On controlling systems with state-variable constraints

State variable constraints may be regions into which the state is forbidden to penetrate or may be physical (“limit stops”). The state-dependent algebraic Riccati equation (SDARE) method can be used to design control systems with constraints of either type. In the former case, a severe penalty function is included in the performance criterion; in the latter case, the physical constraint is modeled by a severely nonlinear spring. Performance is illustrated by an inverted pendulum and the effectiveness of the modeling technique and the SDARE method is demonstrated