Stabilization of state‐constrained switched nonlinear systems in p‐normal form

Abstract

SUMMARYThis paper is concerned with the stabilization problem for a class of state‐constrained switched nonlinear system in p‐normal form in a domain. A key point in the backstepping design procedure is to find a common stabilizing function at each step. A barrier Lyapunov function, which grows to infinity when its arguments approach some limits, is introduced to ensure that the state constraint is not violated at any time. Bounded state feedback controllers of individual subsystems and a common Lyapunov function are explicitly constructed to asymptotically stabilize the closed‐loop system under arbitrary switchings. An example is given to show the effectiveness of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.

Practical stability of switched uncertain nonlinear systems using state-dependent switching laws

“…Given the great diversity of existing switched and impulsive systems, it is possible to find in the literature a corresponding variety of results regarding stability, most of them focused on one of the following two problems: Stability with restricted switching [1][2][3], and stability with arbitrary switching [4][5][6][7][8][9].…”

A new control method for state-constrained nonlinear switched systems with application to chemical process

“…The reason is that it is often difficult to generalize the methods for nonlinear nonswitched systems with constraints to nonlinear switched systems with constraints. Until recently, a barrier Lyapunov function (BLF) was firstly employed in [36] to deal with the tracking control problems for a class of nonlinear systems in strict feedback form with an output constraint, then [37,38] further considered the state-constrained control problems for nonlinear switched systems in strict feedback form (or in p-normal form) by adopting suitable BLFs. In addition, p-times differentiable unbounded functions (PDUFs) have also been used in [39] to handle the control problems of nonlinear switched systems in strict feedback form with output tracking error constraints.…”

Robust adaptive control for a class of semi‐strict feedback systems with state and input constraints

“…Recently, following the idea of tailoring the Lyapunov function to the requirements of the problem, the use of the barrier Lyapunov function (BLF) for the backstepping control of output/state‐constrained systems has been proposed. Up to present, the BLF‐based design has been widely used in various types of nonlinear systems, ranging from strict/semi‐strict feedback uncertain systems to pure‐feedback systems, to output feedback systems, and to many more complex systems such as time‐delay systems, stochastic systems, and switched systems . Besides theoretical contributions, the practical applications of BLF have also been discussed in different areas such as control of marine vessel, electrostatic torsional micromirror, electro‐hydraulic system, robotic manipulator .…”

“…Besides theoretical contributions, the practical applications of BLF have also been discussed in different areas such as control of marine vessel, electrostatic torsional micromirror, electro‐hydraulic system, robotic manipulator . Related works have focused on output constraints problem, whereas other works have dealt with state‐constrained systems. As demonstrated by Tee and Ge, the control design for state‐constrained systems is more difficult than that for output‐constrained systems because the virtual controllers in the backstepping procedure need to satisfy constraints themselves.…”