Fuzzy dynamical system approach for a dual-parameter hybrid-order robust control design

摘要

Robust control for uncertain dynamical systems is considered. The uncertainty is assumed to be bounded, and the fuzzy set theory is adopted to describe the bound. A new dual-parameter hybrid-order robust control design is then proposed in two steps. First, a class of robust controls is designed, taking the advantage of the flexibility in choosing the order and a design parameter. The controls are deterministic and are not IF-THEN fuzzy rules-based. Deterministic performance, including uniform boundedness and uniform ultimate boundedness for the controlled systems is guaranteed. Second, a fuzzy-set theoretic based performance index consisting of average and steady state system performance and control cost is proposed. A constrained optimization problem is formulated with the intension of minimizing the performance index. The objective of the optimization problem is to search for the optimal choice of dual parameters that minimizes the performance index. We show that the solution to the optimization problem always exists. As a result, the resulting control design achieves two concurrent goals: guaranteeing deterministic performance as well as minimizing the performance index. The theory is illustrated by an unmanned aerial vehicle (UAV) system control design. (C) 2019 Elsevier B.V. All rights reserved.