Distributed Nash Equilibrium Seeking of Networked Nonlinear Systems over Directed Graphs

In this paper, the decentralized robust output-feedback tracking control problem is investigated for a class of uncertain nonlinear interconnected systems subject to high order time varying disturbances. Firstly, generalized-proportional-integral observers (GPIOs) are designed for every subsystems such that the disturbances and unmeasured states can be recovered. Then, based on the estimation information of GPIOs and the output-feedback domination approach, a composite decentralized output-feedback controller is constructed. The proposed decentralized control scheme can not only handle the uncertain nonlinear interconnected terms, but also remove the influences the disturbances effectively via feedforward compensation manner. Finally, a practical example is conducted to demonstrate the effectiveness of the proposed control approach.

This paper deals with an adaptive robust tracking control using a multilayer neural network (NN) for a class of nonlinear dynamic systems with unknown time varying state delays. Typical adaptive NN backstepping controllers for uncertain nonlinear systems with time-delay give rise to computation complexity caused by the the repeated derivatives of virtual controllers and nonlinear functions. Moreover, the combined techniques usually result in only uniformly ultimately bounded (UUB) stability caused by the inherent NN approximation error. This paper presents a control scheme that uses an integral sliding mode control as a feedback term and an adaptive neural controller as a feedforward term based on the desired compensation adaptive law (DCAL) technique. First, we develop a new DCAL formulation which avoids the explosion of complexity caused by the general NN backstepping scheme to compensate for nonlinear system uncertainties, bounded system disturbances, and unknown state time delays. Then, using a Lyapunov-Krasovskii (LK) functional, it is shown that the proposed controller renders the class of uncertain nonlinear time-delay systems asymptotically stable.

In this paper, the output feedback control problem is considered for a class of uncertain nonlinear time-delay systems. The system nonlinearities satisfy linear growth condition on unmeasured states multiplied by unknown growth rate and output polynomial function. With appropriate Lyapunov-Krasovskii functional, a memoryless adaptive output feedback controller is developed to guarantee global stability of the nonlinear time-delay systems. The precise knowledge of the time-delay is not required to be known a priori. Furthermore, only one dynamic gain is designed, which makes the controller easier to implement. A numerical example is used to illustrate the effectiveness of the proposed method.

This article considers a distributed Nash equilibrium seeking problem, where the players only have partial access to other players' actions, such as their neighbors' actions. Thus, the players are supposed to communicate with each other to estimate other players' actions. To solve the problem, a leader-following consensus gradient-free distributed Nash equilibrium seeking algorithm is proposed. This algorithm utilizes only the measurements of the player' local cost function without the knowledge of its explicit expression or the requirement on its smoothness. Hence, the algorithm is gradient-free during the entire updating process. Moreover, the analysis on the convergence of the Nash equilibrium is studied for the algorithm with both diminishing and constant step-sizes, respectively. Specifically, in the case of diminishing step-size, it is shown that the players' actions converge to the Nash equilibrium almost surely, while in the case of fixed step-size, the convergence to the neighborhood of the Nash equilibrium is achieved. The performance of the proposed algorithm is verified through numerical simulations.

This paper presents an event‐triggered distributed control protocol designed for scenarios involving Denial‐of‐Service (DoS) attacks within directed communication graphs. We address the consensus problem of uncertain systems by employing neural networks to approximate nonlinear components. Compared with traditional neural network observers, the proposed method incorporates damping terms to ensure the boundedness of neural network estimators. Initially, an auxiliary system was constructed to decouple the consensus problem under a directed communication graph framework. It is demonstrated that the uncertain nonlinear system can achieve consensus through the utilization of information exchanged among neighboring agents. Subsequently, to curtail the consumption of communication resources, we introduce an event‐triggered control protocol based on the aforementioned approach, incorporating an effective event‐triggering function. Building upon the proposed control protocol, we further develop a control strategy tailored for systems under DoS attacks. Furthermore, the event‐triggered mechanism without using global information in trigger condition not only curtails superfluous information exchange among agents but also precludes the occurrence of Zeno behavior (i.e., infinite triggering within a finite time interval). Finally, numerical simulations are carried out to validate the efficacy of the proposed control protocol.

