Periodic event-triggering in distributed receding horizon control of nonlinear systems

How to efficiently use limited system resources in distributed receding horizon control (DRHC) is an important issue. This paper studies the DRHC problem for a class of dynamically decoupled nonlinear systems under the framework of event-triggering, to efficiently make use of the computation and communication resources. To that end, a distributed periodic event-triggered strategy is designed and a detailed DRHC algorithm is presented. The conditions for ensuring feasibility of the designed algorithm and stability of the closed-loop system are developed, respectively. We show that the closed-loop system is input-to-state stable if the energy bound of the disturbances, the triggering condition and the cooperation matrices fulfill the proposed conditions.     

Robust stability analysis of networked systems with varying delays

This article is concerned with networked controlled systems (NCS) with uncertain, varying, bounded transmission delays and asynchronous discrete-time static control laws. It is first shown that the delay variation gives rise to a discrete-time uncertain NCS model; robust stability analysis is carried out via a linear matrix inequality approach which, when combined with a directed parameter search, yields an estimate of robust stability bounds against any variations of the maximum allowable delay (constrained within one sampling period) that the closed-loop system can tolerate. The derived bounds are compared with other techniques relying on the singular values of the perturbed NCS-model. The presented simulation results prove the efficacy of the proposed control scheme.     

Delay-dependent stability analysis and controller synthesis for Markovian jump systems with state and input delays

This paper focuses on the problem of delay-dependent robust stochastic stability analysis and controller synthesis for Markovian jump systems with state and input delays. It is assumed that the delays are constant and unknown, but their upper bounds are known. By constructing a new Lyapunov-Krasovskii functional and introducing some appropriate slack matrices, new delay-dependent stochastic stability and stabilization conditions are proposed by means of linear matrix inequalities (LMIs). An important feature of the results proposed here is that all the robust stability and stabilization conditions are dependent on the upper bound of the delays. Memoryless state feedback controllers are designed such that the closed-loop system is robustly stochastically stable. Some numerical examples are provided to illustrate the effectiveness of the proposed method.     

Input-to-state stability for networked control systems via an improved impulsive system approach

This paper presents a novel impulsive system approach to input-to-state stability (ISS) analysis of networked control systems (NCSs) with time-varying sampling intervals and delays. This approach is based upon the new idea that an NCS can be viewed as an interconnected hybrid system composed of an impulsive subsystem and an input delay subsystem. A new type of time-varying discontinuous Lyapunov-Krasovskii functional, which makes full use of the information on the piecewise-constant input and the bounds of the network delays, is introduced to analyze the ISS property of NCSs. Linear matrix inequality based sufficient conditions are derived for ISS of NCSs with respect to external disturbances. When applied to the approximate tracking problem for NCSs, the derived ISS result provides bounds on the steady-state tracking error. Numerical examples are provided to show the efficiency of the proposed approach.     

Robust stability bounds for multi-delay networked control systems

In this paper, the robust stability of a perturbed linear continuous-time system is examined when controlled using a sampled-data networked control system (NCS) framework. Three new robust stability bounds on the time-invariant perturbations to the original continuous-time plant matrix are presented guaranteeing stability for the corresponding discrete closed-loop augmented delay-free system (ADFS) with multiple time-varying sensor and actuator delays. The bounds are differentiated from previous work by accounting for the sampled-data nature of the NCS and for separate communication delays for each sensor and actuator, not a single delay. Therefore, this paper expands the knowledge base in multiple inputs multiple outputs (MIMO) sampled-data time delay systems. Bounds are presented for unstructured, semi-structured, and structured perturbations.     

具有有界时滞的网络控制系统的镇定

针对具有有界时滞且时滞上界大于一个采样周期的网络控制系统,研究了系统建模和状态反馈镇定问题.在分析有界时滞的所有可能性的基础上,提出一种能够用于处理时变控制律问题的网络控制系统数学模型,进而将该系统的镇定问题转化为镇定一系列模型的鲁棒控制问题.根据 Lyapunov 方法,给出了保证闭环系统稳定的状态反馈控制器.仿真算例验证了所提出方法的有效性.     

