Adaptive state tracking of switched systems based on a hyperstability criterion

The adaptive state tracking problem of switched systems is studied in this paper. The desirable state trajectory is generated by a switched reference model. First, a condition for asymptotical hyperstability of switched systems is proposed and a switching law is designed, which is a generalization of the classical hyperstability condition for non‐switched systems. Then, the result is applied to uncertain switched systems to achieve state tracking. An individual adaptive law is designed for each subsystem such that the Popov inequality is satisfied. Asymptotical state tracking is achieved under non‐persistent exciting input when the error system switches in a certain way. The result is demonstrated by a numerical example and a practical system of Highly Maneuverable Aircraft Technology vehicle, respectively. Copyright © 2013 John Wiley & Sons, Ltd.     

Passivity‐based adaptive output tracking control for switched nonlinear systems with uncertain parameters

This paper addresses the issue of the adaptive output tracking control for switched nonlinear systems with uncertain parameters. The solvability of the tracking control problem for each subsystem is not necessary to hold. Individual update laws corresponding to different unknown parameters are adopted to reduce the conservativeness produced from the adoption of a common undated law. By means of the dual design of the adaptive controllers and a state‐dependent switching law using multiple storage functions technique, several conditions are obtained under which the adaptive output tracking control problem for switched nonlinear systems is solvable. Finally, an example shows the effectiveness of the proposed method.     

基于APC控制的开关磁阻电机性能分析

针对开关磁阻电动机二维有限元计算考虑端部效应问题,为提高其电磁场的计算精确度,根据开关磁阻电动机(SRM)性能及其系统的结构特点,搭建了SRM及其控制系统的整体模型,在电磁场基本理论的基础上,采用有限元法对角度位置控制( APC)控制下的SRM的电磁场进行了数值研究.在理论计算的基础上得出了SRM的输出转矩、相电流波形以及磁链等参量的变化曲线,并对其进行了详细地分析,同时将数值计算结果与实测结果进行比较,验证了二维仿真中考虑绕组端部磁场影响的模型的合理性,为SRM性能优化及温升和噪声地研究提供了理论依据.     

单周期控制的PFC电路切换线性模型

为了深入研究单周期控制技术的系统控制过程和工作机理,采用非线性控制理论,建立电流断续条件下boost变换器的切换线性模型并对模型进行分析.给出了boost变换器运行时三个模式的动力学方程以及各模式间的切换序列,分析了在电流断续条件下的能控性.通过和电压跟随器控制的功率校正电路输出电压作对比,表明了采用单周期控制技术后输出电压超调量更小,动态响应速度更快.分析所采用的方法同样可以用于单周期控制buck、buck-boost变换器电路,为单周期控制技术的推广提供理论依据.     

Model predictive control based switching of multimodal controllers in switched systems

In real systems, there exist physical constraints such as voltage limitations imposed on actuators or state restriction due to their structure. Violation constraints in systems may cause instability, or in the worst case, result in malfunction. In this paper, a switching algorithm of multimodal controllers in switched systems is proposed. The method is based on the model predictive control. Both simulation and experimental results illustrate the effectiveness of the proposed method. © 2008 Wiley Periodicals, Inc. Electr Eng Jpn, 166(3): 73–81, 2009; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20702     

Adaptive fuzzy constraint control for switched nonlinear systems in nonstrict feedback form

In this paper, the adaptive fuzzy controller design problem is investigated for a class of switched nonlinear systems in nonstrict feedback form, in which the unknown functions are considered and are approximated. Moreover, the system states are constrained in corresponding compact. By using Barrier Lypunov function method and backstepping technique, the adaptive fuzzy controller is designed such that all the signals in the closed-loop system are bounded, the system output can track the desired signal to small compact, and all the system states satisfy the constraint conditions. Finally, the simulation results show the effectiveness of the proposed method.     

An adaptive design for quantized feedback control of uncertain switched linear systems

This paper addresses the problem of asymptotic tracking for switched linear systems with parametric uncertainties and dwell‐time switching, when input measurements are quantized due to the presence of a communication network closing the control loop. The problem is solved via a dynamic quantizer with dynamic offset that, embedded in a model reference adaptive control framework, allows the design of the adaptive adjustments for the control parameters and for the dynamic range and dynamic offset of the quantizer. The overall design is carried out via a Lyapunov‐based zooming procedure, whose main feature is overcoming the need for zooming out at every switching instant, in order to compensate for the possible increment of the Lyapunov function at the switching instants. It is proven analytically that the resulting adjustments guarantee asymptotic state tracking. The proposed quantized adaptive control is applied to the piecewise linear model of the NASA Generic Transport Model aircraft linearized at multiple operating points.     