Distributed containment output-feedback control for a general class of stochastic nonlinear multi-agent systems

In this paper, we present a new scheme to design adaptive fuzzy output-feedback controller for uncertain nonlinear systems in the presence of input saturation. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a state filter is designed to estimate unmeasured states. Combining the backstepping recursive design with modular design techniques, a new adaptive fuzzy output control scheme is synthesized. Unlike some existing control schemes for systems with input saturation, the developed controller dose not require assumptions on the states available and nonlinear systems satisfying the matching condition. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin. A simulation is included to illustrate the effectiveness of the proposed approach.

This paper investigates non-fragile exponential H∞ control problems for a class of uncertain nonlinear networked control systems (NCSs) with randomly occurring information, such as the controller gain fluctuation and the uncertain nonlinearity, and short time-varying delay via output feedback controller. Using the nominal point technique, the NCS is converted into a novel time-varying discrete time model with norm-bounded uncertain parameters for reducing the conservativeness. Based on linear matrix inequality framework and output feedback control strategy, design methods for general and optimal non-fragile exponential H∞ controllers are presented. Meanwhile, these control laws can still be applied to linear NCSs and general fragile control NCSs while introducing random variables. Finally, three examples verify the correctness of the presented scheme.

International audience

Output-feedback control of uncertain nonlinear systems using a self-structuring adaptive fuzzy observer

Distributed Nash equilibrium seeking: A gossip-based algorithm

In this article, an event-triggered robust adaptive dynamic programming (ETRADP) algorithm is developed to solve a class of multiplayer Stackelberg-Nash games (MSNGs) for uncertain nonlinear continuous-time systems. Considering the different roles of players in the MSNG, the hierarchical decision-making process is described as the designed value functions for the leader and all followers, which assist to transform the robust control problem of the uncertain nonlinear system into an optimal regulation problem of the nominal system. Then, an online policy iteration algorithm is formulated to solve the derived coupled Hamilton-Jacobi equation. Meanwhile, an event-triggered mechanism is designed to alleviate computational and communication burdens. Moreover, critic neural networks (NNs) are constructed to obtain the event-triggered approximate optimal control polices for all players, which constitute the Stackelberg-Nash equilibrium of the MSNG. By using Lyapunov's direct method, the stability of the closed-loop uncertain nonlinear system is guaranteed under the ETRADP-based control scheme in the sense of uniform ultimate boundedness. Finally, a numerical simulation is provided to demonstrate the effectiveness of the present ETRADP-based control scheme.

This paper addresses the problem of decentralized global stabilization by output feedback for a class of uncertain large-scale nonlinear systems. A new design method based on the homogeneous domination approach and finite-time stabilization technique is developed, which leads to global output feedback stabilization for large-scale uncertain nonlinear systems under a homogeneous growth condition. Firstly, a homogeneous observer and controller is constructed for the nominal system without the perturbing nonlinearities for each subsystem. Then, a scaling gain is introduced into the homogeneous observers and controllers to globally stabilize the uncertain nonlinear systems.

This paper deals with the problem of fault‐tolerant control (FTC) for a class of nonlinear uncertain systems against actuator faults using adaptive logic‐based switching control method. The uncertainties under consideration are assumed to be dominated by a bounding system which is linear in growth in the unmeasurable states but can be a continuous function of the system output, with unknown growth rates. Several types of common actuator faults, e.g., bias, loss‐of‐effectiveness, stuck and hard‐over faults are integrated by a unified fault model. By utilizing a novel adaptive logic‐based switching control scheme, the actuator faults can be detected and automatically accommodated by switching from the stuck actuator to the healthy or even partly losing‐effectiveness one with bias, in the presence of large parametric uncertainty. In particular, two switching logics for updating the gain in the output feedback controllers are designed to ensure the global stability of the nominal (fault‐free) system and the boundedness of all closed‐loop signals of the faulty system, respectively. Two simulation examples of an aircraft wing model and a single‐link flexible‐joint robot are given to show the effectiveness of the proposed FTC controller. Copyright © 2010 John Wiley & Sons, Ltd.

Stability for uncertain nonlinear dissipative systems