Distributed model predictive control of linear systems with persistent disturbances

This article presents a new form of robust distributed model predictive control (MPC) for multiple dynamically decoupled subsystems, in which distributed control agents exchange plans to achieve satisfaction of coupling constraints. The new method offers greater flexibility in communications than existing robust methods, and relaxes restrictions on the order in which distributed computations are performed. The local controllers use the concept of tube MPC – in which an optimisation designs a tube for the system to follow rather than a trajectory – to achieve robust feasibility and stability despite the presence of persistent, bounded disturbances. A methodical exploration of the trades between performance and communication is provided by numerical simulations of an example scenario. It is shown that at low levels of inter-agent communication, distributed MPC can obtain a lower closed-loop cost than that obtained by a centralised implementation. A further example shows that the flexibility in communications means the new algorithm has a relatively low susceptibility to the adverse effects of delays in computation and communication.     

Distributed robust adaptive control for a class of dynamical complex networks against imperfect communications

In this article, a robust tracking control problem of a class of dynamical complex networks is presented through a distributed adaptive approach. Uncertain network topology with unknown coupling strength, delayed and perturbed communications and external disturbances are considered, while the bounds of channel noises and coupling delays and disturbances are assumed to be unknown. Adaptation laws are proposed to estimate the network coupling strength and the upper and lower bounds of communication state errors and disturbances on-line. Based on the information from adaptive schemes, a class of distributed robust adaptive controllers is constructed to automatically compensate for the imperfect network and disturbance effects. Then, according to the Lyapunov stability theory, it is shown that the achievement of tracking for complex networks is effective on imperfect communications and disturbances. The effectiveness of the proposed design is illustrated via a decoupled longitudinal model of an F-18 aircraft.     

Distributed model predictive control of constrained nonlinear systems with communication delays

Distributed model predictive control (MPC), having been proven to be efficient for large-scale control systems, is essentially enabled by communication network connections among involved subsystems (agents). This paper studies the distributed MPC problem for a class of continuous-time decoupled nonlinear systems subject to communication delays. By using a robustness constraint and designing a waiting mechanism, a delay-involved distributed MPC scheme is proposed. Furthermore, the iterative feasibility and stability properties are analyzed. It is shown that, if the communication delays are bounded by an upper bound, and the cooperation weights and the sampling period are designed appropriately, the overall system state converges to the equilibrium point. The theoretical results are verified by a simulation study.     

Delay-dependent resilient-robust stabilisation of uncertain networked control systems with variable sampling intervals

This work is concerned with the robust resilient control problem for uncertain networked control systems (NCSs) with variable sampling intervals, variant-induced delays and possible data dropouts, which is seldom considered in current literature. It is mainly based on the continuous time-varying-delay system approach. Followed by the nominal case, delay-dependent resilient robust stabilising conditions for the closed-loop NCS against controller gain variations are derived by employing a novel Lyapunov–Krasovskii functional which makes good use of the information of both lower and upper bounds on the varying input delay, and the upper bound on the variable sampling interval as well. A feasible solution of the obtained criterion formulated as linear matrix inequalities can be gotten. A tighter bounding technique is presented for acquiring the time derivative of the functional so as to utilise many more useful elements, meanwhile neither slack variable nor correlated augmented item is introduced to reduce overall computational burden. Two examples are given to show the effectiveness of the proposed method.     

有界扰动下约束非线性系统鲁棒经济模型预测控制EI北大核心CSCD

针对未知但有界扰动下约束非线性系统,提出一种新的鲁棒经济模型预测控制(Economic model predictive control,EMPC)策略,保证闭环系统对扰动输入具有输入到状态稳定性(Input-to-state stability,ISS).基于微分对策原理,分别优化经济目标函数和关于最优经济平衡点的鲁棒稳定性目标函数,其中经济最优性与鲁棒稳定性是具有冲突的两个控制目标.利用鲁棒稳定性目标最优值函数构造EMPC优化的隐式收缩约束,建立鲁棒EMPC的递推可行性和闭环系统关于最优经济平衡点相对于有界扰动输入到状态稳定性结果.最后以连续搅拌反应器为例,对比仿真验证本文策略的有效性.     

