Robust reliable sampled-data control for switched systems with application to flight control

This paper addresses the robust reliable stabilisation problem for a class of uncertain switched systems with random delays and norm bounded uncertainties. The main aim of this paper is to obtain the reliable robust sampled-data control design which involves random time delay with an appropriate gain control matrix for achieving the robust exponential stabilisation for uncertain switched system against actuator failures. In particular, the involved delays are assumed to be randomly time-varying which obeys certain mutually uncorrelated Bernoulli distributed white noise sequences. By constructing an appropriate Lyapunov–Krasovskii functional (LKF) and employing an average-dwell time approach, a new set of criteria is derived for ensuring the robust exponential stability of the closed-loop switched system. More precisely, the Schur complement and Jensen's integral inequality are used in derivation of stabilisation criteria. By considering the relationship among the random time-varying delay and its lower and upper bounds, a new set of sufficient condition is established for the existence of reliable robust sampled-data control in terms of solution to linear matrix inequalities (LMIs). Finally, an illustrative example based on the F-18 aircraft model is provided to show the effectiveness of the proposed design procedures.     

Optimization‐based adaptive sliding mode control with application to vehicle dynamics control

This paper presents the design of a new adaptive optimization‐based second‐order sliding mode control algorithm for uncertain nonlinear systems. It is designed on the basis of a second‐order sliding mode control with optimal reaching, with the aim of reducing the control effort while maintaining all the positive aspects in terms of finite‐time convergence and robustness in front of matched uncertainties. These features are beneficial to guarantee good performance in case of vehicle dynamics control, a crucial topic in the light of the increasing demand of semiautonomous and autonomous driving capabilities in commercial vehicles. The new proposal is theoretically analyzed, as well as verified relying on an extensive comparative study, carried out on a realistic simulator of a 4‐wheeled vehicle, in the case of a lateral stability control system.     

Adaptive asymptotic stabilization of switched parametric strict‐feedback systems with switched control

This paper is concerned with the problem of adaptive stabilization for a class of switched linear‐parametric nonlinear systems under arbitrary switching. The traditional adaptive backstepping control is successfully extended to switched systems from nonswitched ones where the asymptotic regulation of system state is not destroyed due to rapid or abrupt changes of switching parameters. A new switched adaptive controller is designed by exploiting a common high‐order Lyapunov function with a σ‐modification mechanism, which can reflect sufficiently the changes of plant by designing different adaptive laws and control laws for different subsystems. An explicit formula for constructing a continuous and piecewise virtual control function is given to remove the restriction where some bound functions have to be constructed blindly by designers in the existing results, which may be somewhat too strict to be applied. A numerical example is provided to validate the proposed approach.     

Switched adaptive control for a class of switched nontriangular nonlinear systems with vanishing control gains

In this paper, the adaptive control problem for a class of switched nontriangular nonlinear systems is investigated, which allows the control gains to vanish at some points. Neither the triangular structure nor the solvability of the adaptive control problem is required for each subsystem. A key point of this work is to solve the adaptive control problem of switched nontriangular nonlinear systems with vanishing control gains by the dual design of the controllers and switching signals. To this end, firstly, a hysteresis‐type control gains‐dependent switching law is designed, which makes the control gain of the active subsystem not vanish and thus the associated designed control input can enter into the active subsystem. Moreover, the designed switching law guarantees a dwell time between any adjacent switching instants, which rules out the Zeno behavior. Secondly, when the adaptive control problem of each subsystem is unsolvable, a sufficient condition ensuring the solvability of the adaptive control problem of switched nontriangular nonlinear systems is developed even if no control input can enter into subsystems at some points. Finally, the effectiveness of the proposed result is illustrated by two examples.     

