Mean‐field games for multiagent systems with multiplicative noises

This paper studies mean‐field games for multiagent systems with control‐dependent multiplicative noises. For the general systems with nonuniform agents, we obtain a set of decentralized strategies by solving an auxiliary limiting optimal control problem subject to consistent mean‐field approximations. The set of decentralized strategies is further shown to be an ε‐Nash equilibrium. For the integrator multiagent systems, we design a set of ε‐Nash strategies by exploiting the convexity property of the limiting problem. It is shown that under the mild conditions, all the agents achieve mean‐square consensus.     

ε-Equilibrium in LQ differential games with bounded uncertain disturbances: robustness of standard strategies and new strategies with adaptation

A finite time multi-persons linear-quadratic differential game (LQDG) with bounded disturbances and uncertainties is considered. When players cannot measure these disturbances and uncertainties, the standard feedback Nash strategies are shown to yield to an ε-(or quasi) Nash equilibrium depending on an uncertainty upper bound that confirms the robustness property of such standard strategies. In the case of periodic disturbances, another concept, namely adaptive concept, is suggested. It is defined an “adaptation period” where all participants apply the standard feedback Nash strategies with the, so-called, “shifting signal” generated only by a known external exciting signal. Then, during the adaptation, the readjustment (or correction) of the control strategies is realized to estimate the effect of unknown periodic disturbances by the corresponding correction of the shifting vector. After that adaptation period, the complete standard strategies including the recalculated shifting signal are activated allowing the achievement of pure (ε?=?0) Nash equilibrium for the rest of the game. A numerical example dealing with a two participants game shows that the cost functional for each player achieves better values when the adaptive approach is applied.     

State feedback control synthesis for networked control systems with packet dropout

This paper is concerned with the problem of H_∞ controller design for networked control systems (NCSs) with time delay and packet dropout. A combined switching and parameter uncertainty‐based method is proposed to deal with time‐varying delay. The proposed method can avoid the high computational complexity of the delay switching‐based method and introduce less conservatism than the parameter uncertainty‐based method. An active varying sampling period method is proposed to make full use of network bandwidth, and a multi‐objective optimization methodology in terms of linear matrix inequalities is used to deal with H_∞ controller design for NCSs with active varying sampling period. The simulation results illustrate the effectiveness of the proposed active varying sampling period method and the less conservatism of the combined switching and parameter uncertainty‐based method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

基于Stackbelberg博弈的认知无线网络速率控制模型

提出了基于Stackelberg博弈的认知无线单跳网络流量速率控制模型。应用反向归纳法对提出的流量速率Stackelberg博弈模型纳什均衡进行了分析,证明了提出的模型纳什均衡存在性及唯一性,并给出了Stackelberg博弈模型纳什均衡解的具体形式。仿真验证了提出的模型正确性,仿真结果表明在模型的纳什均衡处网络总体效用是最优的,且网络效用最大时认知结点可获得最优数据传输速率。     

Insensitive output feedback H ∞ control of delta operator systems with insensitivity to sampling time jitter

The insensitive multi‐objective H _∞ control synthesis problem via dynamic output feedback for linear delta operator systems with insensitivity to sampling time jitter is investigated in the case of small sampling times. The delta‐domain model instead of the standard shift‐domain model is used to avoid the inherent numerical ill‐condition resulting from using the latter model at high sampling rates. Parameter sensitivity function of the transfer function with respect to sampling time is defined to mitigate the effect of sampling time jitter because it may cause significant degradation of the overall system performance. It is worth pointing out that a novel bounded real lemma for delta operator allowing extra degree of freedom for multi‐objective control design is presented by using the well‐known projection lemma. Then, from this new lemma, a two‐step design procedure based on LMI is presented to design insensitive dynamic output feedback controllers such that the resulting closed‐loop system is asymptotically stable and meets the requirement of sensitivity specification. A numerical example is also presented to show the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Output tracking control for networked control systems with time delay and packet dropout

This article studies the problems of H _∞ output tracking performance analysis and controller design for networked control systems (NCSs) with time delay and packet dropout. By using linear matrix inequality (LMI)-based method, H _∞ output tracking performance analysis and controller design are presented for NCSs with constant sampling period. For NCSs with time-varying sampling period, a multi-objective optimisation methodology in terms of LMIs is used to deal with H _∞ output tracking performance analysis and controller design. The designed controllers can guarantee asymptotic tracking of prescribed reference outputs while rejecting disturbances. The simulation results illustrate the effectiveness of the proposed H _∞ output tracking controller design.     

