Huaguang Zhang

Neural-Network-Based Near-Optimal Control for a Class of Discrete-Time Affine Nonlinear Systems With Control Constraints

In this paper, the near-optimal control problem for a class of nonlinear discrete-time systems with control constraints is solved by iterative adaptive dynamic programming algorithm. First, a novel nonquadratic performance functional is introduced to overcome the control constraints, and then an iterative adaptive dynamic programming algorithm is developed to solve the optimal feedback control problem of the original constrained system with convergence analysis. In the present control scheme, there are three neural networks used as parametric structures for facilitating the implementation of the iterative algorithm. Two examples are given to demonstrate the convergence and feasibility of the proposed optimal control scheme.

A Combined Backstepping and Small-Gain Approach to Robust Adaptive Fuzzy Output Feedback Control

In this paper, an adaptive fuzzy output feedback control approach is proposed for single-input-single-output nonlinear systems without the measurements of the states. The nonlinear systems addressed in this paper are assumed to possess unmodeled dynamics in the presence of unstructured uncertainties and dynamic disturbances, where the unstructured uncertainties are not linearly parameterized, and no prior knowledge of their bounds are available. Fuzzy logic systems are used to approximate the unstructured uncertainties, and a state observer is developed to estimate the unmeasured states. By combining the backstepping technique with the small-gain approach, a stable adaptive fuzzy output feedback control method is proposed. It is shown that by applying the proposed adaptive fuzzy control approach, the closed-loop systems are semiglobally uniformly ultimately bounded. The effectiveness of the proposed approach is illustrated from simulation results.

Novel Weighting-Delay-Based Stability Criteria for Recurrent Neural Networks With Time-Varying Delay

In this paper, a weighting-delay-based method is developed for the study of the stability problem of a class of recurrent neural networks (RNNs) with time-varying delay. Different from previous results, the delay interval [0, d(t)] is divided into some variable subintervals by employing weighting delays. Thus, new delay-dependent stability criteria for RNNs with time-varying delay are derived by applying this weighting-delay method, which are less conservative than previous results. The proposed stability criteria depend on the positions of weighting delays in the interval [0, d(t)], which can be denoted by the weighting-delay parameters. Different weighting-delay parameters lead to different stability margins for a given system. Thus, a solution based on optimization methods is further given to calculate the optimal weighting-delay parameters. Several examples are provided to verify the effectiveness of the proposed criteria.

A Novel Infinite-Time Optimal Tracking Control Scheme for a Class of Discrete-Time Nonlinear Systems via the Greedy HDP Iteration Algorithm

In this paper, we aim to solve the infinite-time optimal tracking control problem for a class of discrete-time nonlinear systems using the greedy heuristic dynamic programming (HDP) iteration algorithm. A new type of performance index is defined because the existing performance indexes are very difficult in solving this kind of tracking problem, if not impossible. Via system transformation, the optimal tracking problem is transformed into an optimal regulation problem, and then, the greedy HDP iteration algorithm is introduced to deal with the regulation problem with rigorous convergence analysis. Three neural networks are used to approximate the performance index, compute the optimal control policy, and model the nonlinear system for facilitating the implementation of the greedy HDP iteration algorithm. An example is given to demonstrate the validity of the proposed optimal tracking control scheme.

Global Asymptotic Stability of Recurrent Neural Networks With Multiple Time-Varying Delays

In this paper, several sufficient conditions are established for the global asymptotic stability of recurrent neural networks with multiple time-varying delays. The Lyapunov-Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) approach are employed in our investigation. The results are shown to be generalizations of some previously published results and are less conservative than existing results. The present results are also applied to recurrent neural networks with constant time delays.

