不确定非线性系统自适应镇定的充要条件

研究了一类相当广泛的包含未知参数的非线性控制系统的自适应鲁棒控制问题,这类系统的标称系统包含一些非最小相位非线性系统和一些不存在相对阶的非线性系统．其未知定常参数是线性的．在一定假设条件下,对该类系统给出了存在自适应控制器的充要条件,并采用backstepping方法给出了控制器的设计步骤．所得主要结论没有用到增长性假设、最小相位假设和相对阶的假设．同时,还给出了不存在相对阶及非最小相位的非线性系统的例子,对于后者给出了控制器的设计过程．     

A moving switching sequence approach for nonlinear model predictive control of switched systems with state‐dependent switches and state jumps

In this paper, we propose an approach for real‐time implementation of nonlinear model predictive control (NMPC) for switched systems with state‐dependent switches called the moving switching sequence approach. In this approach, the switching sequence on the horizon moves to the present time at each time as well as the optimal state trajectory and the optimal control input on the horizon. We assume that the switching sequence is basically invariant until the first predicted switching time reaches the current time or a new switch enters the horizon. This assumption is reasonable in NMPC for systems with state‐dependent switches and reduces computational cost significantly compared with the direct optimization of the switching sequence all over the horizon. We update the switching sequence by checking whether an additional switch occurs or not at the last interval of the present switching sequence and whether the actual switch occurs or not between the current time and the next sampling time. We propose an algorithm consisting of two parts: (1) the local optimization of the control input and switching instants by solving the two‐point boundary‐value problem for the whole horizon under a given switching sequence and (2) the detection of an additional switch and the reconstruction of the solution taking into account the additional switch. We demonstrate the effectiveness of the proposed method through numerical simulations of a compass‐like biped walking robot, which contains state‐dependent switches and state jumps.     

Weighted control with ‐stability constraint for switched positive linear systems

This paper is concerned with the problem of control with ‐stability constraint for a class of switched positive linear systems. The ‐stability means that all the poles of each subsystem of the resultant closed‐loop system belong to a prescribed disk in the complex plane. A sufficient condition is derived for the existence of a set of state‐feedback controllers, which guarantees that the closed‐loop system is not only positive and exponentially stable with each subsystem ‐stable but also has a weighted performance for a class of switching signals with average dwell time greater than a certain positive constant. Both continuous‐time and discrete‐time cases are considered, and all of the obtained conditions are formulated in terms of linear matrix inequalities, whose solution also yields the desired controller gains and the corresponding minimal average dwell time. Numerical examples are given to illustrate the effectiveness of the presented approach.Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

切换系统不变集的输出反馈镇定

利用一个非负函数V (x), 推广了小时间状态模可观测和大时间状态模可观测的定义, 提出了小时间V (x)可观测和大时间V (x)可观测的概念. 利用V (x)可观测的概念, 讨论了子系统无源的切换系统不变集的有界输出反馈镇定及动态输出反馈镇定. 利用多Lyapunov函数证明了闭环系统渐近稳定. 仿真例子验证了文中结论正确性.     

具有Neumann边界的分布参数切换系统的容错控制

本文研究了一类具有Neumann边界条件的分布参数切换系统的容错控制问题.当执行器失效或部分失效时,运用Lyapunov函数法和Green公式,获得了闭环切换系统混杂状态反馈容错控制器存在的充分条件.然后运用线性矩阵不等式将容错控制器设计问题转化为一组线性矩阵不等式求可行解的问题,因而可以借助MATLAB中线性矩阵不等式工具箱来完成.同时,运用Poincare不等式减少控制系统设计的保守性.最后通过数值算例,验证所提出设计方法的有效性.     