Decoupling Controller with Disturbance Observer for LTI MIMO Systems

In this paper, a decoupling multivariable control strategy for linear time‐invariant (LTI) multi‐input/multi‐output (MIMO) systems is proposed. The strategy includes a multivariable disturbance observer (MDOB) and a decoupling controller. This MDOB is introduced to improve the system performances when the system encounters severe external disturbances. H₂ optimal scheme is utilized to design the MDOB filter. The controller is developed based on an inverse control method, through which the design process can be simplified. Simulation results certify the effectiveness of the proposed control strategy.     

Robust ℋ︁∞ PID control for multivariable networked control systems with disturbance/noise attenuation

In this paper, we study the design problem of PID controllers for networked control systems (NCSs) with polyhedral uncertainties. The load disturbance and measurement noise are both taken into account in the modeling to better reflect the practical scenario. By using a novel technique, the design problem of PID controllers is converted into a design problem of output feedback controllers. Our goal of this paper is two‐fold: (1) To design the robust PID tracking controllers for practical models; (2) To develop the robust ??_∞ PID control such that load and reference disturbances can be attenuated with a prescribed level. Sufficient conditions are derived by employing advanced techniques for achieving delay dependence. The proposed controller can be readily designed based on iterative suboptimal algorithms. Finally, four examples are presented to show the effectiveness of the proposed methods. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust explicit model predictive control for linear systems via interpolation techniques

This paper presents a novel interpolation‐based model predictive control (IMPC) for constrained linear systems with bounded disturbances. The idea of so‐called ‘pre‐stabilizing’ MPC is extended by making interpolation among several ‘pre‐stabilizing’ MPC controllers, through which the domain of attraction can be magnificently enlarged. Compared with the standard ‘pre‐stabilizing’ MPC, the proposed approach has the advantage of combining the merits of having a large domain of attraction and a good behavior. Furthermore, such an IMPC problem can be solved off‐line by multi‐parametric programming. The optimal solution is given in an explicitly piecewise affine form. A simple algorithm for the implementation of the explicit MPC control laws is also proposed. Copyright © 2009 John Wiley & Sons, Ltd.     

The free‐weight matrix approach to event‐driven output H∞ control of networked control systems

This paper puts forward a new free‐weight matrix method used to analyse Network control systems (NCSs) with the H∞ performance index level based on event‐driven control. Firstly, design a relative triggering mechanism contain the measured output for a linear system with external disturbances. Secondly, in order to reduce the conservativeness an appropriate Lyapunov‐Krasovskii function is constructed. For the integral term generated after the above functional derivation, the free‐weight matrix inequality is selected for scaling. Finally,the sufficient condition that the closed‐loop system represented by the linear matrix inequality (LMI) satisfies the H∞ performance index and the solution of the controller are obtained.The validity of the scheme is confirmed by a given numerical case.     

Robust H ∞ model reference tracking control for networked control systems with communication constraints

This paper studies the problem of H _∞ model reference tracking control for continuous time networked control systems (NCSs) with communication constraints. By using the continuous Jensen inequality, linear matrix inequality (LMI)-based H _∞ model reference tracking controller design for nominal NCSs with controller-to-actuator communication constraints is presented, and a new method is proposed to design H _∞ model reference tracking controllers for NCSs with both controller-toactuator and sensor-to-controller communication constraints. The results are also extended to NCSs with norm-bounded parameter uncertainties. The merits of the proposed methods lie in their less computational complexity and less conservatism, which are achieved by adopting continuous Jensen inequality and proposing new controller design methods, respectively. The simulation results illustrate the effectiveness of the proposed H _∞ model reference tracking controller design for NCSs with communication constraints.     

