State‐constrained robust stabilisation for a class of high‐order switched non‐linear systems

Abstract

This study deals with the problem of robust stabilisation for a class of state-constrained high-order uncertain switched non-linear systems in lower triangular form. Bounded state-feedback controllers are designed to assure that asymptotic stabilisation is achieved in a domain without violation of the state constraint, and all closed-loop signals are bounded, when an appropriate requirement on the initial condition is imposed. Simulation results are provided to show the efficiency of the developed method. IntroductionDuring the past few decades, switched systems have received considerable attention [1][2][3][4][5][6][7][8]. The motivation for the study of such systems stems from two aspects. On the one hand, so many realworld systems can be modelled as switched systems, such as chemical systems, power systems and communication networks [9][10][11][12][13][14]. On the other hand, the switching control strategy has been widely used in various advanced controls, such as in [15][16][17][18][19][20]. When the switching law has no given mode (or is arbitrary), one way to investigate the stability and stabilisation problems is to find a common Lyapunov function (CLF) for all the subsystems. However, finding a CLF for a family of subsystems is still an open problem, even though some progress has been made [21][22][23][24]. Backstepping design technique is a power tool for constructing stabilising controller for non-linear systems in lower triangular form, and many significant developments have been achieved based on this technique [25][26][27][28][29][30]. This design method is, of course, expected to be useful for stabilising a switched non-linear system. However, according to the standard backstepping procedure, backstepping cannot be directly extended to the switched non-linear system in lower triangular form because of the different coordinate transformations for different subsystems [31,32]. Furthermore, the so-called adding a power integrator backstepping design method is proposed in [33][34][35][36], which is used in the controller design for high-order non-linear systems. Nevertheless, there exist only a few results on high-order switched non-linear system in lower triangular form [37,38]. In addition, it is worth pointing out that many systems in practice have states/output constraints. Therefore the constrained control problem of switched systems is of great significance. Unfortunately, these constraints are not widespreadly taken into account in the aforementioned papers. A few exceptions are [39], in which tracking control for switched lower triangular systems with time-varying output constraints is achieved, and [40], which proposed a control design method for a class of switched non-linear systems with full state constraints.On the other hand, there exist several techniques to solve the constrained control problem for linear systems and non-linear systems. In the literature, most of the results are based on the notions of set invariance and admissible set control [41,42]. Model predictive control that repre...

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