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.