A variable structure control approach to the stabilization of uncertain dynamical systems
Abstract
The problem of stabilizing dynamical systems in the presence of disturbances and parameter variations is the main objective of our study. The uncertain quantities are described only in terms of bounds on their possible size; that is no statistical description is assumed. Thus, a deterministic approach was employed. Variable Structure Control theory (VSC) and high-gain feedback methodologies were adopted to examine the stabilization problem of uncertain dynamical systems. We first introduced two high-gain feedback strategies for a class of time-varying nonlinear uncertain systems. The aim of the first controller was to ensure the regulation of the output to zero. The aim of the second controller was to ensure the tracking property of the output of some given reference signal. For both control strategies, we investigated the effects of unmodeled actuator and sensor dynamics on the performance of the closed-loop systems. We then introduced a variable structure controller that guarantees the global uniform ultimate boundedness of a class of uncertain systems. One drawback of those control strategies is that they were unbounded in their nature. However, in most practical systems the designer is faced with hard bounds on the control action. Thus, in the second part of this treatise we focused our attention on the stabilization problem of uncertain systems subject to hard bounds on control action. Based on Lyapunov stability theory, we were able to find estimates of regions of stability with and without the sliding mode requirement. We also examined the effects of the uncertainties on the size and the shape of the estimates. The results found were applied to a two-link planar manipulator, and illustrated by computer simulations. Also, based on some of the theory developed, we proposed a neural controller to stabilize a class of uncertain dynamical systems.
Degree
Ph.D.
Advisors
Zak, Purdue University.
Subject Area
Electrical engineering
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