Abstract:

We consider the singularly perturbed $H^\infty$-optimal control problem under perfect state measurements, for both finite and infinite horizons. We get the exact decomposition of the full-order Riccati equations to the reduced-order pure-slow and pure-fast equations. As a result, the $H^\infty$-optimum performance and suboptimal controllers can be exactly determined from these reduced-order equations. The suggested decomposition allows the development of new effective algorithms of high-order accuracy.