the wave phenomenon encountered in the pressure water conduit connected to the turbine. To facilitate the PID control tuning the turbine and conduit model is linearized and it results in linear time delay system referred to as the neutral system. Particularly, the disturbance rejection is achieved by the PID control response to varying power loads. Finally, the application example demonstrates the turbomachinery control in the offthegrid regime.


15:2515:45, Paper WB2T1.3  
Time Delay Model of Pressure Relief Valves 

Kadar, Fanni  Budapest University of Technology and Economics 
Stepan, Gabor  Budapest Univ of Technology and Economics 
Keywords: Neutral and advanced equations, Stability, Infinite dimensional systems
Abstract: This paper introduces a simplified mechanical model of pressure relief valves extended by a downstream pipe. The distributed parameter model of the system is presented and transformed into a system of neutral delay differential equations. It is shown that the time delay is proportional to the length of the downstream pipe. The analytical investigation of the system proves the stabilizing effect of the pipe length, which is relevant in the safe operation of these valves.


15:4516:05, Paper WB2T1.4  
Proportional Integral Retarded Control of a Proton Exchange Membrane Fuel Cell System 

Ramirez, Adrian  IPICYT 
Gomez, Marco Antonio  Universidad De Guanajuato 
Keywords: Control of linear systems, PID control, Stability
Abstract: In this paper, we propose a derivativedependent controller to regulate the dynamic response of a fuel cell system. Since derivatives are in general difficult to measure or construct reliably, it is a common practice to approximate them using finitedifferences. This approximation, if not performed carefully, may produce undesired control activity or even instability. Here, we propose to engineer the finitedifferences using artificial delays to avoid undesired outcomes thus guaranteeing a stable implementation of the control scheme. Effectiveness of the approach is carried out via timesimulations.


16:0516:25, Paper WB2T1.5  
Active Vibration Control of Axisymmetric Membrane through Partial Pole Placement 

FalcÓn Prado, Ricardo  University Paris Saclay 
Tliba, Sami  Univ ParisSud, CNRS, CentraleSupelec, Université ParisSaclay 
Boussaada, Islam  Laboratoire Des Signaux Et Systemes (L2S) 
Niculescu, SilviuIulian  Laboratory of Signals and Systems (L2S) 
Keywords: Vibration control, Control of linear systems, Stability
Abstract: This paper deals with the problem of active vibration control for a flexible axisymmetric membrane. This mechanical system is equipped with two piezoelectric circular chips where one of them works as an actuator, whereas the other is used as a sensor. Both are glued on the membrane, one on each side, and centered according to its axis of symmetry. The model of this system is obtained from a finite element modelling, leading to a linear statespace model. The design of the proposed controller is based on delayed proportional actions. We exploit a property called Coexisting Real Roots inducing Dominancy to an assignment of spectral values in an appropriate sector corresponding to a desired damping. The aim of this work is to examine the performances of the proposed output feedback controller in terms of vibration damping of the main observable and controllable vibrating modes.


16:2516:45, Paper WB2T1.6  
Stability Charts of a Delayed Model of Vehicle Towing 

Szaksz, Bence Mate  Budapest University of Technology and Economics, Department of A 
Stepan, Gabor  Budapest Univ of Technology and Economics 
Keywords: Vibration control, Infinite dimensional systems, Control of linear systems
Abstract: Because of the finite reaction time of human drivers, the towing process of a brokendown vehicle can often lead to unwanted oscillations. The paper presents a mechanical model of vehicle towing, where the driver of the first car tries to keep a constant velocity, while the driver of the towed vehicle uses the brakes to maintain a desired force in the towing bar; the control of both drivers is subjected to time delay. Stability charts are constructed in the plane of the control parameters showing that the stable region disappears and reappears periodically as the time delay increases.


