New results for near-optimal control of linear multiparameter singularly perturbed systems. (Q1421456)

The linear quadratic optimal control problem for multiparameter singularly perturbed systems in which \(N\) lower-level fast subsystems are interconnected through a higher-level slow subsystem is considered. The main contribution is to propose a new design method for the \(\varepsilon\)-independent controller. Note that this design method is quite different from existing methods such as the two-time-scale design method and the descriptor variable approach. Furthermore, it is proved that the resulting controller achieves \(O(\| \mu^2\| )\) approximation of the optimal cost compared with the existing result for a special case of the fast subsystems. Finally, it is shown that the composite controller obtained by decomposing the full systems and the approximation controller obtained by eliminating \(\varepsilon_j\) from the full controller are identical under a certain condition.