Fault-tolerant control of a polyethylene reactor

This work focuses on fault-tolerant control of a gas phase polyethylene reactor. Initially, a family of candidate control configurations, characterized by different manipulated inputs, is identified. For each control configuration, a bounded nonlinear feedback controller, that enforces asymptotic closed-loop stability in the presence of constraints, is designed, and the constrained stability region associated with it is explicitly characterized using Lyapunov-based tools. Next, a fault-detection filter is designed to detect the occurrence of a fault in the control actuator by observing the deviation of the process states from the expected closed-loop behavior. A switching policy is then derived, on the basis of the stability regions, to orchestrate the activation/deactivation of the constituent control configurations in a way that guarantees closed-loop stability in the event of control system faults. Closed-loop system simulations demonstrate the effectiveness of the fault-tolerant control strategy.     

Non-approximation-based outputs stabilization for switched large-scale nonlinear systems with quantized inputs and sensor uncertainties

A non-approximation-based output feedback control strategy for a class of switched large-scale nonlinear systems with quantized inputs and sensor uncertainties is proposed. A dynamic gain, which is shared by the state observers and controllers of all the subsystems, is designed so that the effects of sensor uncertainties, quantized inputs, unknown parameters, and external disturbances can be compensated. By constructing some common Lyapunov functions (CLFs) shared by the switched systems, it is proved that with the proposed scheme, the closed-loop system stability can be guaranteed under arbitrary switching, and the outputs of all the subsystems can be steered to within arbitrarily small neighborhoods of the origin.     

Adaptive stabilization of a class of uncertain switched nonlinear systems with backstepping control

In this paper, we focus on the problem of adaptive stabilization for a class of uncertain switched nonlinear systems, whose non-switching part consists of feedback linearizable dynamics. The main result is that we propose adaptive controllers such that the considered switched systems with unknown parameters can be stabilized under arbitrary switching signals. First, we design the adaptive state feedback controller based on tuning the estimations of the bounds on switching parameters in the transformed system, instead of estimating the switching parameters directly. Next, by incorporating some augmented design parameters, the adaptive output feedback controller is designed. The proposed approach allows us to construct a common Lyapunov function and thus the closed-loop system can be stabilized without the restriction on dwell-time, which is needed in most of the existing results considering output feedback control. A numerical example and computer simulations are provided to validate the proposed controllers.     

一类离散时间切换混杂系统鲁棒控制

由于切换规则的存在使得切换混杂控制系统的稳定性研究变得极为复杂,如何针对给定的系统设计适当的控制器和切换规则没有统一的方法.本文考虑一类线性不确定离散时间切换混杂系统的鲁棒二次镇定和渐近镇定问题.利用公共李雅普诺夫函数方法和多李雅普诺夫函数方法,分别设计了切换混杂系统鲁棒状态反馈控制器和鲁棒输出反馈控制器,保证了切换混杂系统的二次稳定性和渐近稳定性.仿真结果验证了所提算法的正确有效性.     

一类离散时间切换系统鲁棒控制器设计

考虑一类非线性离散时间切换系统的鲁棒二次镇定和渐近镇定问题．利用公共李亚普诺夫函数方法和多李亚普诺夫函数方法，分别设计了切换系统鲁棒状态反馈控制器和输出反馈控制器，保证了切换系统的二次稳定性和渐近稳定性．仿真结果验证了所提出算法的有效性．     

Passivity analysis and control for discrete-time two-dimensional switched systems in Roesser model

This paper investigates the passivity issues of discrete-time two-dimensional switched systems in Roesser model under a state-dependent switching law. Conditions for passivity of discrete-time two-dimensional switched systems are obtained without the requirement of passivity of subsystems. When the system states are completely available, state feedback controllers and switching laws are designed. In the case of partial state measurements, dynamic output feedback controllers and switching laws depending only on the state of the output feedback controllers are constructed to guarantee passivity of the closed-loop switched system. Finally, numerical examples are provided to illustrate the efficiency of the results.     

Robust control design of a class of nonlinear input- and state-constrained systems

This work focuses on control design for input-output feedback linearizable nonlinear systems with bounded inputs and state constraints in the presence of uncertainty. Controllers based on Lyapunov’s direct method have been synthesized before for this class of nonlinear systems to enforce asymptotic stability in the presence of bounded inputs. However, none of these controllers accounts explicitly for state constraints. In order to address this task, we propose an optimization-based design method for which two properties will be guaranteed simultaneously despite parametric uncertainty, namely, closed-loop stability with bounded inputs and feasibility of the transient in the presence of state constraints.     