WC2T2 
Tactic 2 
Stability, Control and Estimation 
Regular Session 
Chair: Mondie, Sabine  CINVESTAVIPN 
CoChair: Chen, Fei  Northeastern University 

14:4515:05, Paper WC2T2.1  
Optimal Control and Stabilization for Decentralized System with Asymmetric OneStep Delay Information (I) 

Liang, Xiao  Shandong University of Science and Technology 
Zhang, Huanshui  Shandong University 
Xu, Juanjuan  Shandong University 
Keywords: Control of linear systems
Abstract: This paper focuses on the optimal control and stabilization problem for the decentralized system with two players subject to asymmetric onestep delay information. In this scenario, the communication channel from player 1 to player 2 exists a unit delay and the transmission from the reverse direction is blocked which leads to the asymmetric onestep delay information. The contributions of this paper are twofold. Firstly, by virtue of the Pontryagin’s maximum principle, a necessary and sufficient condition for the finite horizon optimal control is derived. Secondly, in terms of two algebraic Riccati equations, it is the first time to give a necessary and sufficient condition for the stabilization in the mean square sense for decentralized system with the asymmetric onestep delay information. Numerical examples about a target tracking system are given to show the effectiveness of the obtained results.


15:0515:25, Paper WC2T2.2  
Robust PID Control of SecondOrder Uncertain Nonlinear System with TimeVarying Delay: An InputOutput Approach (I) 

Li, Yaopo  Northeastern University 
Ma, Dan  Northeastern University 
Keywords: PID control, Nonlinear dynamics, Stability
Abstract: This paper studies the PID robust tracking control problem for secondorder nonlinear systems with timevarying input delay. An inputoutput approach is adopted to show the existence of robust PID control, which can tolerant the timevarying delay and the uncertain nonlinearity. First, the uncertain nonlinearity can be scaled by unknown bounds and the timevarying input delay is approximated by using the threeterm approximation method. Next, the uncertain nonlinear timevarying delay system under PID control can be transferred into two interconnected subsystems, which is prone to be analyzed by the inputoutput approach. Then, by using the scaled smallgain theorem and constructing the LyapunovKrasovskii functional, a sucient condition on the existence of robust PID controller to stabilize the closedloop system against timevarying delay and uncertain nonlinearity is proposed, which implies the tracking performance of the original PID control system. A numerical example is given to demonstrate the eectiveness of the proposed method.


15:2515:45, Paper WC2T2.3  
Stability, Convergence and Bifurcation of a Reduced BoissonadeDe Kepper Model with Delayed Feedback 

Abdulrahuman, Abuthahir  Krea University 
Chakrabarti, Kalyan S  Krea University 
Raina, Gaurav  Indian Institute of Technology Madras 
Keywords: Nonlinear dynamics, Stability
Abstract: We analyze the local stability, convergence and bifurcation properties of a reduced BoissonadeDe Kepper (BD) model, in the presence of timedelayed feedback. We derive conditions to ensure stability, and also investigate the impact of model parameters on the convergence characteristics of the system. The model undergoes a Hopf bifurcation when the conditions for local stability get violated. Using Poincare normal forms and the center manifold theory, we are able to derive explicit analytic expressions for determining the type of the Hopf bifurcation and the stability of the emerging limit cycles. We also considered the impact of either having a quadratic or a cubic term in the model. Our findings show that the quadratic term always yields a subcritical Hopf bifurcation, whereas with a cubic term, the model can switch between a subcritical and a supercritical bifurcation. The insights exhibit the delicate relationship between the form of the nonlinear terms and the resulting system dynamics. Some of the analytical insights are corroborated with numerical computations.


