In this article, a novel hybrid reinforcement $Q$ -learning control method is proposed to solve the adaptive fuzzy $H_{\infty }$ control problem of discrete-time nonlinear Markov jump systems based on the Takagi–Sugeno fuzzy model. First, the core problem of adaptive fuzzy $H_{\infty }$ control is converted to solving fuzzy game coupled algebraic Riccati equation, which can hardly be solved by mathematical methods directly. To solve this problem, an offline parallel hybrid learning algorithm is first designed, where system dynamics should be known as a prior. Furthermore, an online parallel $Q$ -learning hybrid learning algorithm is developed. The main characteristics of the proposed online hybrid learning algorithms are threefold: 1) system dynamics are avoided during the learning process; 2) compared with the policy iteration method, the restriction of the initial stable control policy is removed; and 3) compared with the value iteration method, a faster convergence rate can be obtained. Finally, we provide a tunnel diode circuit system model to validate the effectiveness of the present learning algorithm.

In this article, the sliding mode control issue is investigated for a class of discrete-time Takagi–Sugeno fuzzy networked singularly perturbed systems via an observer-based technique. Moreover, to process the measurement output and schedule the transmission sequence for relieving the communication burden, a logarithmic quantizer and a weighted try-once-discard protocol are synthesized, which can further improve the network bandwidth utilization in networked control systems. Based on the fuzzy observer states, a novel fuzzy sliding surface is established by considering the singularly perturbed parameter properly, and we endeavor to synthesize a sliding mode control law such that the reachability of the prescribed sliding surface could be guaranteed. In addition, by virtue of the convex optimization theory and Lyapunov approach, sufficient conditions are developed to guarantee the asymptotic stability of the sliding mode dynamics as well as the error system with an expected $H_{\infty }$ performance. Finally, a verification example is presented to illustrate the feasibility and effectivity of the proposed method.

This paper discusses the problem of composite $\mathcal {H}_{\infty }$ control for hidden Markov jump systems subject to replay attacks. Since it is difficult to obtain the mode information of the system directly in practice, a hidden Markov model is adopted in this paper to facilitate subsequent works. The hidden state represents the actual system dynamics that cannot be known exactly, but can be observed by the detector. Considering the multi-disturbance phenomenon, one of which is norm bounded and another is produced by an exogenous system, a composite $\mathcal {H}_{\infty }$ control scheme based on disturbance observer is designed to improve the anti-disturbance ability of the system. In addition, with the help of multi-sensor approach, a detection scheme, revealing the attacker's tactics and determining which sensor is assaulted, is presented to withstand replay attacks. Then, a composite disturbance observer-based controller, ensuring that the resulting system is stochastically stable with an expected $\mathcal {H}_{\infty }$ performance under replay attacks, is designed by solving convex optimization problems. Finally, the effectiveness and superiority of the developed method are verified by an example.

In this paper, a novel reinforcement learning-based predefined-time control method for nonlinear servo systems with prescribed performance is proposed under an event-triggered strategy. Firstly, the nonlinear dynamics and control behaviors of the systems can be trained effectively through fuzzy logic systems under the identifier-critic-actor framework. Moreover, by employing the prescribed performance control and a switching event-triggered rule, system tracking performance can be ensured while decreasing the data transmission frequency. With the assistance of the predefined-time stability criteria, the boundedness of system variables and the convergence of tracking errors within a predetermined time can be guaranteed. Comparisons with some existing control schemes are addressed regarding tracking performance and action costs. The availability and superiority of the suggested scheme are verified in the simulations.

This paper investigates the non-fragile $H_{\infty}$ synchronization issue for a class of discrete-time T-S fuzzy Markov jump systems. With regard to the T-S fuzzy model, a novel processing method based on matrix transformation is introduced to deal with the double summation inequality containing fuzzy weighting functions, which may be beneficial to obtain conditions with less conservatism. In view of the fact that the uncertainties may occur randomly in the execution of actuator, a non-fragile controller design scheme is presented by virtue of the Bernoulli distributed white sequence. The main novelty of this paper lies in that the transition probabilities of Markov chain are considered to be piecewise time-varying, and whose variation characteristics are described by the persistent dwell-time switching regularity. Then, based on Lyapunov stability theory, it is concluded that the resulting synchronization error system is mean-square exponentially stable with a prescribed $H_{\infty}$ performance in the presence of actuator gain variations. Finally, an illustrative example about Lorenz chaotic systems is provided to show the effectiveness of the established results.

This work explores the $H_{∞ }$ synchronization issue for singularly perturbed coupled neural networks (SPCNNs) affected by both nonlinear constraints and gain uncertainties, in which a novel double-layer switching regulation containing Markov chain and persistent dwell-time switching regulation (PDTSR) is used. The first layer of switching regulation is the Markov chain to characterize the switching stochastic properties of the systems suffering from random component failures and sudden environmental disturbances. Meanwhile, PDTSR, as the second-layer switching regulation, is used to depict the variations in the transition probability of the aforementioned Markov chain. For systems under double-layer switching regulation, the purpose of the addressed issue is to design a mode-dependent synchronization controller for the network with the desired controller gains calculated by solving convex optimization problems. As such, new sufficient conditions are established to ensure that the synchronization error systems are mean-square exponentially stable with a specified level of the $H_{∞ }$ performance. Eventually, the solvability and validity of the proposed control scheme are illustrated through a numerical simulation.