Predefined‐time backstepping control for a nonlinear strict‐feedback system

Abstract

Two novel predefined‐time control algorithms for a nonlinear strict‐feedback system are proposed in this short communication. It is required that the upper bound of system convergence time is exactly a positive constant parameter in each algorithm, and it can be selected arbitrarily by users. Composite state tracking errors are introduced to the backstepping design process by using some novel smooth time‐varying tuning functions. In order to address the problem of explosion of complexity in the first algorithm, the second algorithm extends the predefined‐time control strategy to a dynamic surface control (DSC) case. Furthermore, the proposed predefined‐time DSC algorithm can guarantee global stability rather than semi‐global stability for the closed‐loop system compared with traditional DSC algorithms. Simulation results show the effectiveness of the two control schemes.

Terminal time regulator‐based exact‐time sliding mode control for uncertain nonlinear systems

“…Remark Compared to other existing predefined‐time controllers that can eliminate settling time overestimation, 24,33 our article proposes a new systematic design method from the perspective of predefined‐time convergent sliding function. The advantage of this method lies in that one can easily accomplish the control design by following a similar design procedure of conventional sliding mode control.…”

“…Remark 3. Compared to other existing predefined-time controllers that can eliminate settling time overestimation, 24,33 our article proposes a new systematic design method from the perspective of predefined-time convergent sliding function.…”

“…The control signal of the proposed control is bounded. In fact, on each sliding surface s i+1 (t) = 0 (i = 1, 2, ..., n − 1) in (31), one can obtain y i (t) = 0, ∀t ≥ ∑ n−i j=1 t f j as given by (33). In addition, for 0 ≤ t < ∑ n−i j=1 t f j , the solution of s i+1 (t) = 0, that is, s i (t), as well as its derivative ̇si (t) is continuously converging to zero for t → ∑ n−i j=1 t f j according to the properties of S-TTR.…”

“…However, only free‐will weak arbitrary time convergence is proved for both first‐order and higher‐order systems. For improvement, in Reference 33, a time‐varying tuning function is used to realize globally predefined‐time stability but it can be quite complex to determine that function especially for a high‐order system. Polynomial‐type sliding mode function is developed, wherein if the sliding mode is retained by an appropriate control input, the system will reach the origin at the predefined terminal time point 34,35 .…”

Adaptive predefined‐time observer design for generalized strict‐feedback second‐order systems under perturbations

“…Recently, predefined‐time stability (PTS) has emerged as an upgrade of finite‐time stability and fixed‐time stability (FxTS) due to its concise and explicit relationship between the UBST and design parameters, 36 which endows PTS with high practical application value under time‐critical scenarios. Fruitful efforts have been put into controller designs with PTS, such as References 36‐39. However, attempts to incorporate PTS into observing states and perturbations are rare.…”