15:4516:05, Paper WC2T2.4  
Observer Design for a Class of Delay Systems Using a Fredholm Transform 

Redaud, Jeanne  Université Paris Saclay, CNRS, CentraleSupélec 
Auriol, Jean  CNRS, Centrale Supelec 
Niculescu, SilviuIulian  Laboratory of Signals and Systems (L2S) 
Keywords: Neutral and advanced equations, Infinite dimensional systems
Abstract: In this paper, we design an observer for a system represented by a general class of Integral Delay Equations (IDE). This class of equations encompasses various systems, from chemical or biological processes to the propagation of electric pulses on excitable media. The available measurement corresponds to a discrete and distributeddelayed value of the state. Under an appropriate spectral observability assumption, an implementable observer is proposed. Inspired by the fact that firstorder hyperbolic Partial Derivative Equations (PDE) and timedelay systems are closely related, we use a PDE formulation and the wellknown backstepping methodology for the design. However, due to integral terms in the dynamics, the use of a Fredholm integral transform is required. We prove its existence and invertibility by using an operator framework. Both proofs derive from the spectral observability assumption. Some test case simulations end the paper.


16:0516:25, Paper WC2T2.5  
Maximum Persistence of Periodic Behavior Leads to Functional Equations 

Verriest, Erik I.  Georgia Inst. of Tech 
Keywords: Robotics, Control of linear systems, Infinite dimensional systems
Abstract: The optimal control problem of connecting any two trajectories with typical behavior, such that this behavior maximally persists during the transient, is put forth and a compact solution is obtained for a general class of behaviors. The behavior is understood in the context of Willems’s theory and is characterized as the kernel of some operator. As a solution exhibiting the same behavior cannot exist, a maximally persistent solution is deﬁned as one that will be as close as possible in a precise sense to the behavior. The problem is linked to the idea of controllability as presented by Willems and draws its roots from quasistatic transitions in thermodynamics, and the embedding problem of Whitney. It is shown that the important class of periodic behaviors, applicable to gaits in locomotion, amounts to modeling by functional diﬀerence and diﬀerential equations.


16:2516:45, Paper WC2T2.6  
Integral Delay Systems: Necessary and Sufficient Stability Conditions in Terms of the Delay Lyapunov Matrix 

Ortiz, Reynaldo  CINVESTAVIPN 
Egorov, Alexey  St. Petersburg State University 
Mondie, Sabine  CINVESTAVIPN 
Keywords: Stability, Lyapunov functionals and Lyapunov matrices
Abstract: A LyapunovKrasovskii functional with prescribed derivative whose construction does not require the stability of the system is introduced. It leads to the presentation of stability/instability theorems. By evaluating the functional at initial conditions depending on the fundamental matrix we are able to present necessary and sufficient stability conditions expressed exclusively in terms of the delay Lyapunov matrix for integral delay systems. Some examples illustrate and validate the stability conditions.


WA31 

Recent Trends in Stability and Stabilization of TimeDelay Systems 
Invited session 
Chair: Ma, Dan  Northeastern University 
CoChair: Boussaada, Islam  Laboratoire Des Signaux Et Systemes (L2S) 
Organizer: Ma, Dan  Northeastern University 
Organizer: Boussaada, Islam  Laboratoire Des Signaux Et Systemes (L2S) 

17:0017:20, Paper WA31.1  
An Improved Result on Stabilization of Switched Linear Systems with TimeVarying Delay (I) 

Hou, Tan  Shanghai Jiao Tong University 
Li, Yuanlong  Shanghai Jiao Tong University 
Lin, Zongli  University of Virginia 
Keywords: Infinite dimensional systems, Control of nonlinear systems, Stability
Abstract: This paper revisits the stability problem for switched linear systems with timevarying delay. In contrast to the existing works, the commonly adopted stable convex combination assumption is relaxed in this paper. For switched systems satisfying the relaxed assumption, we design a state dependent switching strategy, under which the considered system is asymptotically stable at the origin in the presence of timevarying delay. An optimization problem is formulated to estimate the upper bound of time delay. Numerical examples are presented to show that our method is applicable to a larger class of switched systems and leads to greater delay bound.


