Using suboptimal state feedback controllers in certainty equivalence measurement feedback nonlinear H∞ control

First, we extend the standard information state recipe for solving nonlinear H_∞ control problems. The extra freedom in our recipe allows us to use storage functions V which are solutions to HJBI inequalities. This can have great computational advantages, since solving HJBI equations can be much harder than solving HJBI inequalities. Next, we consider the measurement feedback control of linear systems with actuator nonlinearities. We observe that in the absence of disturbance bounds that the information state and therefore the optimal state estimator is easy to compute. Also we show that the verification of an important condition called certainty equivalence is easy to compute for any smooth V. Finally, we introduce disturbance bounds and describe the effect on the information state. A measurement feedback H_∞ controller is designed to operate in the presence of bounded disturbances. For actuator nonlinearities, the controller is the same as the simple one above except for a serious constraint which adds conservatism to the design