Constrained fast finite‐time exact tracking for disturbed nonlinear systems

Abstract

This article investigates the fast finite‐time exact tracking problem for nonlinear systems with time‐varying disturbances. A new composite controller with a finite‐time disturbance observer is proposed to achieve fast finite‐time exact tracking. Furthermore, a new time‐varying barrier power integrator technique is developed to design the controller. This can ensure not only asymmetric/symmetric time‐varying full‐state constraints but also singular‐free continuous control effort. To reduce the complexity of computation, fuzzy logic systems are adopted to approximate complex nonlinearities. Finally, an example of single‐link robot systems subject to time‐varying disturbances is presented to show the validity of the proposed method.

Logic‐based switching finite‐time stabilization with applications in mechatronic systems

“…Finite time stabilization means that by designing a proper feedback controller, all the states of the closed loop systems will become exact zero after finite time. [1][2][3][4][5] However, for asymptotic stabilization, the states will converge to zero in an infinite time. Lots of works [6][7][8][9] have shown that finite time control has some promising features in contrast with asymptotic control.…”

“…Finite time stabilization problem has attracted increasing attention in the past few years. Finite time stabilization means that by designing a proper feedback controller, all the states of the closed loop systems will become exact zero after finite time 1‐5 . However, for asymptotic stabilization, the states will converge to zero in an infinite time.…”

Finite‐time non‐smooth stabilization of cascade output‐constrained switched systems

“…Because finite-time control strategy, which can force the control system to achieve an ideal goal in finite time, has some excellent characteristics such as fast convergence, superior robustness, and disturbance rejection, the research on finite-time stabilization of nonlinear systems has drawn broad and sustained attentions. [1][2][3][4][5][6][7][8][9][10] Numerous works have been conducted on finite-time stability analysis and control strategies. In Reference 2, finite-time stability of continuous but non-Lipschitzian autonomous systems has been investigated and the relationship between regularity properties of Lyapunov function and those of the settling-time function are exposed.…”

“…Because finite‐time control strategy, which can force the control system to achieve an ideal goal in finite time, has some excellent characteristics such as fast convergence, superior robustness, and disturbance rejection, the research on finite‐time stabilization of nonlinear systems has drawn broad and sustained attentions 1‐10 . Numerous works have been conducted on finite‐time stability analysis and control strategies.…”

“…The homogeneity and finite‐time stability of a homogeneous system are linked such that a conclusion that it is finite‐time stable if and only if it is asymptotically stable and has a negative homogeneity degree has been drawn in Reference 3. And then, finite‐time control of various nonlinear systems, such as state/output feedback stabilization, 4,5 sliding mode control, 7 adaptive control, 8 and constrained exact tracking, 10 has been extensively investigated.…”