Decomposition of singularly perturbed optimal tracking problems with a given reference trajectory

For the first time, the problem of optimal tracking with a given reference trajectory and an integral quadratic performance criterion in the presence of singular perturbations is considered. To analyze the singularly perturbed differential systems that arise in solving this problem, the decomposition method is used, which is based on the technique of integral manifolds of fast and slow motions. A suboptimal control is constructed, the use of which leads to a difference in the values of the minimized functional for the optimal and suboptimal controls by an amount of the order of the second power of a small parameter characterizing singular perturbations.