New results on stability of switched continuous-time systems with all subsystems unstable

This paper studies the stability problem of switched continuous-time systems with all subsystems unstable. Switchings can be classified into two categories depending on their dwell time, which are the switching without divergence time and the switching with divergence time. Based on this, stability conditions under the bounded maximum average dwell time (BMADT) switching are established. In addition, by jointly considering the dynamic characteristics of the subsystems before and after switching instants, we also give the stability result via the dwell time with the floating lower and upper bounds. Finally, some simulation results are given to illustrate the advantages of the obtained theoretical results.     

Stability analysis of sample data systems with input missing: A hybrid control approach

In this paper, we establish exponential stability criteria for the sampled-data impulsive control of the linear time-invariant system. With average impulse interval (AII), less conservative conditions are obtained on the exponential stability problem for the sampled-data systems. It is proved that when the AII of the impulsive sequences is fixed, the upper bound of the impulsive intervals could be very large, which guarantees the less conservativeness of the obtained result concerning the sampling intervals. The control input missing is also studied and we establish a new stability criterion for the exponential decay rate and the sampling period which is less conservative than the ones obtained for variable sampling intervals. Two examples are given to show the effectiveness of the obtained result.     

切换系统稳定性研究综述

过去的几十年中,针对切换系统的研究广泛而深入并取得了丰富的成果.本文旨在对该方向的稳定性分析与镇定控制设计、可控可达性等方面提出新的认识.切换手段作为一种“离散控制器”的认识,已越来越被认可.针对这种“控制器”设计方面的研究成果进行分析,为研究者提供新的思路.     

Observer-based stabilization for switched positive system with mode-dependent average dwell time

This paper concerns the exponential stabilization problem for a class of switched positive systems. The switching signal satisfies mode-dependent average dwell time (MDADT) and the state variables are partially unmeasurable. A further explanation of mode-dependent average dwell time is included. By employing a set of quasi-time variables, which is first proposed for switched systems with MDADT, new stability results are obtained for the switched nonlinear systems and the underlying linear systems. Observer-based stabilization controllers, both for single-input case and multi-input case, are designed such that the closed-loop system converges exponentially. The designed observers and controllers are both mode-dependent and quasi-time-dependent, which is proved to be less conservative than the ones only mode-dependent. A simplified design strategy is provided to reduce the computation burden. Illustrative examples are provided to demonstrate the effectiveness of the results.     

Multi-formation control of nonlinear leader-following multi-agent systems

This paper deals with the multi-formation control problem for nonlinear leader-following multi-agent systems. Both the fixed topology case and the switching topology case are considered. The neighbor-based multi-formation control protocols are proposed under the assumption that for one subgroup, the total information received from other subgroups is zero. Then, based on the Lyapunov stability theory combined with the algebraic graph theory, sufficient conditions are established to ensure that the leader-following multi-agent systems with nonlinear dynamics can reach and maintain the desired multi-formation control. Finally, simulation examples are provided to illustrate the effectiveness of the theoretical results.     

Tracking control of nonholonomic mobile agents with external disturbances and input delay

This paper investigates the tracking control problem of chained-form nonholonomic multiagent systems (MASs). In contrast to the existing works in which some algorithms have been designed for ideal conditions, the destructive factors including external disturbances and input delay are considered in the dynamics of the agents in this work. Two distributed controllers are proposed such that the states of the controlled agents can track the states of the target in the presence of external disturbances and input delay. For this purpose, a distributed controller is firstly suggested based on a switching method to solve the tracking control problem for nonholonomic MASs with external disturbances. Then, the proposed control law is extended based on a state predictor for the tracking control of agents in the presence of input delay. The stability analysis of the two distributed controllers is also provided. Simulation results show the promising performance of the proposed algorithms.     

Adaptive fuzzy predictive sliding control of uncertain nonlinear systems with bound-known input delay

In this paper, a new Adaptive Fuzzy Predictive Sliding Mode Control (AFP-SMC) is presented for nonlinear systems with uncertain dynamics and unknown input delay. The control unit consists of a fuzzy inference system to approximate the ideal linearization control, together with a switching strategy to compensate for the estimation errors. Also, an adaptive fuzzy predictor is used to estimate the future values of the system states to compensate for the time delay. The adaptation laws are used to tune the controller and predictor parameters, which guarantee the stability based on a Lyapunov-Krasovskii functional. To evaluate the method effectiveness, the simulation and experiment on an overhead crane system are presented. According to the obtained results, AFP-SMC can effectively control the uncertain nonlinear systems, subject to input delays of known bound.     

H_∞ Control Based on LMIs for a Class of Time-delay Switched Systems

The problem of H∞ stability analysis and control synthesis of switched systems with delayed states under arbitrary switching laws is considered.By means of Lyapunov function and linear matrix inequality tools,sufficient condition of H∞ stability is presented in terms of linear matrix inequalities.Furthermore,the robust H∞ control synthesis via state feedback and output feedback is studied.Finally,a numerical example is given to demonstrate the effectiveness of the proposed method.     

