Evolutionary algorithms with spline approximation as a general solver for optimal control problems

Abstract

Exact solutions of optimal control problems can be obtained only for limited cases of simple reactor models. For the general class of optimal control problems, the complexity of the model equations makes it extremely difficult to solve the problem either analytically or numerically. Various problem-specific methods have been proposed for determining optimal control profiles for batch or fed-batch processes. They have conditions for simplicity or erroneous assumptions. Strictly numerical techniques have been also suggested, such as gradient methods, a differential dynamic program approach, multiple shooting methods, and quasi-linearization methods. These methods have been shown to have shortcomings such as requiring accurate initial guesses, slow convergence to local minima which may be far off from the true minimum, or requiring a priori the form of the profile. The objective of this work is to provide general computation algorithms for various optimal control problems. In this work, evolutionary method is represented for optimizing processes to solve a general class of optimal control policy of process control problems, which is computationally more efficient and conceptually clearer than earlier ones. Evolutionary method and maximum principle methods are compared by simulation results. The advantage of evolutionary programming is that it does not require the expression of Lagrange`s adjoint system and that it can easily implement the inequality constraints on the control variable. In this work, evolutionary programming is combined with the spline method and the smoother control profile could be obtained. With more complicated model equations, the proposed method shows better performance than other methods. It is demonstrated that the evolutionary programming with the spline method can solve a wide range of optimal control problems.