Control of Dynamic Systems via Neural Networks

This report is devoted to the problem of controlling a class of linear time-invariant dynamic systems via controllers based on additive neural network models. In particular, the tracking and stabilization problems are considered. First, we show how to transform the problem of tracking a reference signal by a control system into the stabilization problem. Then, some concepts from the variable structure control theory are utilized to construct stabilizing controllers. In order to facilitate the stability analysis of the closed-loop systems we employ a special state space transformation. This transformation allows us also to reveal connections between the proposed controllers and the additive neural network models

OUTPUT FEEDBACK VARIABLE STRUCTURE CONTROLLERS AND STATE ESTIMATORS FOR UNCERTAIN DYNAMIC SYSTEMS

In this paper we propose a new class of output feedback variable structure controllers and state estimators (observers) for uncertain dynamic systems with hounded uncertainties. No statistical information about the uncertain elements is assumed. A variable structure systems (VSS) approach together with the geometric approach to the analysis and synthesis of system zeros are employed in the synthesis of the proposed output feedback controllers and state estimators. The role of system zeros in the output feedback stabilization and state estimation, using the VSS approach, is discussed. Numerical examples included illustrate the feasibility of the proposed stabilization and state estimation schemes

NEURAL NETWORKS FOR CONSTRAINED OPTIMIZATION PROBLEMS

This paper is concerned with utilizing neural networks and analog circuits to solve constrained optimization problems. A novel neural network architecture is proposed for solving a class of nonlinear programming problems. The proposed neural network, or more precisely a physically realizable approximation, is then used to solve minimum norm problems subject to linear constraints. Minimum norm problems have many applications in various areas, but we focus on their applications to the control of discrete dynamic processes. The applicability of the proposed neural network is demonstrated on numerical examples

Minimizing Quotient Space Norms Using Penalty Functions

A penalty function method approach is proposed to solve the general problem of quotient space norms minimization. A new class of penalty functions is introduced which allows one to transform constrained optimization problems of quotient space norms minimization by unconstrained optimization problems. The sharp bound on the weight parameter is given for which constrained and unconstrained problems are equivalent. Also a computationally efficient bound on the weight parameter is given. Numerical examples and computer simulations illustrate the results obtained

ON SOLVING CONSTRAINED OPTIMIZATION PROBLEMS WITH NEURAL NETWORKS : A PENALTY FUNCTION METHOD APPROACH

This paper is concerned with utilizing analog circuits to solve various linear and nonlinear programming problems. The dynamics of these circuits are analyzed. Then, the previously proposed circuit implementations for solving optimization problems are examined. A new nonlinear programming network and its circuit implementation is then introduced which utilizes the nonlinearities to eliminate the problems encountered in previous circuit implementations