Solving optimal control problems with a cost changing control by evolutionary algorithms

Many mathematical solutions to certain classes of optimal control problems, particularly problems which give rise to 'chattering controls', make some physically unrealistic assumptions in order to solve the problems. These solutions often ignore the cost of changing control and thus fail to give physically realistic results due to the physical reality of this cost in many applications. When this cost is incorporated into the problem, the problem can become very difficult to solve numerically. This paper considers an evolutionary approach to solving optimal control problems which take the cost of changing control into account. A novel chromosome representation and an insert mutation have been proposed and tested against three different problems. The experimental results show that the evolutionary approach is quite competitive in comparison with the existing method based on dynamic programming.