Output regulation for discrete-time nonlinear stochastic optimal control problems with model-reality differences

In this paper, we propose an output regulation approach, whichis based on principle of model-reality differences, to obtain the optimal outputmeasurement of a discrete-time nonlinear stochastic optimal control problem.In our approach, a model-based optimal control problem with adding the ad-justable parameters is considered. We aim to regulate the optimal outputtrajectory of the model used as closely as possible to the output measurementof the original optimal control problem. In doing so, an expanded optimalcontrol problem is introduced, where system optimization and parameter es-timation are integrated. During the computation procedure, the differencesbetween the real plant and the model used are measured repeatedly. In sucha way, the optimal solution of the model is updated. At the end of iteration,the converged solution approaches closely to the true optimal solution of theoriginal optimal control problem in spite of model-reality differences. It is im-portant to notice that the resulting algorithm could give the output residualthat is superior to those obtained from Kalman filtering theory. The accuracyof the output regulation is therefore highly recommended. For illustration, acontinuous stirred-tank reactor problem is studied. The results obtained showthe effciency of the approach proposed