17:2017:40, Paper WA31.2  
Algorithms for Fast Calculation of Spectral Abscissa of Retarded TimeDelay Systems with DelayDependent Coefficients (I) 

Lai, Guihong  Nanjing University of Aeronautics and Astronautics 
Liang, Song  Nanjing University of Aeronautics and Astronautics 
Wang, Zaihua  Nanjing University of Aeronautics and Astronautics 
Keywords: Stability, Spectrum computation and optimization
Abstract: Timedelay systems with delaydependent coefficients arise from different disciplines, but methods and algorithms for stability analysis of this kind of systems are very few compared with the intensive ones for timedelay systems with delayfree coefficients. This paper presents three algorithms for calculating the spectral abscissa of retarded timedelay systems with the delay as a parameter, an index that determines the stability and the decaying rate of the systems. The key step in the algorithms is the use of parametric continuation method to calculate the real part branches by solving initial value problems of an ordinary differential equation derived from the characteristic function, whose initial values are calculated by using the integrationbasedstabilitytest method. Algorithm 1 offers the most direct way to find the spectral abscissa, by using the spectral abscissa at each node onebyone in the meshed delay interval. The computational efficiency decreases when the number of nodes increases. Algorithm 2 provides more choices to improve the computational efficiency in different ways, by reducing the number of nodes of delay, or just by using the real part branches originated from the rightmost characteristic root(s) (RCRs, for short), the second RCRs, or even the third RCRs at only one checking delay. Algorithm 3 is a simplified version of Algorithm 2 when the delay interval is short, with which it is possible to obtain the full picture of spectral abscissa using one real part branch only. The proposed algorithms do not need complicated calculation of critical delay values and identification of crossing direction of characteristic roots at the critical delay values. They work in stability analysis for different kinds of dynamical systems with delays or without delays, with delaydependent coefficients or with delayfree coefficients, and the parameter can be delay or not delay. Special attention should be paid to the case when repeated characteristic roots appear, which is left for future investigation.


17:4018:00, Paper WA31.3  
A Scalable Approach to Compute Delay Margin of a Class of NeutralType Time Delay Systems (I) 

Ramirez, Adrian  IPICYT 
Breda, Dimitri  University of Udine 
Sipahi, Rifat  Northeastern University 


18:0018:20, Paper WA31.4  
Insights into the MultiplicityInducedDominancy for Scalar DelayDifferential Equations with Two Delays (I) 

Fueyo, Sebastien  Inria, SaclayÎleDeFrance Research Center, DISCO Team 
Mazanti, Guilherme  Inria & CentraleSupélec 
Boussaada, Islam  Laboratoire Des Signaux Et Systemes (L2S) 
Chitour, Yacine  Universit'e ParisSud, CNRS, Centralesupelec 
Niculescu, SilviuIulian  Laboratory of Signals and Systems (L2S) 
Keywords: Stability, Control of linear systems
Abstract: It has been observed in recent works that, for several classes of linear timeinvariant timedelay systems of retarded or neutral type with a single delay, if a root of its characteristic equation attains its maximal multiplicity, then this root is the rightmost spectral value, and hence it determines the exponential behavior of the system, a property usually referred to as multiplicityinduceddominancy (MID). In this paper, we investigate the MID property for one of the simplest cases of systems with two delays, a scalar delaydifferential equation of first order with two delayed terms of order zero. We discuss the standard approach based on the argument principle for establishing the MID property for singledelay systems and some of its limitations in the case of our simple system with two delays, before proposing a technique based on crossing imaginary roots that allows to conclude that the MID property holds in our setting.


