This paper presents an optimal integral sliding mode control method based on a pseudospectral method for a class of affine systems with state and control constraints. First, a general form of an integral sliding mode is presented. Integral sliding mode control cannot deal with the problem of states and control constraints, nor can it satisfy the minimization of the cost function. The pseudospectral method has a high convergence speed and performs well in solving optimal control problems with general performance index, endpoint conditions and path constraints. In consideration of these advantages, an optimal integral sliding mode controller is determined by the pseudospectral method. Then, the stability analysis of optimal pseudospectral sliding mode method is discussed. Finally, numerical simulations show the effectiveness of the proposed method. An application example, consisting of an overhead crane system, is investigated to demonstrate the effectiveness and robustness of the proposed technique.
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