高超声速飞行器非线性鲁棒控制律设计

高超声速飞行器具有模型非线性程度高、耦合程度强、参数不确定性大、抗干扰能力弱等特点,其自主控制具有较大的挑战.论文提出了一种基于鲁棒补偿技术和反馈线性化方法的非线性鲁棒控制方法.文中首先采用反馈线性化的方法对纵向模型进行输入输出线性化,实现速度和高度通道的解耦和非线性模型的线性化.针对得到的线性模型,设计包括标称控制器和鲁棒补偿器的线性控制器.基于极点配置原理,设计标称控制器使标称线性系统具有期望的输入输出特性,利用鲁棒补偿器来抑制参数不确定性和外界扰动对于闭环控制系统的影响.基于小增益定理,证明了闭环控制系统的鲁棒稳定性和鲁棒跟踪性能.相比于非线性回路成形控制方法,仿真结果表明了所设计非线性鲁棒控制算法的有效性和优越性.     

基于回路成形的鲁棒增益调度控制器设计

针对目前基于线性变参数系统的增益调度控制设计中存在的控制结构复杂性问题，提出一种基于回路成形的简单且易实现的增益调度控制结构.在此基础上，提出一个鲁棒增益调度控制设计方法.设计过程首先采用补偿器函数使得被控对象奇异值具有期望的形状，以保证被控对象的性能要求，然后利用小增益定理设计一个鲁棒控制器，得到具有良好性能的、结构简单的鲁棒增益调度控制器.最后针对一个化工过程，说明此方法的有效性.     

非线性不确定中立型系统的鲁棒H∞控制

考虑系统外界干扰、系统参数摄动等非线性扰动环节对中立型时滞系统的H∞影响,提出基于Lyapunov稳定性理论的鲁棒H∞控制器的设计思想.利用线性矩阵不等式(LMI)方法,给出了该类具有状态非线性不确定性中立型时滞系统的鲁棒∞控制器的设计实例.在非线性不确定函数满足增益有界的条件下,得到了该类时滞系统满足鲁棒∞性能的一个充分条件.通过求解一个线性矩阵不等式LMI,即可获得鲁棒∞控制器.仿真结果表明了基于Lyapunov稳定性理论,LMI技术设计的控制器克服了系统外界非线性干扰或系统本身非线性参数摄动的影响,实现了闭环系统的H∞性能条件下的渐近稳定,满足了该系统鲁棒H∞控制的要求.     

基于非线性干扰观测器的翼伞鲁棒反步跟踪控制

针对干扰条件下的无人翼伞飞行器路径跟踪控制问题,提出一种基于非线性干扰观测器的反馈增益鲁棒反步控制方法.采用二阶跟踪-微分器设计干扰观测器对系统复合干扰进行估计和补偿,设计了反馈增益反步跟踪控制律,通过合理设计增益参数,消除了部分复杂非线性项,避免了虚拟量高阶导数问题,简化了控制器形式.根据Lyapunov理论设计鲁棒反馈补偿项,在保证稳定性的同时提高了系统的鲁棒性.仿真实验结果验证了所提出方法的有效性.     

模糊输出反馈实现动态不确定非线性系统的几乎干扰解耦

研究一类单输入单输出动态不确定非线性系统的几乎干扰解耦问题. 首先设计一类新型的模糊高增益观测器估计非线性系统的未知状态; 然后结合自适应模糊backstepping 控制、小增益定理和改变供能函数方法, 给出鲁棒自适应模糊控制器的设计. 所设计的控制器不仅可以保证整个闭环系统在输入到状态实际稳定意义下稳定, 同时抑制了干扰对输出的影响. 仿真结果表明了所提出控制方法的有效性.

     

基于H∞回路成形的无人机纵向鲁棒控制器研究

针对无人机飞行参数及气动参数的不确定性问题,根据H∞理论,提出基于回路成形的无人机鲁棒控制器设计方法.以某小型无人机纵向控制系统为例,采用H∞回路成形设计方法,设计了俯仰角保持控制器;通过选取合适的预补偿器和后补偿器,改善系统奇异值曲线形状,应用小增益定理综合H∞鲁棒控制器,并得出鲁棒稳定裕度;进行数字仿真验证,在仿真中加入5 m/s常值风干扰与20％气动参数摄动等不确定性因素,结果表明,闭环系统能在受到干扰后1.1s恢复到平衡状态,且阶跃响应最大调节时间为1.6s,最大超调量为2.4％,说明所设计的控制器具有满意的抗干扰能力和鲁棒稳定性.     

近空间飞行器变增益非线性切换控制器设计

针对变后掠翼近空间飞行器大包络、多工作模态和模型不确定的特点,研究其模态切换过程中姿态的鲁棒跟踪控制问题.首先建立含扰动项的飞行器非线性切换模型,基于反步滑模方法和非线性干扰观测器设计鲁棒控制器,通过公共Lyapunov函数理论证明所设计的控制律能够保证闭环切换系统的稳定性;采用变增益切换控制策略为不同飞行模态设计合适的控制增益,用以提高系统的动态性能.仿真结果验证了所提出方法的有效性和必要性.     

