In this paper, we propose a unit vector control law by output feedback to solve the problem of global exact output tracking for a class of multivariable uncertain plants with nonlinear disturbances. In order to face the nonuniform arbitrary relative degree obstacle, we extend our earlier estimation scheme based on global finite-time differentiators using dynamic gains to a multivariable architecture. A diagonally stable condition over the system high-frequency gain (HFG) matrix has to be assumed. Preserving the simplicity of its mono variable framework, variable gain super-twisting algorithm (STA) is employed to obtain the robust and exact multivariable differentiator. Moreover, state-norm observers for the unmeasured state variables are constructed to upper bound the disturbances as well as to update the differentiator gains, being both state dependent. Uniform global exponential stability and ultimate exact tracking are proved. As an alternative to chattering alleviation, we appeal to the Emelyanov's concept of binary control in order to obtain a continuous control signal replacing the unit vector function in the controller by a high-gain gradient adaptive law with parameter projection. As shown in the existing literature for mono variable systems, the proposed multiparameter binary-adaptive formulation tends to the unit vector control as the adaptation gain increases to infinity, also smoothing the transition from adaptive to sliding mode control. A numerical example is portrayed to illustrate the potentialities of the developed multivariable techniques.
This paper proposes a new adaptive sliding mode control approach via output feedback for a class of nonlinear systems. The sliding-mode based controller can deal with parametric uncertainties and (un)matched disturbances with unknown upper bounds. Finite-time convergence of the tracking error to a predefined neighborhood of the origin of the closed-loop system is proved with guaranteed transient and steady-state performance. Basically, the novelty of our result lies on combining two important adaptation tools: monitoring and barrier functions. The adaptation process is divided into two stages, where an appropriate monitoring function allows for the specification of performance criteria during the transient phase, while the barrier function ultimately confines the tracking error within a small residual set in steady state. Simulation results including an application to Anti-lock Braking System illustrate the advantages of the proposed adaptive control strategy.
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