Prescribing Closed-Loop Behavior Using Nonlinear Model Predictive Control

In this work, we address the problem of control of nonlinear systems to deliver a prescribed closed-loop behavior. In particular, the framework allows for the practitioner to first specify the nature and specifics of the desired closed-loop behavior (e.g., first order with smallest time constant, second order with no more than a certain percentage overshoot, etc.). An optimization based formulation then computes the control action to deliver the best attainable closed loop behavior. To decouple the problems of determining the best attainable behavior and tracking it as closely as possible, the optimization problem is posed and solved in two tiers. In the first tier, the focus is on determining the best closed-loop behavior attainable, subject to stability and tracking constraints. In the second tier, the inputs are tweaked to possibly improve the tracking of the optimal output trajectories given by the first tier. The efficacy of the proposed method and the various specific formulations needed are illustrated through implementation on a linear system subject to output feedback, a nonlinear CSTR subject to uncertainty and rate of change of input constraints, and a reactor separator system. The simulation results demonstrate significantly improved adherence to the prescribed performance criteria over a predictive controller representative of existing approaches.