18:2018:40, Paper WA31.5  
Insights on PolePlacement of Dynamical Systems by PID Control with Guaranteed Delay Robustness (I) 

Boussaada, Islam  Laboratoire Des Signaux Et Systemes (L2S) 
Ma, Dan  Northeastern University 
Chen, Jianqi  City University of Hong Kong 
Bonnet, Catherine  Inria SaclayIleDeFrance 
Niculescu, SilviuIulian  Laboratory of Signals and Systems (L2S) 
Chen, Jie  City University of Hong Kong 
Keywords: PID control, Neutral and advanced equations, Stability
Abstract: The PID control is favored in controlling industrial processes for its ease ofimplementation. In this paper, the multiplicityinduceddominancy property is used in the design of stabilizing PID controllers for some delayed reducedorder plants. More precisely, the controllers gains are tuned using the multiplicity’s algebraic constraints allowing to assign analytically the closedloop solutions’ decay rate. Furthermore, the robustness of the control against uncertain delays is also addressed. An illustrative example completes the presentation.


18:4019:00, Paper WA31.6  
Stabilization with Zero Location Constraints for DelayBased NonCollocated Vibration Suppression (I) 

Silm, Haik  KU Leuven 
Michiels, Wim  KU Leuven 
Vyhlidal, Tomas  Czech Technical Univ in Prague, Faculty of Mechanical Engineerin 
Keywords: Vibration control, Spectrum computation and optimization
Abstract: A generally applicable design of noncollocated vibration absorption by a delayed resonator is proposed. It is grounded in the direct assignment of imaginary axis zeros of the transfer function between the periodic disturbance force and the target. We show that these transmission zeros are characterized as eigenvalues of a delay differentialalgebraic system. Furthermore, a stabilizing local controller is added to the setup in order to widen the range of admissible vibration frequencies. These design requirements are translated into an optimization problem of the spectral abscissa function subjected to zero location constraints. The presented approach and algorithm are validated by a simulation on a three body lumped massspring system.


WB3T1 
Tactic 1 
Recent Advances on Distributed Control of MultiAgent Systems 
Invited session 
Chair: Li, Zhongkui  Peking University 
CoChair: Caiazzo, Bianca  University of Naples Federico II 
Organizer: Li, Zhongkui  Peking University 
Organizer: Lv, Yuezu  Southeast University 

17:0017:20, Paper WB3T1.1  
EventTriggered Weighted Average Consensus in Networks of Dynamic Agents with TimeVarying Delay (I) 

Li, Xiang  Nanjing University of Aeronautics and Astronautics 
Zhu, Jing  Nanjing University of Aeronautics and Astronautics 
Keywords: Consensus problems and synchronization, Networked and multiagent systems, Decentralized and distributed control
Abstract: In this paper, we discuss the weighted average consensus problem of multiagent systems in directed networks with timevarying communication delay based on eventtriggered mechanism. By constructing the Lyapunov function, we obtain the eventtriggered condition, and prove that Zeno behavior will not occur in the system under the condition. Finally, the simulation of the topology of multiagent directed network is carried out to verify the theoretical results.


17:2017:40, Paper WB3T1.2  
Sign Projected Gradient Flow: A ContinuousTime Approach to Convex Optimization with Linear Equality Constraints (I) 

Chen, Fei  Northeastern University 
Ren, Wei  University of California, Riverside 
Keywords: Networked and multiagent systems, Decentralized and distributed control, Consensus problems and synchronization
Abstract: This talk is to present a paper that has been published by Automatica as a Regular Paper (Fei Chen and Wei Ren, ``Sign projected gradient flow: a continuoustime approach to convex optimization with linear equality constraints'', Automatica, 120, 109156, 2020). In that paper, we exploit the possibility of combining nonsmooth control jointly with projected gradient approaches to solve convex optimization problems with linear equality constraints. Our development gives rise to a sign projected gradient method employing only ``coarse'' information, which has finitetime convergence capability and preserves the simplicity and elegance of gradient descent. Our primary objective is to understand the design principle of the projection matrix in the nonsmooth setting and to investigate some key features of the method, such as convergence time. Specifically, we offer a set of convergence results via nonsmooth analysis, revealing that the algorithm guarantees finitetime convergence for a wide range of cost functions, including strongly convex, strictly convex, and convex functions, provided that the proposed design criteria and conditions are satisfied. The results suggest that the choice of the projection matrix might not be unique, which motivates the optimal design issue of the projection matrix to minimize convergence time. We show that the problem can be formulated as a convex optimization problem, which can be solved readily by existing optimization tools. We discuss the possibility of employing the proposed method to solve unconstrained optimization problems, which in turn gives an initial feasible solution to the sign projected gradient flow. We apply the algorithm to solve a formation control problem, and the numerical results show the effectiveness of the algorithm.


