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

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, 125993, Russia

^* e-mail: VMRakityanskij@mai.education

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 switching 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 theMSOMA algorithm, which belongs to the evolutionary group. The MSOMA algorithm is a new algorithm based on the SOMA self-organizing migration algorithm. The modification consists in identifying three leaders among the individuals forming the current population. For each member of the population, two clones are generated with the same position. Thus, in fact, three populations are generated, each of which then realizes a migration cycle (evolutionary process) relative to one of the three selected leaders. A step-by-step algorithm for piecewise-constant, piecewiselinear, quadratic spline and cubic spline methods of control laws approximation is proposed. The effectiveness of the proposed method is demonstrated by the example of solving optimal control problems for switching systems with two and three subsystems. 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 the known solution is carried out.