Aerospace Engineering

The author would like to suggest two further research topics: one is an extension of the study presented in this chapter toward the robust control design for TS-type fuzzy systems with system parametric uncertainties and external disturbances. The problem is to incorporate these robustness issues into the optimal control design approach, and the key to solve this problem may be found in many literatures addressing the robust control approaches such as loop-transfer-recovery approach, guaranteed-cost approach, stochastic approach, and state-estimation approach. However, the difficulty of combining these approaches with the optimal control design method comes from the fact that these approaches are mainly for linear systems. Therefore, the extension of these approaches to nonlinear dynamic systems may be requisite. The other is to develop the optimal control design of TS-type fuzzy systems for tracking problems. Tracking problems assume that the equilibrium point is not the zero state. In linear dynamic systems, tracking problems can be reduced to regulation problems under the assumption that the desired state is known or can be reduced to disturbance-rejection problems under the assumption that the disturbance signal is known. However, in many cases, the desired state or the disturbance signal is not known. Thus, in such cases, some alternatives such as minimax approach and proportional-integral control may be needed. The minimax approach is for the worst-case design such that the disturbance signal maximizes the same performance index that the control input minimizes. And the proportional-integral control can be used to reject the constant disturbances. In the sequel, the minimax approach and the proportional-integral control may provide the solution to the tracking problem of TS-type fuzzy systems.

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