干扰输入影响下离散线性切换系统的反馈控制方法

面对当前使用的平均驻留时间的反馈控制方法、基于切换原理的反馈控制方法受到外界环境干扰,导致控制效果不佳的问题,提出干扰输入影响下离散线性切换系统的反馈控制方法。 分析离散线性切换系统,设定切换信号是唯一的和任意的 2 种情况,由此设计线性切换状态下的反馈控制器,在干扰输入影响下,构建被控对象模型,描述输出反馈问题,简化信号非统一输入过程,确定任意切换时间内存在的 2 个控制量,设计降阶控制律,构造一阶输出反馈律,实现有限时间镇定反馈控制。 实验结果表明,该方法输出的响应曲线与实际最大时延上界为 6 ms 的控制情况一致,说明反馈控制效果较好。     

欠驱动机器人的切换姿态优化及全局稳定控制

讨论了欠驱动两杆机器人控制中存在的控制器切换问题并将其归纳为一类优化问题,提出了一种优化切换姿态并保证全局稳定的控制器设计方案。在系统全局稳定的条件下,将对欠驱动关节的控制能力作为优化目标。采用基于弱控制Lya-punov函数的方法设计摆起控制器;利用线性二次调节器(linear quadratic regulator,LQR)方法设计平衡控制器;使用控制器切换环节实现控制器的最优切换,其中控制器切换环节的设计借助平衡控制器吸引域的概念和遗传算法来实现。仿真实验中,应用该方法得到的控制器不仅能实现控制目标,还能使系统具有更强的抗干扰能力,并缩短18.8%的控制时间。     

Guaranteed cost control of mobile sensor networks with Markov switching topologies

This paper investigates the consensus seeking problem of mobile sensor networks (MSNs) with random switching topologies. The network communication topologies are composed of a set of directed graphs (or digraph) with a spanning tree. The switching of topologies is governed by a Markov chain. The consensus seeking problem is addressed by introducing a global topology-aware linear quadratic (LQ) cost as the performance measure. By state transformation, the consensus problem is transformed to the stabilization of a Markovian jump system with guaranteed cost. A sufficient condition for global mean-square consensus is derived in the context of stochastic stability analysis of Markovian jump systems. A computational algorithm is given to synchronously calculate both the sub-optimal consensus controller gains and the sub-minimum upper bound of the cost. The effectiveness of the proposed design method is illustrated by three numerical examples.     

基于反演设计的机器人操纵臂的变结构控制

针对由电机驱动的机器人操纵臂，研究了非线性系统的变结构控制。在一定的假设条件下。给出了变结构系统中滑动模态存在的条件及变结构控制律设计的方法。然后利用反演设计方法构造变结构控制的切换函数，以获得稳定的滑动模态。将设计方法应用于机器人操纵臂的控制律设计，并进行了仿真研究。     

Robust model predictive control for switched linear systems

Developed is a robust model predictive control scheme for a class of discrete-time switched linear systems. The system is described in linear fractional transformation form in the presence of model uncertainty and induced norm bounded disturbances. The objective is to minimize the upper bound of an infinite horizon cost function subject to a terminal inequality. A Lyapunov function analysis for the switched system shows guaranteed closed-loop stability. Taking into account the switching structure of the system, the predictive control design problem along with sufficient conditions for the existence of a solution is expressed in terms of Riccati–Metzler inequalities. Then, these inequalities are turned into a linear matrix inequality feasibility problem. Three cases are analyzed to demonstrate the performance and effectiveness of the proposed robust model predictive controller for switched discrete-time linear systems.     

Switched systems: Stability and design (review)

Publications concerned with investigation and synthesis of switched systems are reviewed. Frequently used mathematical models of the systems are presented. Attention is focused on the problem of system stability for arbitrary and limited switching signals. Relationship between switched and fuzzy systems is illustrated. Some approaches to synthesizing switched controllers and state observers are considered.     

Decentralized adaptive neural prescribed performance control for high-order stochastic switched nonlinear interconnected systems with unknown system dynamics

In this paper, the problem of decentralized adaptive neural backstepping control is investigated for high-order stochastic nonlinear systems with unknown interconnected nonlinearity and prescribed performance under arbitrary switchings. For the control of high-order nonlinear interconnected systems, it is assumed that unknown system dynamics and arbitrary switching signals are unknown. First, by utilizing the prescribed performance control (PPC), the prescribed tracking control performance can be ensured, while the requirement for the initial error is removed. Second, at each recursive step, only one adaptive parameter is constructed to overcome the over-parameterization, and RBF neural networks are employed to tackle the difficulties caused by completely unknown system dynamics. At last, based on the common Lyapunov stability method, the decentralized adaptive neural control method is proposed, which decreases the number of learning parameters. It is shown that the designed common controller can ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB), and the prescribed tracking control performance is guaranteed under arbitrary switchings. The simulation results are presented to further illustrate the effectiveness of the proposed control scheme.     

