Ziqian Liu

Further Development of Input-to-State Stabilizing Control for Dynamic Neural Network Systems

The authors present an approach for input-to-state stabilizing control of dynamic neural networks, which extends the existing result in the literature to a wider class of systems. This methodology is developed by using the Lyapunov technique, inverse optimality, and the Hamilton-Jacobi-Bellman equation. Depending on the dimensions of state and input, we construct two inverse optimal feedback laws to achieve the input-to-state stabilization of a wider class of dynamic neural network systems. With the help of the Sontags formula, one of two control laws is developed from the creation of a scalar function to eliminate a restriction requiring the same number of states and inputs. In addition, the proposed designs achieve global asymptotic stability and global inverse optimality with respect to some meaningful cost functional. Numerical examples demonstrate the performance of the approach.

Global Robust Stabilizing Control for a Dynamic Neural Network System

This paper presents a new approach for the global robust stabilizing control of a class of dynamic neural network systems. This approach is developed via Lyapunov stability and inverse optimality, which circumvents the task of solving a Hamilton-Jacobi-Isaacs equation. The primary contribution of this paper is the development of a nonlinear Hinfin control design for a class of dynamic neural network systems, which are usually used in the modeling and control of nonlinear affine systems with unknown nonlinearities. The proposed Hinfin control design achieves global inverse optimality with respect to some meaningful cost functional, global disturbance attenuation, and global asymptotic stability provided that no disturbance occurs. Finally, four numerical examples are used to demonstrate the effectiveness of the proposed approach.

Theoretic design of differential minimax controllers for stochastic cellular neural networks

This paper presents a theoretical design of how a minimax equilibrium of differential game is achieved in stochastic cellular neural networks. In order to realize the equilibrium, two opposing players are selected for the model of stochastic cellular neural networks. One is the vector of external inputs and the other is the vector of internal noises. The design procedure follows the nonlinear H infinity optimal control methodology to accomplish the best rational stabilization in probability for stochastic cellular neural networks, and to attenuate noises to a predefined level with stability margins. Three numerical examples are given to demonstrate the effectiveness of the proposed approach.

Design of nonlinear optimal control for chaotic synchronization of coupled stochastic neural networks via Hamilton–Jacobi–Bellman equation

This paper presents a new theoretical design of nonlinear optimal control on achieving chaotic synchronization for coupled stochastic neural networks. To obtain an optimal control law, the proposed approach is developed rigorously by using Hamilton-Jacobi-Bellman (HJB) equation, Lyapunov technique, and inverse optimality, and hence guarantees that the chaotic drive network synchronizes with the chaotic response network influenced by uncertain noise signals. Furthermore, the paper provides four numerical examples to demonstrate the effectiveness of the proposed approach.

Risk-sensitive optimal control for stochastic recurrent neural networks

As a continuation of our study, this paper extends our research results of optimality-oriented control from deterministic recurrent neural networks to stochastic recurrent neural networks, and presents a new theoretical design for the risk-sensitive optimal control of stochastic recurrent neural networks. The design procedure follows the technique of inverse optimality, and obtains risk-sensitive state feedback controllers that guarantee an achievable meaningful cost for a given risk-sensitivity parameter.

Nonlinear optimal control of stochastic recurrent neural networks with multiple time delays

This paper presents a theoretical design of how a nonlinear optimal control is achieved for multiple time-delayed recurrent neural networks under the influence of random perturbations. Our objective is to build stabilizing control laws to accomplish global asymptotic stability in probability as well as optimality with respect to disturbance attenuation for stochastic delayed recurrent neural networks. The formulation of the nonlinear optimal control is developed by using stochastic Lyapunov technique and solving a Hamilton-Jacobi-Bellman (HJB) equation indirectly. To illustrate the analytical results, a numerical example is given to demonstrate the effectiveness of the proposed approach.

Optimal regulation of stochastic cellular neural networks using differential minimax game

In this paper, we present an approach to optimally regulate stochastic cellular neural networks by using differential minimax game. In order to realize the design, we consider the vector of external inputs as a player and that of internal noises as an opposing player. The purpose of this study is to achieve the best rational stabilization in probability for stochastic cellular neural networks, and to attenuate noises to a predefined level with stability margins under an optimal control strategy. A numerical example is given to demonstrate the effectiveness of the proposed approach.

Robust design of adaptive neural controllers for unknown nonlinear systems

In this paper, we extend our previous research results from the stabilization of dynamic neural networks to the stabilization of unknown nonlinear systems, and present an approach of H∞ control for nonlinear systems via dynamic neural networks. The proposed H∞ controller is intended to attenuate the adverse impact of modeling error, considered as a disturbance, to a prescribed level with stability margins. A numerical example demonstrates the performance of stabilizing control on an unstable unknown nonlinear system.

Design of risk-sensitive optimal control for stochastic recurrent neural networks by using Hamilton-Jacobi-Bellman equation

This paper presents a theoretical design for the stabilization of stochastic recurrent neural networks with respect to a risk-sensitive optimality criterion. This approach is developed by using the Hamilton-Jacobi-Bellman equation, Lyapunov technique, and inverse optimality, to obtain a risk-sensitive state feedback controller, which guarantees an achievable meaningful cost for a given risk-sensitivity parameter. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.

Control of Recurrent Neural Networks Using Differential Minimax Game: The Stochastic Case

This paper presents a theoretical design of how a minimax equilibrium of differential game is achieved in a class of large-scale nonlinear dynamic systems, namely the recurrent neural networks. In order to realize the equilibrium, we consider the vector of external inputs as a player and the vector of internal noises (or disturbances or modeling errors) as an opposing player. The purpose of this study is to construct a nonlinear H ∞ optimal control for deterministic noisy recurrent neural networks to achieve an optimal-oriented stabilization, as well as to attenuate noise to a prescribed level with stability margins. A numerical example demonstrates the effectiveness of the proposed approach.© 2010 ASME