Application of the modified self-organizing migration algorithm MSOMA in optimal open-loop control problems

Abstract

The article discusses the application of the metaheuristic algorithm of global constrained optimization for solving the problem of finding the optimal open-loop control for nonlinear continuous deterministic dynamical systems. The quality of control is assessed by the value of the functional defined on individual trajectories. The optimal control problem is reduced to a parametric optimization problem, which is solved using the MSOMA algorithm, which belongs to the evolutionary group. The MSOMA algorithm is a new algorithm based on the SOMA self-organizing migration algorithm. A step-by-step algorithm for piecewise-constant, piecewise-linear, quadratic spline and cubic spline methods of control laws approximation is proposed. The effectiveness of proposed method is demonstrated by the example of solving the problem of optimal control of a chemical process in a mixing reactor and a singular problem of optimal control. The influence of the parameters of the MSOMA algorithm on the quality of the obtained result is investigated. Comparison of the operation of the algorithm with a known solution, as well as with a solution using the original SOMA method is carried out.