基于干扰观测器的不确定线性多变量系统控制

针对不确定线性多变量系统,提出一种基于干扰观测器(Disturbance observer,DOB)的保证系统内部稳定性的控制策略.以简单的结构和少量的计算代价实现鲁棒的控制效果,补偿外界干扰以及内部模型误差.通过引入一个闭环稳定性等价系统,辅助分析基于干扰观测器的多变量控制系统的内部稳定性,探讨在存在外部扰动及内部模型不确定性的情况下系统保证内部稳定的充分条件,指导外环控制器及内环干扰观测器中Q滤波器的设计.通过数值模型上的仿真验证了提出的控制方法的有效性.     

Semi-global sampled-data output feedback disturbance rejection control for a class of uncertain nonlinear systems

This paper investigates the semi-global output feedback disturbance rejection control problem for a class of uncertain nonlinear systems with additive disturbances using linear sampled-data control. Aiming to reject the adverse effects caused by the uncertainties and unknown nonlinear perturbations which may not satisfy the strict feedback or feedforward structure, a new generalised discrete-time extended state observer is proposed to estimate the disturbance at sampling points. An output feedback disturbance rejection control law is then constructed in a sampled-data form which facilitates digital implementations. By selecting adequate control gains and a sufficiently small sampling period to restrain the state growth under a zero-order-hold input, the semi-global asymptotic stability of the hybrid closed-loop system and the disturbance rejection ability are proved. Both numerical example and an application of a single-link robot arm system demonstrate the feasibility and efficacy of the proposed method.     

时变采样周期网络控制系统的鲁棒容错控制器设计

研究具有时变采样周期网络控制系统的执行器失效的完整性问题．假设系统任意两个连续采样间隔具有上界,利用输入时延法,将时变采样周期网络控制系统等价转化为连续时变时延网络控制系统．在此基础上,基于时延条件,应用Ｌｙａｐｕｎｏｖ稳定性理论和线性矩阵不等式（ＬＭＩｓ）方法证明了鲁棒容错控制律的存在条件,设计了鲁棒容错控制器,并给出了系统完整性条件下的最大允许时延的估计方法．仿真结果验证了所提方法的可行性和有效性．     

Multisensor switching control strategy with fault tolerance guarantees

In this paper we propose a novel fault tolerant multisensor switching strategy for feedback control. Each sensor of the proposed multisensor scheme has an associated state estimator which, together with a state feedback gain, is able to individually stabilise the closed-loop system. At each instant of time, the switching strategy selects the sensor-estimator pair that provides the best closed-loop performance, as measured by a control-performance criterion. We establish closed-loop stability of the resulting switching scheme under normal (fault-free) operating conditions. More importantly, we show that closed-loop stability is preserved in the presence of faulty sensors if a set of conditions on the system parameters (such as bounds on the sensor noises, maximum and minimum values of the reference signal, etc.) is satisfied. This result enhances and broadens the applicability of the proposed multisensor scheme since it provides guaranteed properties such as fault tolerance and robust closed-loop stability under sensor fault. The results are applied to the problem of automotive longitudinal control.     

Distributed model predictive control of constrained weakly coupled nonlinear systems

This paper proposes a distributed model predictive control (MPC) strategy for a large-scale system that consists of several dynamically coupled nonlinear systems with decoupled control constraints and disturbances. In the proposed strategy, all subsystems compute their control signals by solving local optimizations constrained by their nominal decoupled dynamics. The dynamic couplings and the disturbances are accommodated through new robustness constraints in the local optimizations. The paper derives relationships among, and designs procedures for, the parameters involved in the proposed distributed MPC strategy based on the analysis of the recursive feasibility and the robust stability of the overall system. The paper shows that, for a given bound on the disturbances, the recursive feasibility is guaranteed if the sampling interval is properly chosen. Moreover, it establishes sufficient conditions for the overall system state to converge to a robust positively invariant set. The paper illustrates the effectiveness of the proposed distributed MPC strategy by applying it to three coupled cart-(nonlinear) spring–damper subsystems.     