网络攻击下一类非线性切换多智能体系统的安全自适应控制

针对一类控制方向未知的非线性切换多智能体系统, 本文研究了在不确定网络攻击下的安全控制问题. 网 络攻击破坏传感器真实数据, 导致系统真实信息无法获取且不能直接用于控制设计. 为此, 通过受攻击状态构建一 组新颖辅助变量来消除网络攻击造成的影响. 此外, 所研究的系统包含更一般的不确定性, 即未知控制方向, 未知常 值参数以及不确定攻击. 这些不确定性在设计过程中相互耦合. 利用Nussbaum型函数并设计自适应律补偿耦合后 的不确定性, 极大降低了系统复杂性. 通过系统性地迭代构造出共同Lyapunov函数, 提出了一套安全自适应控制方 法, 保证了受攻击系统在任意切换下达到渐近输出一致性. 最后, 数值仿真验证了该方法的有效性.     

Observer-based adaptive control of uncertain time-delay switched systems with stuck actuator faults

This paper concerns the observer-based adaptive control problem of uncertain time-delay switched systems with stuck actuator faults. Under the case where the original controller cannot stabilize the faulty system, multiple adaptive controllers are designed and a suitable switching logic is incorporated to ensure the closed-loop system stability and state tracking. New delay-independent sufficient conditions for asymptotic stability are obtained in terms of linear matrix inequalities based on piecewise Lyapunov stability theory. On the other hand, adaptive laws for on-line updating of some of the controller parameters are also designed to compensate the effect of stuck failures. Finally, simulation results for reference [1] model show that the design is feasible and efficient.     

Differential Riccati equation‐based adaptive stabilization for switched linear systems

In this paper, a novel adaptive control design is proposed to stabilize a class of switched linear systems with parametric uncertainties and disturbances. In particular, a family of differential Riccati equations that holds for the finite switching intervals are established, of which the closed‐form solutions are exploited to develop the Lyapunov function for the closed‐loop system. This Lyapunov function is imposed to be decreasing at and between two arbitrary switching instants by solving a group of matrix inequalities, based on which the adaptive controllers for switched linear system with and without disturbances are proposed, respectively. In the nondisturbed setting, asymptotic stability of the adaptive switched linear system is achieved, while the system is bounded in a mean square sense in the disturbed setting. A numerical example of flight control for F4E fighter aircraft is used to illustrate the proposed adaptive control methodology.     

Adaptive tracking control for uncertain switched systems under asynchronous switching

This paper addresses the state‐tracking model reference adaptive control problem for a class of switched systems with parametric uncertainties, where switchings between subsystems and designed adaptive controller are asynchronous. First, we establish a stability criterion for a switched reference model and convert the state‐tracking problem into the stability problem of an error switched system. Then, an adaptive law is designed, and the global practical stability of the error switched system is guaranteed under a class of switching signals characterized by a dwell‐time condition. An electrohydraulic system is given as an example to demonstrate the feasibility and effectiveness of the proposed design method. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust adaptive tracking control for a class of switched time-delay systems with application of vehicle roll dynamic control

The problems of stability and robust tracking control for a class of switched nonlinear systems with uncertain input and state delays are investigated in this study. In the presence of unknown functions and external disturbances, an adaptive fuzzy technique based on nonlinear disturbance observer is used to counteract the effects of external disturbances and approximate unknown functions. For this purpose, it is first assumed that a common Lyapunov function exists for the switched system, and then a new common Lyapunov–Krasovskii functional is built using the terms of the hypothetical common Lyapunov function. By employing this new function, the delay-dependent input-to-state stability (ISS) under an arbitrary switching signal is provided. The robust tracking control problem for this system is investigated next. Finally, to assure ISS and robust tracking performance, an adaptive control law is developed that ensures conditions of the aforementioned hypothetical common Lyapunov function. In addition, to demonstrate the efficiency of the proposed strategy, the aforesaid method is applied to a vehicle roll dynamic as well as a mass-spring system.     