Passivity and feedback passification of switched discrete-time linear systems

This paper focuses on the passivity analysis and feedback passification for switched discrete-time linear systems using multiple storage functions under a certain switching law. Controllers and switching laws are designed based on complete and partial state measurements, respectively. Conditions for strict passivity of a switched discrete-time system are obtained without the requirement of strict passivity of subsystems. In the case of partial state measurements, dynamic output feedback controllers for subsystems are designed, and a switching law depending only on the state of the output feedback controllers is constructed to guarantee strict passivity of the closed-loop switched system. Finally, a numerical example is provided to demonstrate the feasibility of the theoretical results.     

Controller switching based on output prediction errors

We consider a switched nonlinear feedback control strategy for controlling a plant with unknown parameters so that the output asymptotically tracks a reference signal. The controller is selected online from a given set of controllers according to a switching rule based on output prediction errors. For control problems requiring asymptotic tracking of a reference input we provide sufficient conditions under which the switched closed-loop control system is exponentially stable and asymptotically achieves good control even if the switching does not stop, Our results are illustrated with three examples     

Asymptotic stabilization for switched affine systems with time delay: A novel dynamic event-triggered mechanism

This article concentrates on the asymptotic stabilization problem of switched affine systems (SASs) with unmeasurable states and time delay by constructing a novel dynamic event-triggered mechanism (ETM). Given the limited network transmission and the difficulties caused by affine terms in excluding the triggering Zeno behavior, we propose a novel dynamic ETM. It has been shown that the dynamic ETM not only has fewer data transfers than the existing ETM but also avoids Zeno behavior while maintaining asymptotic stability. Then, by constructing a set of dynamic output feedback switched affine controllers and switching laws, delicately incorporating Lyapunov–Krasovskii functionals, an asymptotic stabilization criterion is derived for the closed-loop SASs. The design methods of the controllers and switching laws are skillfully implemented by solving a set of linear matrix inequalities. Finally, an application example of the flyback DC–DC converter is offered to verify the proposed algorithm.     

Predictive control of switched nonlinear systems with scheduled mode transitions

In this work, a predictive control framework is proposed for the constrained stabilization of switched nonlinear systems that transit between their constituent modes at prescribed switching times. The main idea is to design a Lyapunov-based predictive controller for each constituent mode in which the switched system operates and incorporate constraints in the predictive controller design which upon satisfaction ensure that the prescribed transitions between the modes occur in a way that guarantees stability of the switched closed-loop system. This is achieved as follows: For each constituent mode, a Lyapunov-based model predictive controller (MPC) is designed, and an analytic bounded controller, using the same Lyapunov function, is used to explicitly characterize a set of initial conditions for which the MPC, irrespective of the controller parameters, is guaranteed to be feasible, and hence stabilizing. Then, constraints are incorporated in the MPC design which, upon satisfaction, ensure that: 1) the state of the closed-loop system, at the time of the transition, resides in the stability region of the mode that the system is switched into, and 2) the Lyapunov function for each mode is nonincreasing wherever the mode is reactivated, thereby guaranteeing stability. The proposed control method is demonstrated through application to a chemical process example.     

Global stabilization for a class of switched nonlinear feedforward systems

The problem of global stabilization for a class of switched nonlinear feedforward systems under arbitrary switchings is investigated in this paper. Based on the integrator forwarding technique and the common Lyapunov function method, we design bounded state feedback controllers of individual subsystems to guarantee asymptotic stability of the closed-loop system. A common coordinate transformation of all subsystems is exploited to avoid individual coordinate transformations for subsystems that are required when applying the forwarding recursive design scheme. An example is provided to demonstrate the effectiveness of the proposed design method.     

Passivity‐based asymptotic stabilization for switched nonlinear systems using the sampled integral stabilization technique

The asymptotic stabilization problem is studied for a cascade connection of passive switched nonlinear systems and a passive switched nonlinear system in this paper. When each subsystem is asymptotically zero state detectable and passive on active time intervals, asymptotic stabilization is achieved via co‐design of switching laws and controllers without damping injection. First, an output‐feedback controller is designed to asymptotically stabilize a cascade connection of two passive switched systems if outputs are measurable. Second, when the output of the first switched system is noisy or unmeasurable, a sampled integral stabilization (SIS) technique is employed to investigate asymptotical stabilization of a cascade connection by measuring only the storage function of the second switched system. Finally, as a special case of a cascade connection, the SIS technique is used to stabilize a passive switched system without damping injection. Under this circumstance, the controller is designed by sampling the integral of the passive output. The two‐link robot manipulator is provided to illustrate the effectiveness of the SIS technique.     