17:4018:00, Paper WB3T1.3  
Optimal Sensor Scheduling for Complex Networks with a Distributed Remote Estimation Framework (I) 

Duan, Peihu  Peking University 
Lv, Yuezu  Southeast University 
Keywords: Filtering and estimation, Networked and multiagent systems, Automotive
Abstract: This paper investigates optimal sensor scheduling for state estimation of complex networks over shared transmission channels. A network of sensors are adopted to measure and estimate the system states in a distributed way, where a sensor corresponds to a node. Then, the estimates are transmitted to the associated nodes via a cloud center, in the presence of onestep time delay and packet loss. Due to limited transmission capability, only a part of sensors are allowed to send information at each step. The goal is to seek an optimal policy minimizing the overall estimation errors for nodes. Based on a distributed state estimation framework, this problem is reformulated as a Markov decision process (MDP) problem, where the onestage reward for each node is strongly coupled. The feasibility of the problem reformulation is ensured with a rigorous proof. Besides, an easytocheck condition is provided to guarantee the existence of an optimal deterministic and stationary policy. Moreover, it is found that a threshold structure is possessed by optimal policies, which can be used to reduce the computational complexity of obtaining these policies. Generally, this paper first presents an optimal sensor scheduling scheme for multiple coupled processes based on MDP, more general than these with only independent processes. Finally, the effectiveness of the theoretical results are illustrated by several simulation examples.


18:0018:20, Paper WB3T1.4  
Containment Control of MultiAgent Systems Over Directed Graphs: A Delay Robustness Perspective (I) 

Ma, Xueyan  Northeastern University 
Li, Yaopo  Northeastern University 
Ma, Dan  Northeastern University 
Keywords: Networked and multiagent systems, PID control, Control of linear systems
Abstract: This paper investigates the delay range optimization for robust containment control of firstorder multiagent systems over directed graphs. The purpose is to find the maximum allowable delay range within which the multiagent system can achieve containment robustly under P and PD containment control protocols subject to communication delay. This means that a group of follower agents converge to the convex hull formed by the multiple leader agents under a distributed control protocol. In this paper we focus on a continuous firstorder multiagent system in which each individual agent has an unstable real pole. The connected graph among agents is directed graph, and followers can receive information from leaders as well as from other followers, in which each leader has at least one global accessible path for all followers, and leaders do not communicate with each other. By using the frequency domain analysis method, we provide the exact expression and the bounds on the maximal allowable delay range for robust containment control of multiagent systems. The results show that the position of the pole and the network connectivity will affect the delay bound. Finally, numerical examples are given to illustrate the effectiveness of our proposed results.


18:2018:40, Paper WB3T1.5  
On the Exponential LeaderTracking Control for HighOrder MultiAgent Systems Via Distributed PI Strategy in Presence of Heterogeneous TimeVarying Delays 

Caiazzo, Bianca  University of Naples Federico II 
Lui, Dario Giuseppe  University of Naples Federico II 
Petrillo, Alberto  University of Naples Federico II 
Santini, Stefania  Univ of Napoli Federico II Italy 
Keywords: Decentralized and distributed control, Lyapunov functionals and Lyapunov matrices, Consensus problems and synchronization
Abstract: This paper deals with the exponential leadertracking consensus control problem of highorder MultiAgent Systems (MASs) sharing information via a nonideal communication network. To emulate a more realistic environment, a specific timevarying delay has been associated at each communication link within the network, whose value, at each time instant, depends on the real conditions of the communication channel. To solve this problem, a fullydistributed delayed ProportionalIntegral (PI) control protocol able to guarantee the exponential stability of the entire delayed closedloop MAS is proposed. The stability of this latter is analytically proved by exploiting LyapunovKrasovskii theory combined with Halanay Inequality, thus obtaining exponential stability conditions expressed as a feasible Linear Matrix Inequality (LMI) problem. Exemplary numerical simulations corroborate the effectiveness of the theoretical derivation.


