A New Numerical Method for Optimal Control of a Class of Hybrid Systems

Radiss Alipour

doi:10.17485/ijst/2014/v7i9.1

Abstract

Optimal control of uncertain hybrid systems is a major concern in control engineering. For optimal control of hybrid systems, there are a variety of direct methods, including parametric control and state-based parametric control. A reason that indirect methods are less used for optimal control of hybrid systems is difficulty in working with it and its primary valuing. The present study develops a new numerical method for optimal control of hybrid systems which decreases special restrictions of optimal control functions of hybrid systems per provided solution by a Bellman inequality. The obtained results show that an optimal control problem can be easily solved by converting it to an optimization problem. In addition, the used method obtained more accurate numerical value of the performance index. The results showed that the proposed method leads to greater convergence of the algorithm used in optimal control problems. The efficiency and performance of the proposed method was tested by an application example. Keywords: Bellman Inequality, Hybrid Systems, Optimal Control, Optimization Problems

Highlights

Optimal control of hybrid systems plays a key role in many applications, including economics, finance and engineering
Numerical methods to solve optimization problems dates to Bellman’s work, since application of numerical discussions in solving optimal control, many complexities have been triggered in optimal control problems and their applications; in addition, numerical solutions of these problems have considerably changes, which both add to accuracy of solutions and extend their application in different problems
Numerical methods for solving optimal control problems can be divided into two main classes: 1) direct methods, 2) indirect methods

Summary

Introduction

Optimal control of hybrid systems plays a key role in many applications, including economics, finance and engineering The purpose of this category of controls is to minimize cost or maximize revenue. Hybrid systems include systems which are the result of interactions between discrete and continuous dynamical systems The study of such systems has been further accelerated in recent years. The present study develops a new numerical method for optimal control of a class of hybrid systems by dynamic programming and optimizing properties. Stochastic Hybrid Systems are an important class of hybrid systems including models in which the behavioural variations around the impulse response are related to their stochastically systemic behaviour For analysis of these systems, which are commonly observed in response to unwanted mutations, general approximates of Markov decision processes are used. Due to the fact that the system is not ideal and its non-linear relations, divergence can be avoided by approximations derived from optimal control methods and using polynomials[16]

Framework of Single-stage Hybrid Systems

Formulation

Constraints Required for Cost Optimization

A Practical Example

Discussion

Conclusion