Application of a Memetic Algorithm for the Optimal Control of Bunches of Trajectories of Nonlinear Deterministic Systems with Incomplete Feedback

Abstract

The application of a hybrid memetic constrained minimization algorithm that uses the ideas of evolutionary methods operating the concept of population and the algorithms of simulation and mutual learning of the population’s individuals for designing the optimal control of bunches of trajectories of nonlinear deterministic systems with incomplete feedback is proposed. Memetic algorithms use the concept of meme as a unit of information transmission between individuals of the population. In the proposed algorithm, the meme is a promising solution obtained in the course of executing a procedure to find an extremum. Since the proposed method uses a number of different heuristic procedures for solving the problem, in particular, the simulated annealing, ant colony optimization methods, and the path-relinking procedure for accelerating the search, the algorithm is a hybrid modified one. To demonstrate the efficiency of the proposed approach, the problem of stabilization and attitude control of a satellite is solved and the results are compared with those obtained using the local variation method.