Robust H(∞) control of uncertain switched systems defined on polyhedral sets with Filippov solutions

This paper considers the control problem of a class of uncertain switched systems defined on polyhedral sets known as piecewise linear systems where, instead of the conventional Carathéodory solutions, Filippov solutions are studied. In other words, in contrast to the previous studies, solutions with infinite switching in finite time along the facets and on faces of arbitrary dimensions are also taken into account. Firstly, established upon previous studies, a set of linear matrix inequalities are brought forward which determines the asymptotic stability of piecewise linear systems with Filippov solutions. Subsequently, bilinear matrix inequality conditions for synthesizing a robust controller with a guaranteed H(∞) performance are presented. Furthermore, these results has been generalized to the case of piecewise affine systems. Finally, a V-K iteration algorithm is proposed to deal with the aforementioned bilinear matrix inequalities. The validity of the proposed method is verified through the analysis of two simulation examples.     

A new fractional-order sliding mode controller via a nonlinear disturbance observer for a class of dynamical systems with mismatched disturbances

This paper investigates the stabilization and disturbance rejection for a class of fractional-order nonlinear dynamical systems with mismatched disturbances. To fulfill this purpose a new fractional-order sliding mode control (FOSMC) based on a nonlinear disturbance observer is proposed. In order to design the suitable fractional-order sliding mode controller, a proper switching surface is introduced. Afterward, by using the sliding mode theory and Lyapunov stability theory, a robust fractional-order control law via a nonlinear disturbance observer is proposed to assure the existence of the sliding motion in finite time. The proposed fractional-order sliding mode controller exposes better control performance, ensures fast and robust stability of the closed-loop system, eliminates the disturbances and diminishes the chattering problem. Finally, the effectiveness of the proposed fractional-order controller is depicted via numerical simulation results of practical example and is compared with some other controllers.     

ROBUST CONTROL OF GAS TUNGSTEN ARC WELDING SYSTEM

The robust control law for gas tungsten arc welding dynamic process, which is a typical sampled-data system and full of uncertainties, is presented. By using the Lyapunov second method, the robust control and robust optimal control for a class of sampled-data systems whose underlying continuous-time systems are subjected to structured uncertainties are discussed in time-domain. As a result, some sufficient conditions of robust stability and the corresponding robust control laws are derived. All these results are designed by solving a class of linear matrix inequalities (LMIs) and a class of dynamic optimization problem with LMIs constraints respectively. An example adapted under some experimental conditions in the dynamic process of gas tungsten arc welding system in which the controlled variable is the backside width of weld pool and controlling variable pulse duty ratio, is worked out to illustrate the proposed results, it is shown that the sampling period is the crucial design parameter.     

Stochastic stability and stabilization of Markov jump linear systems with instantly time-varying transition rates: A unified framework

This paper investigates the stochastic stability and stabilization problems of non-homogeneous Markov jump linear systems (NHMJLSs) characterized by instantly unconditionally time-varying transition rates (TRs). The novelty of the study lies in proposing a systematic method for achieving finite dimensional conditions with an acceptable degree of conservativeness for the stability and the stabilization problems of the system. In this framework, by first processing the time-varying TRs, a finite number of uncertain but time-constant TR matrices are obtained. Then, a high-level switching signal is constructed for the system, which models the contribution of each possible time-constant TR matrix. Based on the results, the NHMJLS is reformed into an uncertain switching structure referred to as the associated switched Markov jump linear system (AS-MJLS). Finally, by taking advantage of the new representation, sufficient conditions are obtained to ensure the stability and stabilizability of the system, also the controller gains are designed. The proposed framework provides a realistic representation as well as practically solvable analysis and synthesis conditions for the NHMJLS. It also leads to less conservative results compared with the existing well-known techniques. Comparative simulation studies for a single-machine infinite-bus (SMIB) power system subject to stochastically varying load demonstrate the efficiency and superiority of the method.     

Finite-time stabilization for a class of nonholonomic feedforward systems subject to inputs saturation

This paper studies the problem of finite-time stabilization by state feedback for a class of uncertain nonholonomic systems in feedforward-like form subject to inputs saturation. Under the weaker homogeneous condition on systems growth, a saturated finite-time control scheme is developed by exploiting the adding a power integrator method, the homogeneous domination approach and the nested saturation technique. Together with a novel switching control strategy, the designed saturated controller guarantees that the states of closed-loop system are regulated to zero in a finite time without violation of the constraint. As an application of the proposed theoretical results, the problem of saturated finite-time control for vertical wheel on rotating table is solved. Simulation results are given to demonstrate the effectiveness of the proposed method.