Neural networks-based adaptive finite-time prescribed performance fault-tolerant control of switched nonlinear systems

In this article, the adaptive finite-time fault-tolerant control problem is considered for a class of switched nonlinear systems in nonstrict-feedback form with actuator fault. The problem of finite-time fault-tolerant control is solved by introducing a finite-time performance function. Meanwhile, the completely unknown nonlinear functions exist in the switched system are identified by the neural networks. Based on the common Lyapunov function method with adaptive backstepping technique, the finite-time fault-tolerant controller is designed. The proposed control strategy can guarantee that the tracking error converges to a prescribed zone at a finite-time and all system variables remain semiglobally practical finite-time stable. Numerical examples are offered to verify the feasibility of the theoretical result.     

Finite-time asynchronous control of linear time-varying switched systems

In the framework of asynchronous control, finite-time stabilization and finite-time bounded stabilization of linear time-varying (LTV) switched systems are investigated. A necessary and sufficient condition for finite-time stability (FTS) of LTV switched systems is proposed based on differential matrix inequalities (DMIs). Moreover, we extend the FTS result to the case of finite-time boundedness (FTB), and present a sufficient condition of FTB for LTV switched systems using the average dwell time method which can be used for design proposes. Then we turn to the design problem of asynchronously switched control to guarantee FTS or FTB of LTV switched systems and give a sufficient condition for the state feedback stabilization in the form of nonlinear DMIs (NDMIs). A numerical method is proposed to solve NDMIs approximately. Finally, two examples are given to illustrate the validity of the results.     

Model reference adaptive control for nonlinear switched systems under asynchronous switching

In this paper, the problem of model reference adaptive control for nonlinear switched systems with parametric uncertainties is investigated. Asynchronous switching between subsystems and adaptive controllers is also considered. Firstly, a state feedback adaptive controller is designed. Then, sufficient conditions ensuring the global practical stability of the error switched system with average dwell time are proposed. The boundedness of all signals in the closed‐loop system is guaranteed by the proposed adaptive controller. Finally, a practical example is given to demonstrate the validity of the main results. Copyright © 2016 John Wiley & Sons, Ltd.     

Reliable nonfragile tracking control for switched systems with external disturbances

With the assistance of reliable control technique, the nonfragile tracking problem has been proposed in this paper for a class of switched systems with external disturbances under the aegis of modified repetitive controller. Notably, the designed repetitive controller is used to improve the tracking performance of the addressed switched systems. Preciously, the influence of external disturbances are estimated through the improved equivalent-input-disturbance strategy, wherein the effect caused by the external disturbances to the output channel are reduced by the aid of modified repetitive control strategy. The fundamental intention of this control synthesis is that the output of the system precisely tracks the reference signal even in the presence of external disturbances and gain fluctuations. For that cause, Lyapunov stability technique in conjunction with average dwell time approach is implemented to obtain adequate conditions in the shape of linear matrix inequalities which insists the exponential stability for the addressed system. Ultimately, the efficiency and supremacy of the proposed control schemes are justified via two numerical examples, wherein it is exposed to view that the developed control strategy is capable of good tracking performance and also estimates the external disturbances efficiently.     

Guaranteed cost control with pole constraints for uncertain discrete-time switched systems

For a class of discrete-time switched systems with norm-bounded uncertainties and a quadratic cost index, the problem of designing a guaranteed cost state feedback controller with pole constraints is considered. A sufficient condition on the existence of robust guaranteed controllers is derived by a quadratic Lyapunov function approach together with linear matrix inequality (LMI) technique. Based on a constructed switching law, the closed-loop system is quadratic D-stable and the closed-loop cost function value is not more than a specified upper bound. Furthermore, the design of suboptimal guaranteed cost controllers is turned into a convex optimization problem with linear matrix inequalities constraints. A numerical example demonstrates the effect of the proposed design approach. __________ Translated from Control and Decision, 2007, 22(11): 1269–1273 [译自: 控制与决策]     

离散时延切换系统的鲁棒控制

针对一类子系统为离散时延系统并且参数具有不确定性的切换系统,研究了鲁棒控制以及H∞扰动抑制问题。通过为每个子系统施加状态反馈并基于多李雅普诺夫函数法,分别给出了保证闭环系统渐近稳定的鲁棒控制器以及具有H∞扰动抑制性能控制器的设计方法。控制器参数可通过一组矩阵不等式获得,使用将待解不等式转化为双线性矩阵不等式并采用巡回迭代算法对其求解。通过仿真例子说明了设计方法的有效性。     

Robust controller for a class of uncertain switched fuzzy systems

A robustness control of uncertain switched fuzzy systems is presented. Using the switching technique and the Lyapunov function method, a continuous state feedback controller is built to ensure that for all allowable uncertainties the relevant closed-loop system is asymptotically stable. Furthermore, a switching strategy that achieves system global asymptotic stability of the uncertain switched fuzzy system is given. In this model, each subsystem of the switched system is an uncertain fuzzy system, and a common parallel distributed compensation controller is presented. The main condition is given in the form of convex combinations which are more solvable. This method transforms a certain switched system and has strong robustness for various system parameters. Simulations show the feasibility and the effectiveness of this method. Translated from Journal of Northeastern University, 2006, 27(7): 713–715 [译自: 东北大学学报 (自然科学版)]     