Full‐complexity polytopic robust control invariant sets for uncertain linear discrete‐time systems

This paper presents an algorithm for the computation of full‐complexity polytopic robust control invariant (RCI) sets, and the corresponding linear state‐feedback control law. The proposed scheme can be applied for linear discrete‐time systems subject to additive disturbances and structured norm‐bounded or polytopic uncertainties. Output, initial condition, and performance constraints are considered. Arbitrary complexity of the invariant polytope is allowed to enable less conservative inner/outer approximations to the RCI sets whereas the RCI set is assumed to be symmetric around the origin. The nonlinearities associated with the computation of such an RCI set structure are overcome through the application of Farkas' theorem and a corollary of the elimination lemma to obtain an initial polytopic RCI set, which is guaranteed to exist under certain conditions. A Newton‐like update, which is recursively feasible, is then proposed to yield desirable large/small volume RCI sets.     

Reduced order model predictive control for constrained discrete‐time linear systems

A reduced order model predictive control (MPC) is discussed for constrained discrete‐time linear systems. By employing a decomposition method for finite‐horizon linear systems, an MPC law is obtained from a reduced order optimization problem. The decomposition enables us to construct pairs of initial state and control sequence which have large influence on system responses, and it also characterizes the standard LQ control. The MPC law is obtained based on a combination of the LQ control and dominant input sequences over the prediction horizon. The proposed MPC method is illustrated with numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.     

Necessary and sufficient conditions for regional stabilisability of generic switched linear systems with a pair of planar subsystems

In this article, the regional stabilisability issues of a pair of planar LTI systems are investigated through the geometrical approach, and easily verifiable necessary and sufficient conditions are derived. The main idea of the article is to characterise the best case switching signals based upon the variations of the constants of the integration of the subsystems. The conditions are generic as all possible combinations of the subsystem dynamics are considered.     

Robust control and fault detection for continuous‐time switched systems subject to a dwell time constraint

This paper is concerned with the simultaneous robust control and fault detection problem for continuous‐time switched systems subject to a dwell time constraint. To meet the control and detection objectives under the constraint, the controller/detectors matching different time intervals are first constructed in an output feedback framework. A state‐dependent switching law that obeys the dwell time constraint is then designed such that the closed‐loop switched system is asymptotically stable and also with the robust and detection performance. Further, the proposed switching law is dependent only on the partial measurable states of the closed‐loop system, which is applicable when the states of system mode are fully unavailable. Thus, our result extends the existing ones in state‐dependent switching and state‐feedback frameworks. Finally, a numerical example is given to illustrate the effectiveness of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

切换非线性系统的分布式模型预测控制

针对一类具有预先指定切换序列的切换非线性系统,研究了具有通信信道干扰和时滞测量的分布式模型预测控制问题.在每个子系统都存在镇定控制器的假设下,利用基于Lyapunov函数的模型预测控制器设计了分布式模型预测控制器,并给出了闭环切换非线性系统最终有界的充分条件.最后,通过仿真结果表明了分布式模型预测控制策略的有效性.     

Delay‐dependent robust stability analysis for switched time‐delay systems with polytopic uncertainties

In this paper, sufficient conditions are provided for the stability of switched retarded and neutral time‐delay systems with polytopic‐type uncertainties. It is assumed that the delay in the system dynamics is time‐varying and bounded. Parameter‐dependent Lyapunov functionals are employed to obtain criteria for the exponential stability of the system in the form of linear matrix inequality (LMI). Free‐weighting matrices are then provided to express the relationship between the system variables and the terms in the Leibniz–Newton formula. Numerical examples are presented to show the effectiveness of the results. Copyright © 2014 John Wiley & Sons, Ltd.     

LMI-based model predictive control for switched nonlinear systems

This paper proposes an LMI approach to model predictive control of nonlinear systems with switching between multiple modes. In this approach, at each mode, the nonlinear system is divided to a linearized model in addition to a nonlinear term. A sum of squares (SOS) optimization problem is presented to find a quadratic bound for the nonlinear part. The stability condition of the switching system is obtained by using a discrete Lyapunov function and then the sufficient state feedback control law is achieved so that guarantees the stability of the system and also minimizes an infinite prediction horizon performance index. Moreover, two other LMI optimization problems are solved at each mode in order to find the maximum area region of convergence of the nonlinear system inscribed in the region of stability. The performance and effectiveness of the proposed MPC approach are illustrated by two case studies.     