18:4019:00, Paper WB3T1.6  
Simplifying Consensus Stability Analysis of MultiAgent Systems Using the Concept of Convex Directions for Quasipolynomials 

Gomez, Marco Antonio  Universidad De Guanajuato 
Ramirez, Adrian  IPICYT 
Keywords: Stability, Consensus problems and synchronization, Networked and multiagent systems
Abstract: This paper addresses the consensus stability problem in a class of multiagent system (MAS) with delays. We take three consensus protocols from the open literature and construct the corresponding stability maps in the space of control parameters using a decomposition of the network into a finite number of subsystems of reduced dimension. By inspecting the stability maps, we recognize that stability of the overall networks is determined by only two subsystems. The observed stability “peculiarity”, shared by the three MAS under study, is not by chance. The notion of convex directions for stable quasipolynomials offers, indeed, a solid theoretical explanation of this fact.


WC3T2 
Tactic 2 
Control of TimeDelay Systems with Uncertainty 
Invited session 
Chair: Xu, Juanjuan  Shandong University 
CoChair: Oguchi, Toshiki  Tokyo Metropolitan University 
Organizer: Zhang, Huanshui  Shandong University 
Organizer: Xu, Juanjuan  Shandong University 

17:0017:20, Paper WC3T2.1  
Solution to the FBSDEs with State Delay (I) 

Ma, Tianfu  Shandong University 
Xu, Juanjuan  Shandong University 
Zhang, Huanshui  Shandong University 
Keywords: Control of linear systems
Abstract: This paper is concerned with a kind of forwardbackward stochastic difference equations with state delay. By introducing a class of Riccatitype equations, the explicit solution of the FBSDEs is given by establishing a nonhomogeneous relationship between the backward and forward stochastic processes. Considering the existence of time delay, historical forward information is involved in the relationship.


17:2017:40, Paper WC3T2.2  
Stackelberg Game for DiscreteTime Stochastic Linear Systems with Time Delay (I) 

Liu, Jingmei  Shandong University 
Wang, Wei  Shandong University 
Xu, Juanjuan  Shandong University 
Zhang, Huanshui  Shandong University 
Keywords: Control of linear systems, Economics, Filtering and estimation
Abstract: In this paper, we study the openloop Stackelberg strategy of stochastic Stackelberg game with time delay. The main contribution is to give the explicit Stackelberg strategy in terms of Riccati equations. The key to solving the problem is the explicit solvability of the forward and backward stochastic difference equations (FBSDEs). Moreover, the optimal costs are indicated by using the initial value of the state.


17:4018:00, Paper WC3T2.3  
LQR for Ito Systems with Input Delays (I) 

Wang, Hongxia  Shandong University of Science and Technology 
Zhang, Huanshui  Shandong University 
Keywords: Control of linear systems, Infinite dimensional systems
Abstract: Linear quadratic regulation (LQR) is very fundamental in modern control theory. The theory has been developing for several decades. However, the LQR problem for stochastic systems with input delays still remains outstanding. The paper focuses on the LQR problem for Ito stochastic systems with two control channels and a delay, which will pave a way to approach the corresponding H∞ control problem. In contrast with the single channel problem,this problem is more typical and involved since the two channels problem actually encounters interaction between channels besides the delay. The paper focuses on providing a necessary and sufficient solvability condition and optimal control. The sufficiency is proved by finding a suitable value functional and completing the square. The necessary condition is obtained by the variant of the calculus of variations. What’s more important, due to that the result is given based on coupling ordinary and partial differential equations, we present the analytic solution to these equations.The idea is also suitable for handling the LQR problem for Ito stochastic systems with multiple control channels and multiple delays.