Adaptive fuzzy switched control design for uncertain nonholonomic systems with input nonsmooth constraint

In this paper, a fuzzy adaptive switched control approach is proposed for a class of uncertain nonholonomic chained systems with input nonsmooth constraint. In the control design, an auxiliary dynamic system is designed to address the input nonsmooth constraint, and an adaptive switched control strategy is constructed to overcome the uncontrollability problem associated with x₀(t₀) = 0. By using fuzzy logic systems to tackle unknown nonlinear functions, a fuzzy adaptive control approach is explored based on the adaptive backstepping technique. By constructing the combination approximation technique and using Young's inequality scaling technique, the number of the online learning parameters is reduced to n and the ‘explosion of complexity’ problem is avoid. It is proved that the proposed method can guarantee that all variables of the closed-loop system converge to a small neighbourhood of zero. Two simulation examples are provided to illustrate the effectiveness of the proposed control approach.     

Full state constraints-based adaptive control for switched nonlinear pure-feedback systems

This paper investigates the problem of full state constraints-based adaptive control for a class of switched nonlinear pure-feedback systems under arbitrary switchings. First, the switched pure-feedback system is transformed into a switched strict-feedback system with non-affine terms based on the mean value theorem. Then, by exploiting the common Lyapunov function (CLF) method, the Barrier Lyapunov function method and backstepping, state feedback controllers of individual subsystems and a common Barrier Lyapunov function (CBLF) are constructed, which guarantee that all signals in the closed-loop system are global uniformly bounded under arbitrary switchings, and full state constraints are not violated. Furthermore, the tracking error can converge to a bounded compact set. Two examples, which include a single-link robot as a practical example, are provided to demonstrate the effectiveness of the proposed design method.     

Multiple Lyapunov functions‐based adaptive neural network tracking control of uncertain switched nonlinear systems

In this paper, the problem of adaptive neural network (NN) tracking control of a class of switched strict‐feedback uncertain nonlinear systems is investigated by state‐feedback, in which the solvability of the problem of adaptive NN tracking control for individual subsystems is unnecessary. A multiple Lyapunov functions (MLFs)–based adaptive NN tracking control scheme is established by exploiting backstepping and the generalized MLFs approach. Moreover, based on the proposed scheme, adaptive NN controllers of all subsystems and a state‐dependent switching law simultaneously are constructed, which guarantee that all signals of the resulting closed‐loop system are semiglobally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin. The scheme provided permits removal of a technical condition in which the adaptive NN tracking control problem for individual subsystems is solvable. Finally, the effectiveness of the design scheme proposed is shown by using two examples.     

Approximation-based adaptive fuzzy tracking control for a class of switched nonlinear pure-feedback systems

In this paper, the problem of adaptive fuzzy tracking control is investigated for switched nonlinear pure-feedback systems under arbitrary switching. By utilising mean value theorem, the considered pure-feedback systems are transformed into a class of switched nonlinear strict-feedback systems. Compared with the existing results, a priori knowledge of control directions is not required. On the other hand, differing from the existing literatures, the piecewise switched adaptive laws are designed to replace the common adaptive laws, which can reduce the conservativeness. Furthermore, the difficulties from how to deal with the unknown control directions and design common virtual control are overcome. Based on the backstepping technique and the common Lyapunov functions, an adaptive fuzzy control scheme is developed to guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded with the tracking error converging to a neighbourhood of the origin. Simulation results are provided to demonstrate the effectiveness of the proposed techniques.     

Decentralised adaptive control for a class of stochastic switched interconnected nonlinear systems

In this paper, we focus on the problem of adaptive stabilisation for a class of interconnected uncertain switched stochastic nonlinear systems. Classical adaptive and backstepping technique are employed for control synthesis. Instead of estimating the switching parameters directly, we design the adaptive controller based on the estimations of bounds on switching time-varying parameters. A smooth function is introduced to deal with the difficulties caused by unknown interactions and tuning function approach is used to circumvent the overparameter problem. It is shown that under the action of the proposed controller all the signals of the overall closed-loop systems are globally uniformly bounded in probability under arbitrary switching. Simulation results are presented to illustrate the effectiveness of the proposed approach.     

