Nonlinear control of constrained linear systems: regulation and tracking

An optimization-based procedure is used to design nonlinear controllers for linear dynamical systems subject to hard constraints on controls and states. The controller stabilizes the system and regulates to the origin or tracks the output of an exosystem which generates a reference signal. Firstly, a linear controller which maintains zero tracking error is determined. Secondly, a finite set of initial states is selected. For each initial state a control, which steers the combined state to the zero error manifold in a finite time is determined using numerical optimization. A nonlinear feedback control law is then constructed using the solutions to this finite set of open-loop optimal control problems. The solution method permits incremental improvement to the control law in those regions of state space where simulation reveals improvement is desirable