18:0018:20, Paper WC3T2.4  
SynchronizationBased Prediction Control for Nonlinear Systems with Parameter Uncertainties and Input TimeDelay 

Machida, Ryuta  Tokyo Metropolitan University 
Oguchi, Toshiki  Tokyo Metropolitan University 
Keywords: Control of nonlinear systems, Prediction based control, Observer design
Abstract: This paper considers a control method for a class of nonlinear systems with parameter uncertainties and input timedelay. In particular, we propose a controller design method for Lur'e type nonlinear systems by using a predictor based on anticipating synchronization. The feature of the predictor is that it has a closedloop structure. Therefore it is expected to have robustness for the model mismatch. In this paper, we derive a stability criterion for the whole system, including the state predictor and feedback. After that, we clarify how to design the coupling gain of the predictor to guarantee the stability of the whole system under parameter uncertainties. Numerical simulations illustrate the validity of the proposed method.


18:2018:40, Paper WC3T2.5  
Robust Analysis of Linear Systems with Uncertain Delays Using PIEs 

Wu, Shuangshuang  Tsinghua University 
Peet, Matthew M  Arizona State University 
Sun, Fuchun  Tsinghua Univ 
Hua, Changchun  Yanshan Univ 
Keywords: Lyapunov functionals and Lyapunov matrices, Robustness, Stability
Abstract: This paper establishes a PIE (Partial Integral Equation)based technique for the robust stability and H_infty performance analysis of linear systems with interval delays. The delays considered are timeinvariant but uncertain, residing within a bounded interval excluding zero. We first propose a structured class of PIE systems with parametric uncertainty, then propose a Linear PI Inequality (LPI) for robust stability and H_infty performance of PIEs with polytopic uncertainty. Next, we consider the problem of robust stability and H_infty performance of multidelay systems with interval uncertainty in the delay parameters and show this problem is equivalent to robust stability and performance of a given PIE with parametric uncertainty. The robust stability and H_infty performance of the uncertain timedelay system are then solved using the LPI solver in the MATLAB PIETOOLS toolbox. Numerical examples are given to prove the effectiveness and accuracy of the method. This paper adds to the expanding field of PIE approach and can be extended to linear partial differential equations.


18:4019:00, Paper WC3T2.6  
Characterization and Computation of the Strong H2 Norm for Delay Differential Algebraic Systems 

Michiels, Wim  KU Leuven 
Gomez, Marco Antonio  Universidad De Guanajuato 
Jungers, Raphaël M.  Université Catholique De Louvain 
Keywords: Robust control
Abstract: The H2 norm of an exponentially stable system described by Delay Differential Algebraic Equations (DDAEs) might be infinite, due to the existence of hidden feedthrough terms and it might become infinite as a result of infinitesimal changes to the delay parameters. We first introduce the notion of strong H2 norm of semiexplicit DDAEs, a robustified measure that takes into account delay perturbations, and we analyze its properties. Next, we discuss necessary and sufficient finiteness criteria for the strong H2 norm in terms of a frequency sweeping test over a hypercube, and in terms of a finite number of equalities involving multidimensional powers of a finite set of matrices. As the main contribution, we present a strengthened, sufficient, condition for finiteness of the strong H2 norm, which has significantly better scalability properties in terms of both the dimension of the system and the number of delays. We show that the satisfaction of the novel condition is equivalent to the existence of a simultaneous block triangularization of the matrices of the delay difference equation associated to the DDAE. The latter is instrumental to a novel regularization procedure that allows to transform the DDAE to a neutral type system with the same transfer matrix, without any need for differentiation of inputs or outputs and enabling the framework of Lyapunov matrices for computing the H2 norm.

 