Abstract
We first investigate the fundamental properties of the mechanical system related to the control design. Then, a new optimal robust control is proposed for mechanical systems with fuzzy uncertainty. Fuzzy set theory is used to describe the uncertainty in the mechanical system. The desirable system performance is deterministic (assuring the bottom line) as well as fuzzy (enhancing the cost consideration). The proposed control is deterministic and is not the usual if–then rule based. The resulting controlled system is uniformly bounded and uniformly ultimately bounded proved via the Lyapunov minimax approach. A performance index (the combined cost, which includes average fuzzy system performance and control effort) is proposed based on the fuzzy information. The optimal design problem associated with the control can then be solved by minimizing the performance index. The resulting control design is systematic and is able to guarantee the deterministic performance, as well as minimizing the cost. In the end, a mechanical system is chosen for demonstration.
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