Abstract:
This thesis proposes a framework that provides suboptimal control laws for a class of
minimum-phase nonlinear systems. This class includes systems whose state dynamics are an
algebraic sum of their linear and nonlinear sub-dynamics. We propose a systematic method
of designing a robust and optimal control law which essentially consists of two components -
a linear and a nonlinear. It is shown that the proposed control scheme achieves stabilization
while providing suboptimality for the class of systems under consideration. Furthermore, the
framework provides for a mechanism which is suitable for handling tracking and regulation
problems for the class of minimum-phase nonlinear systems by using the Internal Model
Principle.
A striking feature of the proposed framework is the flexibility of starting with synthesizing
a Linear-Quadratic-Regulator for linear sub-dynamics of the system and then including a
nonlinear control component that stabilizes the nonlinear sub-dynamics of the system. The
flexibility offered by the proposed framework is applied firstly to a general class of linear
parameter-varying and linear time-varying systems. We extend the flexibility obtained for
these two systems to the class of minimum-phase nonlinear systems which are decomposable
through existence of an appropriate transformation into their linear and nonlinear subdynamics.
Moreover, we also propose a simplified approach to obtain an approximate yet
practical solution to the nonlinear optimal control problem by replacing the requirement
of solving Hamilton-Jacobi-Bellman equations with that of the Riccati partial differential
equations, and then synthesizing the nonlinear component of the control law to achieve robust
and suboptimal stabilization.