Data-driven optimal control of switched linear autonomous systems

In this paper, a novel data-driven optimal control approach of switching times is proposed for unknown continuous-time switched linear autonomous systems with a finite-horizon cost function and a prescribed switching sequence. No a priori knowledge on the system dynamics is required in this approach. First, some formulas based on the Taylor expansion are deduced to estimate the derivatives of a cost function with respect to the switching times using system state data. Then, a data-driven optimal control approach based on the gradient decent algorithm is designed, taking advantage of the derivatives to approximate the optimal switching times. Moreover, the estimation errors are analysed and proven to be bounded. Finally, simulation examples are illustrated to validate the effectiveness of the approach.     

不确定时滞切换系统的鲁棒滑模控制

该文研究了一类具有非匹配不确定性和非线性扰动的时滞切换系统的滑模控制问题.首先,针对每个子系统设计对应的时滞依赖滑模面,利用驻留时间方法,给出了由滑动模态方程组成的切换系统鲁棒渐近稳定的充分条件;然后设计了滑模控制器,使得闭环系统的状态能够到达滑模面上,产生滑动模态.最后,仿真实例说明所提出方法的有效性.     

Model reference robust adaptive control for a class of uncertain switched linear systems

In this paper, we proposed a model reference robust adaptive control approach for a class of uncertain switched linear systems, in which subsystems of the switched linear system are in control canonical form. The control architecture is composed of a switched reference system (SRS) and a switched adaptive controller (SAC). The SRS specifies the desired dynamics of the uncertain switched linear system, while the SAC makes the uncertain switched linear system dynamics track the SRS dynamics. By multiple Lyapunov functions method, we prove that the closed‐loop switched system is uniformly bounded under arbitrary switching laws, provided that a linear matrix inequality (LMI)‐based sufficient condition is satisfied. We apply the proposed approach to a typical servo‐hydraulic positioning system. The simulation results show that the proposed approach is fairly insensitive to disturbances, uncertainties and non‐smoothly varying dynamics, and performs better than a proportional‐derivative controller or a minimal controller synthesis controller. Copyright © 2011 John Wiley & Sons, Ltd.     

切换对称组合系统的稳定性

首次提出了切换对称组合系统的概念, 研究了此类系统在任意切换下渐近稳定的条件, 同时分别利用多李雅普诺夫函数方法和单李雅普诺夫函数方法, 给出使切换对称组合系统渐近稳定的切换律, 利用切换对称组合系统的结构特点, 使其切换律的设计条件得到简化.     

Asymptotic sliding mode control approach to adaptive distributed tracking problem for multi-agent nonlinear delayed systems

In this article, a sliding mode coordinated decentralised state-feedback model reference adaptive control is developed for a class of large-scale uncertain multi-agent systems with time-varying delays in the nonlinear interconnections. The design procedure is based on a combination of the model coordination concept and a sliding mode control methodology. Novel decentralised controller parameterisations that are robust to unknown information exchange delays and to external disturbances with unknown bounds are proposed. Two different controllers are designed: one with discontinuous and one with continuous control action, respectively.     

Robust asynchronous bumpless transfer for switched linear systems

This study is concerned with the asynchronous bumpless transfer (ABT) problem for a class of switched linear systems with external disturbances. Asynchronous switching or transfer implies that the transfers between sub-controllers and between sub-plants are asynchronous, and ABT is to ensure that there is no controller/plant-induced bumps or undesirable transients to the process. Specifically, the ABT process is first divided into two parts: robust performance bumpless transfer (RPBT) between sub-plants and robust control bumpless transfer (RCBT) between sub-controllers. Then, with a set of pre-given sub-plants under disturbances and corresponding sub-controllers, the RPBT and RCBT design schemes are, respectively, proposed. The designed RPBT and RCBT compensators are based on model reference adaptive sliding mode control such that the switched system can perform smooth transitions during the whole asynchronous switching process. Furthermore, by using average dwell time technique, the condition for guaranteeing the switched closed-loop system to be stable under ABT is developed. Finally, numerical simulations demonstrate the effectiveness of the proposed method.