Jose P. Perez

Input-to-state stability (ISS) analysis for dynamic neural networks

In this paper a novel approach to assess the stability of dynamic neural networks is presented. Using a Lyapunov function, we determine conditions to guarantee input-to-state stability (ISS) which also ensures global asymptotic stability (GAS). The applicability of these conditions is illustrated by two examples.

Nonlinear adaptive trajectory tracking using dynamic neural networks

In this paper the adaptive nonlinear identification and trajectory tracking are discussed via dynamic neural networks. By means of a Lyapunov-like analysis we determine stability conditions for the identification error. Then we analyze the trajectory tracking error by a local optimal controller. An algebraic Riccati equation and a differential one are used for the identification and the tracking error analysis. As our main original contributions, we establish two theorems: the first one gives a bound for the identification error and the second one establishes a bound for the tracking error. We illustrate the effectiveness of these results by two examples: the second-order relay system with multiple isolated equilibrium points and the chaotic system given by Duffing equation.

Stability analysis of dynamic neural control

Abstract In this paper, the authors summarize their research related to dynamic neural control. In particular, results on nonlinear system identification, nonlinear trajectory tracking, and input-to-state stability (ISS) of dynamic neural networks are presented. The main analysis tool utilized is the Lyapunov approach. References for the detailed demonstrations are given. We illustrate the applicability of the results by means of examples.

USING DYNAMIC NEURAL NETWORKS TO GENERATE CHAOS: AN INVERSE OPTIMAL CONTROL APPROACH

This Letter suggests a new approach to generating chaos via dynamic neural networks. This approach is based on a recently introduced methodology of inverse optimal control for nonlinear systems. Both Chens chaotic system and Chuas circuit are used as examples for demonstration. The control law is derived to force a dynamic neural network to reproduce the intended chaotic attractors. Computer simulations are included for illustration and verification.

Input-to-state stabilization of dynamic neural networks

As a continuation of their previous published results, in this paper the authors propose a new methodology, for input-to-state stabilization of a dynamic neural network. This approach is developed on the basis of the recent introduced inverse optimal control technique for nonlinear control. An example illustrates the applicability of the proposed approach.

RECURRENT NEURAL CONTROL FOR ROBOT TRAJECTORY TRACKING

This paper extends the results previously obtained for trajectory tracking of unknown plants using recurrent neural networks. The proposed controller structure is composed of a neural identifier and a control law defined by using the inverse optimal control approach, which has been improved so that less inputs than states are needed. The proposed new control scheme is applied to the control a robotic manipulator model.

Robust adaptive nonlinear system identification and trajectory tracking by dynamic neural networks

We analyze adaptive nonlinear identification and trajectory tracking using a dynamic neural network, with the same state space dimension as the system. We assume the system space state completely measurable. By means of a Lyapunov-like analysis we determine stability conditions for the identification error. We then analyze the trajectory tracking error when the adaptive controller is utilized. For the identification analysis we use an algebraic Riccati equation and for the tracking error a differential one using online adapted parameters of the neural network. The structure of our scheme is composed-by two parts: the neural network identifier and the tracking controller. As our main contributions, we establish two theorems: the first one gives a bound for the identification error, and the second one establish a bound for the tracking error.

Trajectory tracking for delayed recurrent neural networks

This paper deals with the problem of trajectory tracking for delayed recurrent neural networks. The tracking error is global asymptotic stabilized by a control law derived on the basis of a Lyapunov-Krasovsky functional. Then, it is established that this control law minimizes a meaningful cost functional. Applicability of the approach is illustrated by means of an example

Adaptive recurrent neural control for noisy chaos synchronization

AbJtract- In this paper, we presont an adaptive recurrent neural control for trajectory tracking of noisy unknown nonlinear systems. Trajectory tracking error stability is analyzed by means of the stochastic system extension for the Lyapunov methodology. The applicability of the proposed structure is illustrated, via simulations, with a relevant complex task: noisy chaos synchronization.

Real-Time Chaos Stabilization Via Inverse Optimal Control

This paper reports a hardware implementation for real-time global asymptotic stabilization of the chaotic Chens system from the inverse optimal control approach