Robust control for a class of nonlinear networked systems with stochastic communication delays via sliding mode conception

This paper deals with the robust control problem for a class of uncertain nonlinear networked systems with stochastic communication delays via sliding mode conception (SMC). A sequence of variables obeying Bernoulli distribution are employed to model the randomly occurring communication delays which could be different for different state variables. A discrete switching function that is different from those in the existing literature is first proposed. Then, expressed as the feasibility of a linear matrix inequality (LMI) with an equality constraint, sufficient conditions are derived in order to ensure the globally mean-square asymptotic stability of the system dynamics on the sliding surface. A discretetime SMC controller is then synthesized to guarantee the discrete-time sliding mode reaching condition with the specified sliding surface. Finally, a simulation example is given to show the effectiveness of the proposed method.     

Stability and Stabilization of Networked Control Systems Under Limited Communication Capacity and Variable Sampling

This paper investigates the problem of quantized feedback control for networked control systems (NCSs) with time‐varying delays and time‐varying sampling intervals, wherein the physical plant is a continuous‐time, and the control input is a discrete‐time signal. By using an input delay approach and a sector bound method, the network induced delays, the signal quantization and sampling intervals are presented in one framework in the case of the state and the control input by quantization in a logarithmic form. We exploit a novel Lyapunov functional with discontinuity, taking full advantage of the NCS characteristic information including the bounds of delays, the bounds of sampling intervals and quantization parameters. In addition, it has been shown that the Lyapunov functional is decreased at the jump instants. Furthermore, we use the Leibniz‐Newton formula and free‐weighting matrix method to obtain the stability analysis and stabilization conditions which are dependent on the NCS characteristic information. The proposed stability analysis and stabilizing controller design conditions can be presented in term of linear matrix inequalities, which have less conservativeness and less computational complexity. Four examples demonstrate the effectiveness of the proposed methods.     

离散Markov跳变系统事件触发H∞量化输出反馈控制

主要研究了基于事件触发机制的离散Markov跳变系统的量化H∞输出反馈控制问题,对系统的建模、稳定性分析、控制器设计等三个方面进行了研究。首先,提出了事件触发通信机制来确定当前采样数据是否能够传输到控制器当中。其次,在传感器与控制器之间引入对数量化器,利用扇形有界方法,量化采样数据达到降低网络中的数据传输速率的目的。接下来,考虑网络诱导时延建立一种具有外部扰动的Markov跳变时滞系统。构造Lyapunov-Krasovskii 泛函,得到使闭环系统渐近稳定且满足H∞性能指标的充分条件,在此基础上设计相应的输出反馈控制器。最后通过数值仿真来证明本文所提方法的有效性。     

Robust consensus algorithm for second-order multi-agent systems with external disturbances

This article investigates the problem of robust consensus for second-order multi-agent systems with external disturbances. Based on a non-smooth backstepping control technique, a class of novel continuous non-smooth consensus algorithms are proposed for the multi-agent network with/without communication delays. The controller design is divided into two steps. First, for the kinematic subsystem, the velocity is regarded as a virtual input and designed such that the states consensus can be achieved asymptotically. Then for the dynamic subsystem, a finite-time control law is designed such that the virtual velocity can be tracked by the real velocity in a finite time. Under the proposed control law, it is shown that if the communication topology graph contains a directed spanning tree, the states consensus can be achieved asymptotically in the absence of disturbances. In the presence of disturbances, the steady-state errors of any two agents can reach a small region around the origin. By building a relationship between control parameters and the bound of steady tracking errors, it is demonstrated that the disturbance rejection performance of the resulting closed-loop system can be enhanced by adjusting the fractional power in the non-smooth controller. Finally, an example is given to verify the efficiency of the proposed method.