Linear−quadratic optimal control and nonzero‐sum differential game of forward−backward stochastic system

An existence and uniqueness result for one kind of forward–backward stochastic differential equations with double dimensions was obtained under some monotonicity conditions. Then this result was applied to the linear‐quadratic stochastic optimal control and nonzero‐sum differential game of forward–backward stochastic system. The explicit forms of the optimal control and the Nash equilibrium point are obtained respectively. We note that our method is effective in studying the uniqueness of Nash equilibrium point. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust tracking control design for uncertain robotic systems with persistent bounded disturbances

In this study, a robust nonlinear L_∞‐gain tracking control design for uncertain robotic systems is proposed under persistent bounded disturbances. The design objective is that the peak of the tracking error in time domain must be as small as possible under persistent bounded disturbances. Since the nonlinear L_∞ ‐gain optimal tracking control cannot be solved directly, the nonlinear L_∞ ‐gain optimal tracking problem is transformed into a nonlinear L_∞ ‐gain tracking problem by given a prescribed disturbance attenuation level for the L_∞ ‐gain tracking performance. To guarantee that the L_∞ ‐gain tracking performance can be achieved for the uncertain robotic systems, a sliding‐mode scheme is introduced to eliminate the effect of the parameter uncertainties. By virtue of the skew‐symmetric property of the robotic systems, sufficient conditions are developed for solving the robust L_∞ ‐gain tracking control problems in terms of an algebraic equation instead of a differential equation. The proposed method is simple and the algebraic equation can be solved analytically. Therefore, the proposed robust L_∞ ‐gain tracking control scheme is suitable for practical control design of uncertain robotic systems. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Dual scheduling and quantised control for networked control systems with communication constraints

A novel integrated design scheme of average dwell time scheduling strategy, dynamic bandwidth allocation policy and quantised control for a collection of networked control systems (NCSs) with time delay and communication constraints is proposed in this paper. A scheduling policy is presented to accommodate the limitation of communication capacity which depends on the convergence rate of closed-loop system and divergence rate of open-loop plant. Linear programming technique is adopted to dynamically allocate bit rate for each node and the strategy is used to make trade-offs between the network utilisation and the control performance which provides an effective way of optimising the quality of control (QoC) and the quality of service (QoS) for NCSs. Mid-tread uniform quantisers update the quantisation rules according to the assignment of the bit rate and convert the quantised state into a kind of input saturation with bounded disturbances. Taking into account the effect of dual scheduling strategy and quantisation, the NCSs are modelled as discrete-time switched systems with bounded disturbances. Furthermore, a scheduling and quantised feedback control co-design procedure is proposed for the simultaneous stabilisation of the collection of networked subsystems. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.     

Constrained piecewise linear systems with disturbances: Controller design via convex invariant sets

This paper presents two control strategies under the time optimal control and model predictive control frameworks for constrained piecewise linear systems with bounded disturbances (PWLBD systems). Each of the proposed approaches uses an inner convex polytopal approximation of the non‐convex domains of attraction and results in simplified control laws that can be determined off‐line via multi‐parametric programming. These control strategies rely on invariant sets of PWLBD systems. Thereby, approaches for the computation of the disturbance invariant outer bounds of the minimal disturbance invariant set, F_∞, and convex polytopal disturbance invariant sets are presented. The effectiveness of the approaches is assessed through numerical examples. Copyright © 2007 John Wiley & Sons, Ltd.     

Distributed Nash Equilibrium Seeking for General Networked Games With Bounded Disturbances

This paper is concerned with anti-disturbance Nash equilibrium seeking for games with partial information. First, reduced-order disturbance observer-based algorithms are proposed to achieve Nash equilibrium seeking for games with first-order and second-order players, respectively. In the developed algorithms, the observed disturbance values are included in control signals to eliminate the influence of disturbances, based on which a gradient-like optimization method is implemented for each player. Second, a signum function based distributed algorithm is proposed to attenuate disturbances for games with second-order integrator-type players. To be more specific, a signum function is involved in the proposed seeking strategy to dominate disturbances, based on which the feedback of the velocity-like states and the gradients of the functions associated with players achieves stabilization of system dynamics and optimization of players’ objective functions. Through Lyapunov stability analysis, it is proven that the players’ actions can approach a small region around the Nash equilibrium by utilizing disturbance observer-based strategies with appropriate control gains. Moreover, exponential (asymptotic) convergence can be achieved when the signum function based control strategy (with an adaptive control gain) is employed. The performance of the proposed algorithms is tested by utilizing an integrated simulation platform of virtual robot experimentation platform (V-REP) and MATLAB.      