基于麦克斯韦应力法的双绕组无轴承开关磁阻电机新型数学模型

现有的双绕组无轴承开关磁阻电机麦克斯韦应力法数学模型忽略了相互垂直方向上径向悬浮力的耦合,但当转子偏离定转子齿极中心对齐位置较大时存在较强的耦合,故现有模型难以满足高精确度稳定悬浮控制要求。选择一种计及相互垂直方向悬浮力耦合的新积分路径,建立了基于麦克斯韦应力法的双绕组无轴承开关磁阻电机新型数学模型,同时为计及电机磁路的饱和特性,采用最小二乘法对铁心材料的非线性磁化曲线进行拟合,求解考虑磁饱和的各气隙磁密。通过与有限元仿真结果对比,验证了所建模型不仅揭示了相互垂直方向上径向悬浮力的耦合关系,考虑了磁饱和特性,且具有精确度良好、计算量小等优点,为实现高精度稳定悬浮控制奠定了基础。     

Fuzzy adaptive optimal control for nonlinear switched systems with actuator hysteresis

This article considers the issue of fuzzy adaptive dynamic programming control of nonlinear switched systems with arbitrary switchings and unknown uncertain functions and actuator hysteresis nonlinearities. The whole control approach is made of switching feedforward controller and optimal switching feedback controller. To get over the hardness of arbitrary switching structure and the issue of “explosion of complexity”, the common Lyapunov function theory and dynamic surface control method are utilized in the recursive design technique. By using fuzzy logic systems to model unknown inner dynamics and unknown cost functions, a novel fuzzy adaptive optimal switching control strategy is developed. Meanwhile, uniformly ultimately boundedness of all weights in the controlled systems are proved by the proposed control method, and the tracking performance is guaranteed in an optimal manner. Subsequently, a numerical simulation study is used to test the effectiveness of the presented control strategy.     

Switched adaptive stabilization of switched nonlinearly parameterized cascade systems and its application to a two inverted pendulums

This paper studies adaptive control of switched nonlinearly parameterized cascade systems. No solvability of the adaptive control problem for subsystems is required. By exploiting the multiple Lyapunov functions method and the parameter separation technique and the tool of adding a power integrator, we develop a new switched adaptive control approach for the explicit construction of adaptive controllers of subsystems and a proper switching law that solves the adaptive stabilization problem. A key feature of the proposed adaptive controllers is its switched property, namely, each subsystem has its individual update law. A two‐inverted pendulum as a practical example is also provided to demonstrate the effectiveness of the proposed design method. Copyright © 2014 John Wiley & Sons, Ltd.     

Switching‐based state tracking of model reference adaptive control systems in the presence of intermittent failures of all actuators

This paper investigates the state tracking problem for a class of model reference adaptive control systems with intermittent failures of all actuators. We consider the case that all actuators may suffer failures simultaneously. The concepts of failure frequency and unavailability rate are introduced to describe the failures. Because of the actuator failures, the error system is modeled as a switched system. Then, the notion of global practical stability of switched systems is presented, and sufficient conditions are provided to guarantee the global practical stability of the error system. An example of HiMAT vehicle and the simulation results demonstrate the feasibility and effectiveness of the proposed design method. Copyright © 2013 John Wiley & Sons, Ltd.     

基于换相过程控制的开关磁阻电动机转矩波动最小化研究

转矩波动是开关磁阻电动机较为突出的问题，在对开关磁阻电动机转矩模型分析的基础上，提出了一种控制策略用于解决换相过程中转矩平滑过渡的问题，详细讨论了该控制策略的一种在线控制方案，理论分析表明该方法能减小转矩波动，且效果较好，通过对12／4极三相开关磁阻电动机的仿真和实验研究，验证了所提方案的可行性。     

A small‐gain approach for adaptive output‐feedback NN control of switched pure‐feedback nonlinear systems

This paper investigates the problem of adaptive output‐feedback neural network (NN) control for a class of switched pure‐feedback uncertain nonlinear systems. A switched observer is first constructed to estimate the unmeasurable states. Next, with the help of an NN to approximate the unknown nonlinear terms, a switched small‐gain technique‐based adaptive output‐feedback NN control scheme is developed by exploiting the backstepping recursive design scheme, input‐to‐state stability analysis, the common Lyapunov function method, and the average dwell time (ADT) method. In the recursive design, the difficulty of constructing an overall Lyapunov function for the switched closed‐loop system is dealt with by decomposing the switched closed‐loop system into two interconnected switched systems and constructing two Lyapunov functions for two interconnected switched systems, respectively. The proposed controllers for individual subsystems guarantee that all signals in the closed‐loop system are semiglobally, uniformly, and ultimately bounded under a class of switching signals with ADT, and finally, two examples illustrate the effectiveness of theoretical results, which include a switched RLC circuit system.