期刊
IEEE TRANSACTIONS ON CYBERNETICS
卷 50, 期 5, 页码 2223-2236出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCYB.2018.2883729
关键词
Games; Uncertainty; Robust control; Cost function; Control design; Fuzzy set theory; Fuzzy systems; leader-follower; optimal design; Riccati equation; robust control; Stackelberg strategy
类别
资金
- National Natural Science Foundation of China [11572121]
- Independent Research Projects of State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body in Hunan University [71375004]
- China Scholarship Council [201606130100]
This paper investigates the robust control for dynamical systems subject to uncertainty. The uncertainty is assumed to be (possibly fast) time varying and bounded. The bound is unknown but lies within a prescribed fuzzy set (hence the fuzzy dynamical system). We propose an approach for the robust control design which is implemented in two steps. First, a class of robust controls is proposed based on tunable parameters. The proposed controls are deterministic and are not conventionally IF-THEN rules based. By the Lyapunov minimax approach, we prove that the proposed controls are able to guarantee deterministic system performance, namely, uniform boundedness and ultimate uniform boundedness. Second, optima seeking from the proposed controls is considered to improve fuzzy system performance. We formulate the optima-seeking problem as a two-player (one leader and one follower) Stackelberg game by developing two cost functions, each of which is in charge of one tunable parameter (i.e., the player). Each cost function consists of an average fuzzy system performance index and the associated player's control effort. We show that the solution of the optimal design problem (i.e., the optima of the tunable parameters), which is called the Stackelberg strategy, always exists and how to obtain the backwards-induction outcome is provided. Simulation results on the walking control of a biped robot model are presented for demonstration.
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