Parallel design of suboptimal regulators for singularly perturbed systems with multiple-time scales

The problem for near optimal control of linear systems with multiple-time-scale singular perturbations is studied by a descriptor variable approach. The near optimum regulator problem with multiple-time-scale singular perturbations is decomposed into a number of N+1 subregulator problems. The solutions are mutually independent, and are standard solutions of Riccati equations without parasitic parameters. The algorithm for parallel solutions of these subregulator problems is presented. A hierarchical combination of these suboptimal regulators leads to the near-optimal feedback controller. The spectral factorization of the linear quadratic regulator (LQR) shows that for small and unknown singularly perturbed parameters, the near-optimal controller will preserve the robustness gain and phase margin as established in the optimal LQR