Solving multiobjective random interval programming problems by a capable neural network framework

Abstract

In this paper, the stability of a class of nonlinear control systems is analyzed. We first construct an optimal control problem by inserting a suitable performance index, which this problem is referred to as an infinite horizon problem. By a suitable change of variable, the infinite horizon problem is reduced to a finite horizon problem. We then present a feedback controller designing approach for the obtained finite horizon control problem. This approach involves a neural network scheme for solving the nonlinear Hamilton Jacobi Bellman (HJB) equation. By using the neural network method, an analytic approximate solution for value function and suboptimal feedback control law is achieved. A learning algorithm based on a dynamic optimization scheme with stability and convergence properties is also provided. Some illustrative examples are employed to demonstrate the accuracy and efficiency of the proposed plan. As a real life application in engineering, the stabilization of a micro electro mechanical system is studied.