Direct Adaptive Fuzzy Based Backstepping Control of Semi Strict Feedback Nonlinear Systems

In this paper, a direct adaptive fuzzy tracking control is proposed for a class of uncertain single-input single-output nonlinear semi-strict feedback systems. Based on Takagi-Sugeno type fuzzy systems, a direct adaptive fuzzy tracking controller is developed by using the backstepping approach. The main advantage of the developed method is that for an n-th order system, only one parameter is needed to be adjusted online. It is proven that, under the appropriate assumptions, the developed scheme can achieve that the output system converges to a small neighborhood of the reference signal and all the signals in the closed-loop system remain bounded. The efficacy of the proposed algorithm is investigated by an illustrative simulation example of one link robot.

Tracking Control of Uncertain High-Order Nonlinear Systems with Odd Rational Powers and the Dead-Zone Input:A Direct Fuzzy Adaptive Control Method

This work studies the tracking issue of uncertain nonlinear systems.The existence of odd rational powers,multiple unknown parameters and the dead-zone input add many difficulties for control design.During procedures of the control design,by introducing an appropriate Lyapunov function,utilizing recursive control method and the inequality technique,some appropriate intermediate auxiliary control laws are designed under the hypothesis that nonlinear terms in the system are known.When those nonlinear terms are unknown,by employing the powerful approximation ability of fuzzy systems,the intermediate auxiliary control laws are approximated recursively and used to construct the virtual control.Finally,a new fuzzy adaptive tracking controller is constructed to ensure a small tracking error and the boundedness of all states.In this paper,the overparameterization problem is significantly avoided since only two adaptive laws are adopted.Numerical and practical examples are used to verify the raised theory.