Adaptive unit vector control of multivariable systems using monitoring functions

Abstract

Summary An adaptive sliding‐mode unit vector control approach based on monitoring functions to deal with disturbances of unknown bounds is proposed. An uncertain multivariable linear system is considered with a quite general class of nonsmooth disturbances. Global stabilization/tracking is demonstrated using either state or output feedback. The proposed adaptation method makes the control gain less conservative, becoming large enough when the disturbance grows and becoming smaller when it decreases, leading to reduced chattering effects. In contrast to previous methods, the new switching scheme is able to guarantee a prespecified transient time, maximum overshoot, and steady‐state error for multivariable uncertain plants. The proposed technique is applied to the trajectory tracking control of a surface vessel subjected to ocean currents, wind, and waves. Simulations are presented to show the performance of the new adaptation scheme in this adverse scenario of possibly growing, temporarily large, or vanishing exogenous disturbances.

Robust Output-Feedback Control in a Dynamic Positioning System via High Order Sliding Modes: Theoretical Framework and Experimental Evaluation

“…In which ξ w = ξ 4 ξ 5 ξ 6 T is the first-order wave motion component. Assumption 6: The only directly measured state is the vessel 2D position and attitude composed of both the lowfrequency and wave-frequency motions (11). The filter estimates other system states required for control feedback.…”

“…In [9] and in [10], numerical and experimental results for SMCs with notch wave filtering have been produced and discussed. An approach for multivariable SMC control of a Surface Vessel was presented in [11], not addressing, however, the state estimation problem and high-frequency wave filtering. In [12], the SM controller with feedback from a Nonlinear Passive Observer was proposed.…”

Event‐triggered adaptive finite‐time prescribed performance tracking control for uncertain nonlinear systems

“…The tracking control for nonlinear systems has attracted many scholars to engage in both theoretical and application research. [1][2][3][4] Especially, after backstepping method, one of the most popular controller design methods, was proposed, 5 many control methods were combined to achieve tracking control for nonlinear systems, such as H ∞ control, adaptive control, sliding mode, dynamic surface, fuzzy/neural approximation, and so on. There have been many relevant achievements in this area for different types of nonlinear systems, such as switched systems, multiple input multiple output (MIMO) systems, stochastic systems, discrete-time systems, time-varying systems, and fractional systems.…”

“…The tracking control for nonlinear systems has attracted many scholars to engage in both theoretical and application research 1‐4 . Especially, after backstepping method, one of the most popular controller design methods, was proposed, 5 many control methods were combined to achieve tracking control for nonlinear systems, such as H ∞ control, adaptive control, sliding mode, dynamic surface, fuzzy/neural approximation, and so on.…”

Controle Vetorial Unitário Adaptativo via Funções de Barreira e Monitoração

“…No entanto, o conjunto residual não podia ser completamente caracterizado. Esse problema foi superado em Hsu et al (2019). Além disso, loc.…”