Performance regulation in discrete event and hybrid dynamical systems using IPA

This paper considers a performance regulation technique for a class of timed discrete-event and hybrid dynamical systems, aimed at an output tracking of a given setpoint reference. The regulator, designed for simplicity and efficiency of computation, consists of a variable-gain integrator that yields effective tracking despite abrupt changes to the system. The gain is computed in real time by infinitesimal perturbation analysis, and the resultant control system displays wide stability margins as well as considerable robustness to modeling and computing errors. In particular, we consider errors resulting from approximations that are made to the controller's gains in order to speed up their computations. Previous analysis was carried out under assumptions of differentiable sample-performance functions which serve to approximate a steady-state (expected-valued) function. We dispense with these two assumptions which often are unrealistic in time-varying systems. The paper proves convergence of the regulation technique and demonstrates the results on simulation examples.