Funnel‐like prescribed tracking control for uncertain nonlinear stochastic switched systems

This paper deals with the funnel‐like prescribed tracking control problem for a class of uncertain nonlinear stochastic switched systems. An improved performance technique is developed to restrain the fluctuation at the moment of switches and a new algorithm is proposed to address the funnel‐like prescribed tracking problem. First, a dynamic gain‐based switched K‐filter is constructed to estimate the unmeasured state information of the switched system. Subsequently, the performance technique is applied to prescribe output tracking error and restrain fluctuations of the system. Thereafter, the dynamic output feedback switched controller is designed by the use of the backstepping method. Moreover, based on the Lyapunov stability theory, it is proved strictly that all signals of the resulting closed‐loop system are bounded in probability if the switching signal satisfies the average dwell time. Finally, a numerical simulation is presented to illustrate the effectiveness of the proposed theoretical results.     

Tube‐based robust nonlinear model predictive control

This paper extends tube‐based model predictive control of linear systems to achieve robust control of nonlinear systems subject to additive disturbances. A central or reference trajectory is determined by solving a nominal optimal control problem. The local linear controller, employed in tube‐based robust control of linear systems, is replaced by an ancillary model predictive controller that forces the trajectories of the disturbed system to lie in a tube whose center is the reference trajectory thereby enabling robust control of uncertain nonlinear systems to be achieved. Copyright © 2011 John Wiley & Sons, Ltd.     

Plug-and-play model predictive control based on robust control invariant sets

We consider the problem of designing decentralized controllers for large-scale linear constrained systems composed by a number of interacting subsystems. As in Riverso et al. (2013b), (i) the design of local controllers requires limited transmission of information from other subsystems and (ii) the addition/removal of a subsystem triggers the design of local controllers for child subsystems only. These properties enable Plug-and-Play (PnP) operations, and we show how to perform them while preserving global stability of the origin and constraint satisfaction. We improve several aspects of the PnP design procedure proposed in Riverso et al. (2013b) and, using recent results in the computation of Robust Control Invariant (RCI) sets, we show that all critical steps in the design of a local controller can be solved through Linear Programming (LP). Finally, an application of the proposed design procedure to a large-scale mechanical system is presented.     

多面体不确定线性系统具有约束满足保证的预测控制

基于不变集理论, 拓展了Chiscil等人提出的约束不变预测控制方法(ICPC), 提出了一种适用于带约束多面体不确定线性系统的预测控制的框架. 其关键在于为针对标称系统设计的在线优化问题附加适当的额外的鲁棒可行约束. 若优化问题在初始阶段可行, 则此约束可保证在线优化问题始终可行, 从而保证了实际系统中约束条件的始终满足. 同时提出了闭环系统鲁棒稳定的一个充分条件, 可为成本函数的选择提供指导以保证预测控制器的鲁棒镇定.     

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.     

Adaptive disturbance rejection for strict‐feedback switched nonlinear systems using multiple Lyapunov functions

This paper investigates the problem of global disturbance rejection for switched nonlinear systems in strict‐feedback form with unknown exosystem where the solvability of the disturbance rejection problem for subsystems is not assumed. First, a sufficient condition for the solvability of the global disturbance rejection problem is given. As an extension of the classic concept of internal model for non‐switched systems, a new concept of switched internal model is proposed. Second, in order to solve the problem in question, a constructive adaptive control methodology is established on the basis of the multiple Lyapunov functions method, backstepping, and the changing supply functions technique. Finally, an example is provided to demonstrate the effectiveness of the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd.