### 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.
*