Optimization and Systems Theory Seminar
Thursday, April 5, 2001, 14.00-15.00, Room 3721, Lindstedtsvägen 25

Professor Alberto Isidori
Department of Informatics and Systems
University of Rome
Rome, Italy
E-mail: isidori@giannutri.caspur.it

Nonlinear output regulation with adaptive internal model

Internal-model based control schemes efficiently address the problem of tracking/rejecting families of exogenous inputs, all those that can be thought as generated by a fixed autonomous finite-dimensional dynamical system (the initial condition of which identifies the actual, unknown, exogenous input affecting the plant). In this sense, they generalize the classical way in which integral-control based schemes cope with constant but unknown disturbances. However, the main limitation of these schemes is that a precise model of the system that generates all exogenous inputs must be available, to be replicated in the control law. This limitation is not sensed in a problem of set point control, where the uncertain exogenous input is constant and thus obeys a trivial, parameter independent, differential equation but becomes immediately evident in the problem of rejecting e.g. a sinusoidal disturbance of unknown amplitude and phase. An internal-model based controller is able to cope with uncertainties on amplitude and phase of the exogenous sinusoid, but the frequency at which the internal-model oscillates must exactly match the frequency of the exogenous sinusoid: any mismatch in such frequencies results in a nonzero steady-state error.

Motivated by the interest in removing such a limitation, we address the problem of designing an internal-model based control scheme in which the ``natural frequencies" of the internal model are automatically tuned so as to match those of an exosystem which is totally unknown (except for an upper bound on its dimension). In this context, we provide a control scheme that is able to successfully address the problem of asymptotically tracking/rejecting any family of exogenous inputs generated by some (fixed dimensional, but otherwise completely unknown) autonomous dynamical system, for a significant class of nonlinear systems, in the presence of possibly large parameter uncertainties.

Calendar of seminars
Last update: March 21, 2001 by Anders Forsgren, anders.forsgren@math.kth.se.