Distributed cooperative H∞ optimal tracking control of MIMO nonlinear multi-agent systems in strict-feedback form via adaptive dynamic programming

The design of distributed cooperative H_∞ optimal controllers for multi-agent systems is a major challenge when the agents’ models are uncertain multi-input and multi-output nonlinear systems in strict-feedback form in the presence of external disturbances. In this paper, first, the distributed cooperative H_∞ optimal tracking problem is transformed into controlling the cooperative tracking error dynamics in affine form. Second, control schemes and online algorithms are proposed via adaptive dynamic programming (ADP) and the theory of zero-sum differential graphical games. The schemes use only one neural network (NN) for each agent instead of three from ADP to reduce computational complexity as well as avoid choosing initial NN weights for stabilising controllers. It is shown that despite not using knowledge of cooperative internal dynamics, the proposed algorithms not only approximate values to Nash equilibrium but also guarantee all signals, such as the NN weight approximation errors and the cooperative tracking errors in the closed-loop system, to be uniformly ultimately bounded. Finally, the effectiveness of the proposed method is shown by simulation results of an application to wheeled mobile multi-robot systems.     

Observer‐Based H∞ Control for Continuous‐Time Networked Control Systems

This paper is concerned with the observer‐based H_∞ control for continuous‐time networked control systems (NCSs) considering packet dropouts and network‐induced delays. The packet dropouts and network‐induced delays in the sensor‐to‐controller (S‐C) channel and network‐induced delays in the controller‐to‐actuator (C‐A) channel are taken into full consideration. By taking the non‐uniform distribution characteristic of the arrival instants of actually adopted controller inputs into account, a new model for continuous‐time NCSs is established. To reduce the conservatism of modelling, a linear estimation‐based measurement output estimation method is introduced. Based on the newly established model and a Lyapunov functional, new controller design methods are proposed. A numerical example is given to illustrate the effectiveness and merits of the derived results.     

Event‐triggered observer‐based robust H∞ control for networked control systems with unknown disturbance

In this article, the event‐triggered robust H_∞ control is studied for a class of uncertain networked control systems (NCSs) subject to unknown state and variable disturbance. First, aiming to decrease the unnecessary transmissions of sampled data, an efficient adaptive event‐triggered scheme (AETS) is presented, which can reflect the full real‐time variation of addressed NCSs and help to reduce the conservativeness. Second, based on the triggered output signals and disturbance model, two effective observers are, respectively, exploited to estimate the state and disturbance, which are further utilized to reject the disturbance and design the controller. By using the overall closed‐loop system and selecting an augmented Lyapunov‐Krasovskii functional, two sufficient conditions on jointly designing the adaptive event scheme, observers, and controller are established via linear matrix inequality forms, which can guarantee the global exponential stability and ensure H_∞ performance. Finally, some simulations and comparisons in a numerical example are provided to demonstrate the effectiveness of the derived results.     

Composite antidisturbance control for nonlinear systems via nonlinear disturbance observer and dissipative control

This paper investigates the design problem of composite antidisturbance control for a class of nonlinear systems with multiple disturbances. First, a novel nonlinear disturbance observer‐based control scheme is constructed to estimate and compensate the disturbance modeled by the nonlinear exosystem. Then, by combining the dissipative control theory, a linear matrix inequality‐based design method of composite antidisturbance control is developed such that the augmented system is exponentially stable in the absence of unmodeled disturbances, and is dissipative in the presence of unmodeled disturbances. In this case, the original closed‐loop system is exponentially stable in the presence of modeled disturbances. Subsequently, two special cases of composite antidisturbance control are derived with H_∞ performance and passivity, respectively. Finally, the proposed method is applied to control A4D aircraft to show its effectiveness.