Nonfragile Near-Optimal Control of Stochastic Time-Varying Multiagent Systems With Control- and State-Dependent Noises

On Consensus of Second-Order Multiagent Systems With Actuator Saturations: A Generalized-Nyquist-Criterion-Based Approach

In this article, a frequency-domain approach is developed to deal with the global consensus problem for a class of general second-order multiagent systems (MASs) subject to actuator saturations. By employing the describing function and the generalized Nyquist criterion, the global consensus problem is thoroughly investigated for both undirected and directed topologies. First, the describing function is introduced to characterize the actuator saturations in the s -plane, and the inherent representation error is quantitatively analyzed from a frequency-domain perspective. Then, by means of the Kronecker product, the addressed consensus problem of the MAS is transformed into a corresponding stability analysis problem for a certain multi-input-multi-output (MIMO) system and, consequently, the generalized Nyquist criterion for MIMO systems is exploited to derive the condition for the global consensus of the MAS where the impact from the actuator saturation is explicitly reflected. Finally, numerical simulations are provided to illustrate the validity of the proposed theoretical result.

Learning and Near-Optimal Control of Underactuated Surface Vessels With Periodic Disturbances

In this article, we propose a novel learning and near-optimal control approach for underactuated surface (USV) vessels with unknown mismatched periodic external disturbances and unknown hydrodynamic parameters. Given a prior knowledge of the periods of the disturbances, an analytical near-optimal control law is derived through the approximation of the integral-type quadratic performance index with respect to the tracking error, where the equivalent unknown parameters are generated online by an auxiliary system that can learn the dynamics of the controlled system. It is proved that the state differences between the auxiliary system and the corresponding controlled USV vessel are globally asymptotically convergent to zero. Besides, the approach theoretically guarantees asymptotic optimality of the performance index. The efficacy of the method is demonstrated via simulations based on the real parameters of an USV vessel.

Control Design With Optimization for Fuzzy Steering-by-Wire System Based on Nash Game Theory

In this article, we apply a high-order control to a dynamical system with uncertainty. There are two characteristics. First, the uncertain part, which is time-varying but bounded, is described in a fuzzy aspect. Specifically, the uncertainty lies within a fuzzy set and the bound is regarded as a fuzzy number. Second, the systems are uniformly bounded and uniformly ultimately bounded with a deterministic controller based on the Lyapunov theory. To obtain better system performance and lower control input, we apply the noncooperative game theory to optimize the parameters by establishing a Nash game. Then, the D-operation is proposed for the uncertainty related to fuzzy numbers. Finally, we perform the numerical simulations of the steering-by-wire system for verification.

Continuous-Time Distributed Policy Iteration for Multicontroller Nonlinear Systems

In this article, a novel distributed policy iteration algorithm is established for infinite horizon optimal control problems of continuous-time nonlinear systems. In each iteration of the developed distributed policy iteration algorithm, only one controller's control law is updated and the other controllers' control laws remain unchanged. The main contribution of the present algorithm is to improve the iterative control law one by one, instead of updating all the control laws in each iteration of the traditional policy iteration algorithms, which effectively releases the computational burden in each iteration. The properties of distributed policy iteration algorithm for continuous-time nonlinear systems are analyzed. The admissibility of the present methods has also been analyzed. Monotonicity, convergence, and optimality have been discussed, which show that the iterative value function is nonincreasingly convergent to the solution of the Hamilton-Jacobi-Bellman equation. Finally, numerical simulations are conducted to illustrate the effectiveness of the proposed method.

Observer-Based Fuzzy Output-Feedback Control for Discrete-Time Strict-Feedback Nonlinear Systems With Stochastic Noises

This paper focuses on the observer-based output-feedback control (OBOFC) problem for a class of discrete-time strict-feedback nonlinear systems (DTSFNSs) with both multiplicative process noises and additive measurement noises. A state observer is first designed to estimate immeasurable system states, and then a novel observer-based backstepping control framework is proposed for DTSFNSs with known model information. To be specific, virtual control laws and the actual control law are derived using a variable substitution method that gets rid of the repeated accumulation of measurement noises in the recursive process. Furthermore, for technical derivation, the multiplicative noise is successively bounded by state estimation errors and controlled errors. Stability conditions are obtained to guarantee the exponential mean-square boundedness of the closed-loop system. Moreover, the nonlinear modeling uncertainties are taken into account to better reflect engineering practices. In virtue of the universal approximation property of fuzzy-logic systems, a fuzzy observer and the corresponding fuzzy output-feedback controller are simultaneously constructed to derive the stability criteria by using novel weight updated laws. Simulation studies are performed to test the validity of the proposed OBOFC scheme.

Resilient Control of Wireless Networked Control System Under Denial-of-Service Attacks: A Cross-Layer Design Approach

The resilient control refers to the control methodology which provides an interdisciplinary solution to secure the control system. In this paper, the resilient control problem is investigated for a class of wireless networked control systems (WNCS) under a denial-of-service (DoS) attack. In the presence of the DoS attacker, the control command sent by the transmitter may be interfered, which can cause the degradation of the signal-to-interference-plus-noise ratio and further lead to packet dropout phenomenon. Such a packet dropout phenomenon is described by a two-state Markov-chain. A cross-layer view is adopted toward the security issue of the considered WNCS. The Nash power strategies and optimal control strategy in the delta-domain are obtained in the cyber- and physical-layer, respectively. Based on the obtained strategies, the coupled-design problem is solved which aims to drive the underlying control performance to the desired security region by dynamically manipulating the cyber-layer pricing parameters. Finally, a numerical simulation is conducted to verify the validity of the proposed methodology.

Observer-Based Consensus Control for Discrete-Time Multiagent Systems With Coding-Decoding Communication Protocol

In this paper, the consensus control problem is investigated for a class of discrete-time networked multiagent systems (MASs) with the coding-decoding communication protocol (CDCP). Under a directed communication topology, an observer-based control scheme is proposed for each agent by utilizing the relative measurement outputs between the agent itself and its neighboring ones. The signal delivery is in a digital manner, which means that only the sequence of finite coded signals is sent from the observer to the controller. To be specific, the observed data is encoded to certain codewords by a designed coder via the CDCP, and the received codewords are then decoded by the corresponding decoder at the controller side. The purpose of the addressed problem is to design an observer-based controller such that the close-loop MAS achieves the expected consensus performance. First, with the help of the input-to-state stability theory, a theoretical framework for the detectability is established for analyzing and designing the CDCP. Then, under such a communication protocol, some sufficient conditions for the existence of the proposed observer-based controller are derived to guarantee the asymptotic consensus of the MASs. In addition, the controller parameter is explicitly determined in terms of the solution to certain matrix inequalities associated with the information of the communication topology. Finally, a simulation example is given to demonstrate the effectiveness of the developed control strategy.