Robust Global Exponential Synchronization of Uncertain Chaotic Delayed Neural Networks via Dual-Stage Impulsive Control

This paper is concerned with the robust exponential synchronization problem of a class of chaotic delayed neural networks with different parametric uncertainties. A novel impulsive control scheme (so-called dual-stage impulsive control) is proposed. Based on the theory of impulsive functional differential equations, a global exponential synchronization error bound together with some new sufficient conditions expressed in the form of linear matrix inequalities (LMIs) is derived in order to guarantee that the synchronization error dynamics can converge to a predetermined level. Furthermore, to estimate the stable region, a novel optimization control algorithm is established, which can deal with the minimum problem with two nonlinear terms coexisting in LMIs effectively. The idea and approach developed in this paper can provide a more practical framework for the synchronization of multiperturbation delayed chaotic systems. Simulation results finally demonstrate the effectiveness of the proposed method.

Stability Analysis of Markovian Jumping Stochastic Cohen–Grossberg Neural Networks With Mixed Time Delays

In this letter, the global asymptotical stability analysis problem is considered for a class of Markovian jumping stochastic Cohen-Grossberg neural networks (CGNNs) with mixed delays including discrete delays and distributed delays. An alternative delay-dependent stability analysis result is established based on the linear matrix inequality (LMI) technique, which can easily be checked by utilizing the numerically efficient Matlab LMI toolbox. Neither system transformation nor free-weight matrix via Newton-Leibniz formula is required. Two numerical examples are included to show the effectiveness of the result.

Data-Driven Robust Approximate Optimal Tracking Control for Unknown General Nonlinear Systems Using Adaptive Dynamic Programming Method

In this paper, a novel data-driven robust approximate optimal tracking control scheme is proposed for unknown general nonlinear systems by using the adaptive dynamic programming (ADP) method. In the design of the controller, only available input-output data is required instead of known system dynamics. A data-driven model is established by a recurrent neural network (NN) to reconstruct the unknown system dynamics using available input-output data. By adding a novel adjustable term related to the modeling error, the resultant modeling error is first guaranteed to converge to zero. Then, based on the obtained data-driven model, the ADP method is utilized to design the approximate optimal tracking controller, which consists of the steady-state controller and the optimal feedback controller. Further, a robustifying term is developed to compensate for the NN approximation errors introduced by implementing the ADP method. Based on Lyapunov approach, stability analysis of the closed-loop system is performed to show that the proposed controller guarantees the system state asymptotically tracking the desired trajectory. Additionally, the obtained control input is proven to be close to the optimal control input within a small bound. Finally, two numerical examples are used to demonstrate the effectiveness of the proposed control scheme.

An iterative adaptive dynamic programming method for solving a class of nonlinear zero-sum differential games

In this paper, a new iterative adaptive dynamic programming (ADP) method is proposed to solve a class of continuous-time nonlinear two-person zero-sum differential games. The idea is to use the ADP technique to obtain the optimal control pair iteratively which makes the performance index function reach the saddle point of the zero-sum differential games. If the saddle point does not exist, the mixed optimal control pair is obtained to make the performance index function reach the mixed optimum. Stability analysis of the nonlinear systems is presented and the convergence property of the performance index function is also proved. Two simulation examples are given to illustrate the performance of the proposed method.

A Comprehensive Review of Stability Analysis of Continuous-Time Recurrent Neural Networks

Stability problems of continuous-time recurrent neural networks have been extensively studied, and many papers have been published in the literature. The purpose of this paper is to provide a comprehensive review of the research on stability of continuous-time recurrent neural networks, including Hopfield neural networks, Cohen-Grossberg neural networks, and related models. Since time delay is inevitable in practice, stability results of recurrent neural networks with different classes of time delays are reviewed in detail. For the case of delay-dependent stability, the results on how to deal with the constant/variable delay in recurrent neural networks are summarized. The relationship among stability results in different forms, such as algebraic inequality forms, M-matrix forms, linear matrix inequality forms, and Lyapunov diagonal stability forms, is discussed and compared. Some necessary and sufficient stability conditions for recurrent neural networks without time delays are also discussed. Concluding remarks and future directions of stability analysis of recurrent neural networks are given.