任意相对阶下非线性切换系统的事件触发漏斗控制

针对一类具有任意相对阶且带有部分非输入到状态稳定逆动态的非线性切换系统, 提出一种动态事件触 发漏斗跟踪控制方案. 首先, 引入一个虚拟输出将任意相对阶的非线性切换系统转换为相对阶为一的非线性切换系 统. 其次, 设计各子系统的事件触发漏斗控制器和切换的动态事件触发机制, 解决候选事件触发漏斗控制器和子系 统之间的异步切换问题, 所提方案消除已有文献中为所有子系统设计共同控制器带来的保守性. 在一类具有平均驻 留时间切换信号的作用下, 保证切换闭环系统的所有信号都是有界的, 且跟踪误差一直在预设的漏斗内演化, 并排 除采样中的奇诺现象. 最后, 一个仿真例子验证方案的实用性和有效性.     

基于状态观测器的一类非线性系统的模糊鲁棒控制

利用T－S模型对一类非线性不确定系统进行模糊建模,在此基础上研究模糊鲁棒观测器及模糊状态鲁棒控制器的设计,并证明所设计的模糊鲁棒观测器和模糊状态鲁棒控制器具有全局渐近稳定性质。     

Observer-based control of piecewise-affine systems

This paper presents a new synthesis method for both state and dynamic output feedback control of a class of hybrid systems called piecewise-affine (PWA) systems. The synthesis procedure delivers stabilizing controllers that can be proven to give either asymptotic or exponential convergence rates. The synthesis method builds on existing PWA stability analysis tools by transforming the design into a closed-loop analysis problem wherein the controller parameters are unknown. More specifically, the proposed technique formulates the search for a piecewise-quadratic control Lyapunov function and a piecewise-affine control law as an optimization problem subject to linear constraints and a bilinear matrix inequality. The linear constraints in the synthesis guarantee that sliding modes are not generated at the switching. The resulting optimization problem is known to be hard, but suboptimal solutions can be obtained using the three iterative algorithms presented in the paper. The new synthesis technique allows controllers to be designed with a specified structure, such as a combined regulator and observer. The observers in these controllers then enable switching based on state estimates rather than on measured outputs. The overall design approach, including a comparison of the synthesis algorithms and the performance of the resulting controllers, is clearly demonstrated in four simulation examples.     

一类Lipschitz 非线性切换系统基于观测器的 H∞ 输出跟踪控制

针对一类Lipschitz非线性切换系统,研究基于观测器的H∞输出跟踪控制问题.借助微分中值定理,将Lipschitz非线性切换系统转化为线性参数切换系统.当状态变量不可测或不易测时,利用多Lyapunov函数方法,同时设计观测器、基于观测器的跟踪控制器和滞后切换信号,使得系统满足H∞输出跟踪性能.最后通过仿真例子表明了设计方法的有效性.     

离散线性切换系统的一致有限时间稳定分析和反馈控制及其在网络控制系统中的应用

研究了一类离散线性切换系统的一致有限时间稳定性分析和反馈镇定．基于线性矩阵不等式技术,给出了在任意切换信号作用下,离散线性切换系统有限时间稳定和有限时间有界的充分条件,并给出了离散线性切换控制系统一致有限时间状态反馈控制器的设计方法．将上述分析结果应用于一类丢包有界的网络控制系统,得到了保证其有限时间稳定的反馈控制器．最后,通过两个数值仿真例子验证了所提方法的有效性．     

一类线性时变系统的输出反馈控制

基于线性时不变系统能控能观标准型变换及非线性系统高增益观测器方法,本文研究了一类线性时变系统 的输出反馈控制问题. 通过引入时变的状态变量坐标变换,分别设计了线性时变系统的状态反馈控制器、状态观测器以及基于 状态观测器的输出反馈控制器. 进一步地,本文分别证明了观测器动态误差是渐近收敛于零的,而状态反馈控制器以及输出反馈控制器可以 保证闭环系统的渐近稳定性.