A Hierarchical Control Design Framework for Fuzzy Mechanical Systems With High-Order Uncertainty Bound

Abstract

Control design and performance enhancement for uncertain mechanical systems are pursued in this article. Uncertainty in a physical system is often inevitable in practice, which is best characterized by its possible bound. Mechanical systems with uncertain nonlinearity are considered. Furthermore, even the knowledge of the coefficients in the bound is unknown, which can only be described by its fuzzy association to a set. In controlling the system, there is a hierarchical performance requirement. The first level is deterministic, including uniform boundedness and uniform ultimate boundedness. This is the part the system must meet regardless of the actual value of the uncertainty. The second level is optimality, in terms of minimizing a fuzzy-theoretic performance index. We propose a novel control design with a tunable design parameter. The control guarantees the first-level performance when the design parameter falls in a range. We, then, take the advantage of this range flexibility to address the second-level requirement. The optimal choice of the design parameter can be made by solving an optimization problem. This problem is completely solved. Both the analytic (i.e., closed form) expressions of the design parameter and the resulting minimum cost are given. As a result, we accomplish a two-level control design task.