Application of Migrating Optimization Algorithms in Problems of Optimal Control of Discrete-Time Stochastic Dynamical Systems

The problem of finding the optimal open-loop control for discrete-time stochastic dynamical systems is considered. It is assumed that the initial conditions and external influences are random. The average value of the Bolza functional defined on individual trajectories is minimized. It is proposed to solve the problem by means of classical and modified migrating optimization algorithms. The modification of the migrating algorithm consists of cloning the members of the initial population and choosing different strategies of migratory behavior for the main population and for populations formed by clones. At the final stage of the search for an extremum, an intensively clarifying migration cycle is implemented with the participation of three leaders of the populations participating in the search process. Problems of optimal control of bundles of trajectories of deterministic discrete dynamical systems, as well as individual trajectories, are considered as special cases. Seven model examples illustrating the performance of the proposed approach are solved.