Optimal stochastic control of nonlinear systems

Abstract An algorithm is proposed for the feedback control of nonlinear systems, the observations of which are corrupted with noise of unknown statistics. The feedback loop contains a nonlinear Kalman filter, which produces sequential least‐square estimates of the state of the system, and a controller designed to minimize an instantaneous performance criterion based on the state estimates. The scheme requires the on‐line integration of n ( n + 3)/2 differential equations, where n is the number of unknown states and parameters. The scheme is applied to the feedback control of a CSTR with a first‐order exothermic reaction the temperature measurements of which are corrupted with random noise.