Journal
IEEE TRANSACTIONS ON CYBERNETICS
Volume 52, Issue 7, Pages 7151-7163Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCYB.2020.3035414
Keywords
Uncertainty; Games; Robust control; Mechanical systems; Game theory; Cost function; Fuzzy set theory; Cooperative game theory; fuzzy set theory; mechanical systems; optimal design; robust control; uncertainty
Categories
Funding
- National Natural Science Foundation of China [52005302]
- Elite Plan [0104060540418]
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This study uses fuzzy set theory to describe uncertain dynamical systems and proposes a robust control method. By using cooperative game and performance indices, the optimal solution can be found while ensuring control performance.
There is uncertainty in the system, and we consider that uncertainty is (possibly fast) time varying, but with definite bound. Fuzzy set theory is used to describe the inexact boundary and then the problem of robust control of uncertain dynamical systems is studied. Based on two adjustable design parameters, a robust control method for general mechanical systems is proposed. The control is deterministic, not the conventional IF-THEN rule based. By using the Lyapunov minimax approach, it is proved that the proposed control can guarantee system performance to be uniformly bounded and uniformly ultimately bounded. In order to find the optimal solution in the prescribed range, a two-player cooperative game is used. To reduce costs while ensuring control performance, two performance indices are developed, each of which is controlled by an adjustable parameter (i.e., player). Both necessary and sufficient conditions for Pareto-optimality are established. Using these conditions, the Pareto-optimal solution can be obtained. The effectiveness of the control design is demonstrated by the simulation of the two-body pendulum.
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