Adaptive cross backstepping control for a class of nonstrict feedback nonlinear systems with partial state constraints

Abstract

The tracking control problem for a class of partial state constrained nonlinear system is studied in this article. The system is divided into two semistrict feedback nonlinear subsystems, one is state constrained and the other is state free. By means of state transformation, the state constraint problem is transformed into the bounded problem of the transformed function. Compared with the barrier Lyapunov function (BLF) method, it not only solves the state constraint problem but also circumvents the feasibility check on virtual controllers. Based on the cross backstepping control, the constrained controller and unconstrained controller are designed simultaneously. It solves the coupling problem effectively in the design of cross processing control. On the other hand, dynamic surface control is used which effectively avoids “computation explosion” caused by backstepping control. The designed controllers can ensure the error signals converge to a small neighbourhood of zero and keep the asymmetric time‐varying constraints on system partial states are satisfied for all the time. Finally, simulation experiments are carried out on a hyperchaotic Rössler system to verify the efficacy of the control scheme.

Asymmetric time‐varying BLF‐based model‐free hybrid force/position control for SEA‐based 2‐DOF manipulator

“…Then, a time‐variant BLF‐based controller is proposed for an upper limb exoskeleton, 16 the tracking error was kept in a decreasing boundary by BLF to make the subject's motion trajectory more closely match the desired trajectory. And the BLF is also widely used to deal with state constraints 17 and output constraints 18 . A symmetric integral BLF‐based controller is proposed for manipulators, 19 in which the full‐state constraint on the manipulators is achieved by setting preset boundaries on position and velocity by BLF, respectively.…”

Adaptive Event-Triggered Finite-Time Tracking of Output-Constrained High-Order Nonlinear Systems with Time-Varying Powers

“…Compared with the BLF-based constrained control method, NM-based counterpart can directly deal with the original state/output constraints, and thus, the undesirable feasibility conditions in [3] can be removed. Based on these two methods, fruitful results were obtained; see [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and other papers.…”

Cross backstepping sliding mode control using integral barrier Lyapunov function for cross‐strict feedback systems

“…Also, in this paper, the proposed controller is able to reject the uncertainties, which fulfills the more general conditions, that is, the upper bound of the uncertainty in $$i{\rm{th}},\ i\ = \ 1, \ldots ,2n,( {nth} )$$ channel is made up of not only the states $${x}_1, \ldots ,{x}_i$$, but also $${x}_{i + 1}( u )$$, which is viewed as the virtual control input. Therefore, our contribution is to extend the controllers with cross backstepping approach, presented in [26], in order to reject a more general class of uncertainties.…”

“…In [26] the tracking control problem for a class of partial state constrained cross‐strict feedback non‐linear system is studied. In spite of the fact that it is compared with the current studies, matched and mismatched uncertainties are regarded in [26], but the key assumption on the uncertain terms (i.e. $${D}_i$$, $$i\ = \ 1, \ldots ,2n$$) is that they are bounded by known and positive functions of states $${x}_1, \ldots ,{x}_i$$ (i.e.…”