Junyi Wang

Output regulation of state-coupled linear multi-agent systems with globally reachable topologies

This paper investigates output regulation problem of state-coupled linear certain and uncertain multi-agent systems with globally reachable topologies. Distributed dynamic state feedback control law is introduced to realize the regulator problem and a general global method for error regulation is established. The Jordan canonical form is used to stabilize the closed-loop control system. Sylvester equation and internal model theory are adopted to achieve the objectives of output regulation for every initial condition in the state space. Finally, numerical simulations are utilized to show the effectiveness of the obtained results.

Mode-Dependent Stochastic Synchronization for Markovian Coupled Neural Networks With Time-Varying Mode-Delays

This paper investigates the stochastic synchronization problem for Markovian hybrid coupled neural networks with interval time-varying mode-delays and random coupling strengths. The coupling strengths are mutually independent random variables and the coupling configuration matrices are nonsymmetric. A mode-dependent augmented Lyapunov-Krasovskii functional (LKF) is proposed, where some terms involving triple or quadruple integrals are considered, which makes the LKF matrices mode-dependent as much as possible. This gives significant improvement in the synchronization criteria, i.e., less conservative results can be obtained. In addition, by applying an extended Jensens integral inequality and the properties of random variables, new delay-dependent synchronization criteria are derived. The obtained criteria depend not only on upper and lower bounds of mode-delays but also on mathematical expectations and variances of the random coupling strengths. Finally, two numerical examples are provided to demonstrate the feasibility of the proposed results.

Sampled-Data Synchronization Analysis of Markovian Neural Networks With Generally Incomplete Transition Rates

This paper investigates the problem of sampled-data synchronization for Markovian neural networks with generally incomplete transition rates. Different from traditional Markovian neural networks, each transition rate can be completely unknown or only its estimate value is known in this paper. Compared with most of existing Markovian neural networks, our model is more practical because the transition rates in Markovian processes are difficult to precisely acquire due to the limitations of equipment and the influence of uncertain factors. In addition, the time-dependent Lyapunov–Krasovskii functional is proposed to synchronize drive system and response system. By applying an extended Jensen’s integral inequality and Wirtinger’s inequality, new delay-dependent synchronization criteria are obtained, which fully utilize the upper bound of variable sampling interval and the sawtooth structure information of varying input delay. Moreover, the desired sampled-data controllers are obtained. Finally, two examples are provided to illustrate the effectiveness of the proposed method.

Consensus robust output regulation of discrete-time linear multi-agent systems

This paper deals with consensus robust output regulation of discrete-time linear multi-agent systems under a directed interaction topology. The digraph is assumed to contain a spanning tree. Every agent or subsystem is identical and uncertain, but subsystems have different external disturbances. Based on the internal model and general discrete-time algebraic Riccati equation, a distributed consensus protocol is proposed to solve the regulator problem. A numerical simulation demonstrates the effectiveness of the proposed theoretical results.

Sampled-data synchronization for complex networks based on discontinuous LKF and mixed convex combination

Abstract This paper investigates the sampled-data synchronization problem of delayed complex networks with aperiodic sampling interval based on enhanced input delay approach. By introducing an improved discontinuous Lyapunov–Krasovskii functional (LKF), new delay-dependent synchronization criteria are obtained using Wirtinger׳s integral inequality and mixed convex combination, which fully utilize the upper bound on variable sampling interval and the sawtooth structure information of varying input delay. The derived criteria are less conservative than the existing ones. In addition, the desired sampled-data controllers are obtained by solving a set of linear matrix inequalities. Finally, numerical examples are provided to demonstrate the feasibility of the proposed method.

Stochastic synchronization for Markovian coupled neural networks with partial information on transition probabilities

This paper focuses on stochastic synchronization for Markovian coupled neural networks with partial information on transition probabilities and random coupling strengths. The coupling configuration matrices are not restricted to be symmetric, and the coupling strengths are mutually independent random variables. By designing a novel augmented Lyapunov-Krasovskii functional and using reciprocally convex combination technique and the properties of random variables, new delay-dependent synchronization criteria in terms of linear matrix inequalities are derived. The obtained criteria depend not only on upper and lower bounds of delay but also on mathematical expectations and variances of random coupling strengths. Numerical examples are provided to verify the effectiveness of the presented results.

Synchronization analysis for static neural networks with hybrid couplings and time delays

Abstract This paper deals with the synchronization problem for delayed static neural networks with hybrid couplings. When the static neural networks are affected by hybrid couplings, it is hard to deal with a large number of highly interconnected dynamical units in such a complex system. In order to solve this complicated problem, a new method is proposed to deal with the Kronecker product, and to make the synchronization problem to be easily analyzed. Further, based on the obtained result, by using the augmented Lyapunov–Krasovskii functional (LKF) method, multitude Kronecker product terms can be handled, which can introduce more relaxed conditions by employing the new type of augmented matrices with the Kronecker product operation. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed synchronization scheme.

Sampled-Data Synchronization of Markovian Coupled Neural Networks With Mode Delays Based on Mode-Dependent LKF

This paper investigates sampled-data synchronization problem of Markovian coupled neural networks with mode-dependent interval time-varying delays and aperiodic sampling intervals based on an enhanced input delay approach. A mode-dependent augmented Lyapunov–Krasovskii functional (LKF) is utilized, which makes the LKF matrices mode-dependent as much as possible. By applying an extended Jensen’s integral inequality and Wirtinger’s inequality, new delay-dependent synchronization criteria are obtained, which fully utilizes the upper bound on variable sampling interval and the sawtooth structure information of varying input delay. In addition, the desired stochastic sampled-data controllers can be obtained by solving a set of linear matrix inequalities. Finally, two examples are provided to demonstrate the feasibility of the proposed method.

Optimal tracking control for completely unknown nonlinear discrete-time Markov jump systems using data-based reinforcement learning method

In this paper, we develop a novel optimal tracking control scheme for a class of nonlinear discrete-time Markov jump systems (MJSs) by utilizing a data-based reinforcement learning method. It is not practical to obtain accurate system models of the real-world MJSs due to the existence of abrupt variations in their system structures. Consequently, most traditional model-based methods for MJSs are invalid for the practical engineering applications. In order to overcome the difficulties without any identification scheme which would cause estimation errors, a model-free adaptive dynamic programming (ADP) algorithm will be designed by using system data rather than accurate system functions. Firstly, we combine the tracking error dynamics and reference system dynamics to form an augmented system. Then, based on the augmented system, a new performance index function with discount factor is formulated for the optimal tracking control problem via Markov chain and weighted sum technique. Neural networks are employed to implement the on-line ADP learning algorithm. Finally, a simulation example is given to demonstrate the effectiveness of our proposed approach.

Local Synchronization Criteria of Markovian Nonlinearly Coupled Neural Networks With Uncertain and Partially Unknown Transition Rates

In this paper, the local synchronization problem of Markovian nonlinearly coupled neural networks with uncertain and partially unknown transition rates is investigated. Each transition rate in this Markovian nonlinearly coupled neural networks model is uncertain or completely unknown because the complete knowledge on the transition rates is difficult and the cost is probably high. By applying the Lyapunov–Krasovskii functional, a new integral inequality combining with free-matrix-based integral inequality and further improved integral inequality, the less conservative local synchronization criteria are obtained. The new delay-dependent local synchronization criteria containing the bounds of delay and delay derivative are given in terms of linear matrix inequalities. Finally, a simulation example is provided to illustrate the effectiveness of the proposed method.