Nonlinear robust H∞ control.

A new theory is proposed for the full-information finite and infinite horizontime
robust H∞ control that is equivalently effective for the regulation and/or tracking
problems of the general class of time-varying nonlinear systems under the presence of
exogenous disturbance inputs. The theory employs the sequence of linear-quadratic and
time-varying approximations, that were recently introduced in the optimal control
framework, to transform the nonlinear H∞ control problem into a sequence of linearquadratic
robust H∞ control problems by using well-known results from the existing
Riccati-based theory of the maturing classical linear robust control. The proposed
method, as in the optimal control case, requires solving an approximating sequence of
Riccati equations (ASRE), to find linear time-varying feedback controllers for such
disturbed nonlinear systems while employing classical methods. Under very mild
conditions of local Lipschitz continuity, these iterative sequences of solutions are
known to converge to the unique viscosity solution of the Hamilton-lacobi-Bellman
partial differential equation of the original nonlinear optimal control problem in the
weak form (Cimen, 2003); and should hold for the robust control problems herein. The
theory is analytically illustrated by directly applying it to some sophisticated nonlinear
dynamical models of practical real-world applications. Under a r -iteration sense, such
a theory gives the control engineer and designer more transparent control requirements
to be incorporated a priori to fine-tune between robustness and optimality needs. It is
believed, however, that the automatic state-regulation robust ASRE feedback control
systems and techniques provided in this thesis yield very effective control actions in
theory, in view of its computational simplicity and its validation by means of classical
numerical techniques, and can straightforwardly be implemented in practice as the
feedback controller is constrained to be linear with respect to its inputs.