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Adaptive Fuzzy Tracking Control of Uncertain Nonlinear Systems Subject to Actuator Dead Zone With Piecewise Time-Varying Parameters

The application of most existing adaptive dead-zone compensation schemes is limited to the situation where the dead-zone parameters remain unchanged during the system operation. If this is not the case in practice, the closed-loop system stability may no longer be ensured with those schemes because the negative-definite or negative semi-definite property of Lyapunov function may not be satisfied when the dead-zone parameters change in real time. Also, the Lyapunov function is not differentiable from the view on the whole time when the dead-zone parameters change piecewise. Motivated by the observations, in this paper we investigate the output tracking problem for uncertain nonlinear systems in the presence of actuator dead-zone nonlinearity with piecewise time-varying parameters. Technically, by using the projection technique and a modified tuning functions approach, a new adaptive fuzzy control design and a new piecewise Lyapunov function analysis are then developed. It is established that in addition to the system stability, a better quantification of the system performance is achieved in the sense that the tracking error will be controlled within prescribed bounds regardless of the abrupt jumps of the parameters. Finally, simulation results demonstrate the obtained theoretical findings.