Fallback Approximated Constrained Optimal Output Feedback Control under Variable Parameters

Safety critical control problems often require the availability of fallback strategies, in case of failure of the main control scheme, sensors or actuators. Those controllers should provide safe operation or emergency shut down of the system under all circumstance. They should also be able to operate subject to reduced information, and limited computation power. We propose a verifiable and efficiently implementable output feedback controller based on an approximated explicit solution of a constrained optimal control problem. The control law is derived by solving an infinite horizon optimal control problem utilizing Al'brekht's Method to obtain power series expansions. The feedback control law is a polynomial in terms of the measurements and estimated parameters, thus the online evaluation can be done efficiently. We provide conditions for convergence and existence of the optimal control law and the corresponding value function. Simulation results for the control of a non-linear quadcopter example show the effectiveness of the proposed strategy.