Discrete Global Descent Method And Genetic Algorithm For Optimal Discrete-Valued Control Problems

The use of optimal control is a very broad range of disciplines. It discusses the optimal choice of decision variables, construction method for finding the optimal decision variables and to study the theoretical properties of these methods and their practical effect. Today, optimal control technology in space technology, systems engineering, economic management, decision-making, population control and many other fields has played a wide range of applications. However, in many practical appl- ications, the control can only take values from a discrete set, for example, battery management submarines, ships of the optimal driving strategy, the switching amplifier design and so on. For these optimal control problems, we need to find the switching point and the corresponding discrete control values. Since the control value takes from a discrete set and the switching point is continuous, this is a mixed-integer optimal control optimization problem. Integer variables on the optimal solution of the problem (especially mixed-integer linear programming) and the continuous optimal control Problem has made great progress, but on a combination of both problems, the research field is still the NP problem.In this paper, we try to do some exploration on the aspects of the theory and algorithm, and adopt discrete global descent method and the dual approach to try this mixed integer solutions of optimal control problem, denoted by MIOCP.The basic structure of this paper is as follows: In chapter.1,we give the overview and basics of discrete optimal control problem. In chapter.2 we use discrete global descent method to solve discrete optimal control problem. Here we take the discrete control value from some continuous integers, such as 1,2,3…. First, the discrete optimal control problem is transformed into a discrete optimization problem and a two-level optimization problems of standard optimal control problem. Standard optimal control problem can be solved by existing optimization software package MISER 3.2 , and the discrete optimization problem in this paper will use the discrete global descent method, Last, a numerical example is solved by our method to verify its effectiveness. In chapter.3, we use the Genetic algorithm to solve discrete optimal control problem. First, we represent the research situation of the genetic algorithm. Then, we give a schema to solve discrete optimal control problem by genetic algorithm. Finally we use MATLAB to implement this algorithm and show its effectiveness.