Direct adaptive fuzzy control of nonlinear descriptor systems

This paper deals with direct adaptive fuzzy control for uncertain affine nonlinear descriptor sys- tems. Two cases are considered: in the first one it is assumed that the control gain is known while in the second one it is an unknown-but-bounded symmetric positive definite matrix. To account for uncertainties in the system dynamics, a fuzzy system is employed to directly approximate the unknown ideal controller. The adjustable parameters of the fuzzy system are up- dated by either a Lyapunov-based adaptative law in the first case, or a gradient descent algorithm minimising a suitable quadratic cost function in the second case. Furthermore, an auxiliary compensating signal is de- signed to guarantee that the tracking error asymptot- ically vanishes in both cases. Simulation results show how the proposed methods exhibit satisfactory perfor- mance thus demonstrating their effectiveness.