Flexible Structure Control of Unmatched Uncertain Nonlinear Systems via Passivity-based Sliding Mode Technique

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This paper considers the problem of passivity-based sliding mode control of uncertain nonlinear systems. For this purpose, two cases are studied. In the first case, it is assumed that only the matched uncertainties exist in the system dynamics. In this case, the passivity-based control approach is used to design an appropriate sliding manifold with a flexible structure such that the asymptotic stability of the reduced-order model (i.e., the motion equations on the proposed sliding manifold) is guaranteed. In the second case, both matched and unmatched uncertainties are considered in the system dynamics and thus the reduced-order model has uncertain terms. In this case, the modified Lyapunov redesign technique is combined with the passivity-based control method for design of robust sliding manifold. The function that is basically used in the classical Lyapunov redesign method is the signum function, which is not differentiable. Since, for evaluating the derivative of the sliding manifold its equation must be differentiable, a new additional continuous control term is suggested. In addition, the robust practical stabilization of the motion equations is guaranteed without considering any limitation on the upper bound of the unmatched uncertainties. Finally, computer simulations are performed for a practical example (flexible spacecraft) and also a numerical example to demonstrate the ability of the proposed controller in robust stabilization of uncertain nonlinear dynamical systems.