基于FBFN 的鲁棒仿生学习系统设计及在运动平衡控制中的应用

针对两轮直立式机器人的运动平衡控制问题,结合OCPA 仿生学习系统,基于模糊基函数,设计了一 种鲁棒仿生学习控制方案．它不需要动力学系统的先验知识,也不需要离线的学习阶段．鲁棒仿生学习控制器主要 包括仿生学习单元、增益控制单元和鲁棒自适应单元3 部分．仿生学习单元由模糊基函数网络（FBFN）实现,FBFN 不仅执行操作行为产生功能,逼近动力学系统的非线性部分,同时也执行操作行为评价功能,并利用性能测量机制 提供的误差测量信号,产生取向值信息,对操作行为产生网络进行调整．增益控制单元的作用是确保系统的稳定性 和性能,鲁棒自适应单元的作用是消除FBFN 的逼近误差及外部干扰．此外,由于FBFN 的参数是基于李亚普诺夫 稳定性理论在线调整的,因此进一步确保了系统的稳定性和学习的快速性．理论上证明了鲁棒仿生学习控制器的稳 定性,仿真实验结果验证了其可行性和有效性．     

一类模糊P I D 控制器的鲁棒优化设计

研究一类模糊 PID控制器的鲁棒设计。以小增益定理分析得到该模糊 PID控制系统稳定性条件。针对参数摄动系统的“最坏点”,用该稳定性条件作为约束 ,采用遗传算法对标称系统的性能进行优化 ,求得优化鲁棒控制器。以倒立摆为例进行鲁棒模糊 PID控制器的设计 ,实验结果表明了该方法的有效性     

一类非仿射非线性不确定系统自适应鲁棒控制

针对一类结构和参数均未知且控制方向未知的不确定非仿射非线性系统,提出了一种鲁棒自适应控制算法.基于中值定理将非仿射系统转化为具有线性结构的时变系统,在此基础上,利用参数投影估计算法对有界时变参数进行辨识,参数辨识误差和外界干扰采用非线性阻尼项进行补偿.同时将动态面控制(DSC)和反推法相结合,消除了反推法的计算膨胀问题,并采用Nussbaum型函数处理系统中方向未知的不确定控制增益函数,避免了可能存在的控制器奇异值问题.最后,采用解耦反推,基于李雅普诺夫稳定性定理证明了闭环系统的半全局一致最终有界.仿真结果验证了所设计控制方案的可行性与有效性.     

Small-gain theory for stability and control of dynamical networks: A Survey

This paper provides a personal account of the small-gain theory as a tool for stability analysis, control synthesis, and robustness analysis for interconnected uncertain systems. A milestone in modern control theory is the development of a transformative stability criterion known as the classical small-gain theorem proposed by George Zames in 1966, that surpasses Lyapunov theory in that there is no need to construct Lyapunov functions for the finite-gain stability of feedback systems. Under the small-gain framework, a feedback system composed of two finite-gain stable subsystems remains finite-gain stable if the loop gain is less than one. Despite its apparent simplicity at first sight, Zames’s small-gain theorem plays a crucial role in the development of linear robust control theory. Borrowing techniques in modern nonlinear control, especially Sontag’s notion of input-to-state stability (ISS), the first generalized, nonlinear ISS small-gain theorem proposed by one of the authors in 1994 overcomes the two shortcomings of Zames’s small-gain theorem. First, the use of nonlinear gains allows to consider strongly nonlinear, interconnected systems. Second, the role of initial conditions is made explicit so that both internal Lyapunov stability and external input-output stability can be studied in a unified framework. In this survey paper, we first review early developments in the nonlinear small-gain theory for interconnected systems of various types such as continuous-time systems, discrete-time systems, hybrid systems and time-delay systems, along with applications in robust nonlinear control. Then, we describe how to obtain a network small-gain theory for large-scale dynamical networks that are comprised of more than two interacting nonlinear systems. Constructive methods for the generation of Lyapunov functions for the total network are presented as well. Finally, this paper discusses how the network/nonlinear small-gain theory can be applied to obtain innovative solutions to quantized and event-based nonlinear control problems, that are important for the development of a complete theory of controlling cyber-physical systems subject to communications and computation constraints.     

iISS and ISS dissipation inequalities: preservation and interconnection by scaling

In analysis and design of nonlinear dynamical systems, (nonlinear) scaling of Lyapunov functions has been a central idea. This paper proposes a set of tools to make use of such scalings and illustrates their benefits in constructing Lyapunov functions for interconnected nonlinear systems. First, the essence of some scaling techniques used extensively in the literature is reformulated in view of preservation of dissipation inequalities of integral input-to-state stability (iISS) and input-to-state stability (ISS). The iISS small-gain theorem is revisited from this viewpoint. Preservation of ISS dissipation inequalities is shown to not always be necessary, while preserving iISS which is weaker than ISS is convenient. By establishing relationships between the Legendre–Fenchel transform and the reformulated scaling techniques, this paper proposes a way to construct less complicated Lyapunov functions for interconnected systems.     

New results in global stabilization for stochastic nonlinear systems

This paper presents new results on the robust global stabilization and the gain assignment problems for stochastic nonlinear systems. Three stochastic nonlinear control design schemes are developed. Furthermore, a new stochastic gain assignment method is developed for a class of uncertain interconnected stochastic nonlinear systems. This method can be combined with the nonlinear small-gain theorem to design partial-state feedback controllers for stochastic nonlinear systems. Two numerical examples are given to illustrate the effectiveness of the proposed methodology.     

Input-to-state stability of infinite-dimensional control systems

We develop tools for investigation of input-to-state stability (ISS) of infinite-dimensional control systems. We show that for certain classes of admissible inputs, the existence of an ISS-Lyapunov function implies the ISS of a system. Then for the case of systems described by abstract equations in Banach spaces, we develop two methods of construction of local and global ISS-Lyapunov functions. We prove a linearization principle that allows a construction of a local ISS-Lyapunov function for a system, the linear approximation of which is ISS. In order to study the interconnections of nonlinear infinite-dimensional systems, we generalize the small-gain theorem to the case of infinite-dimensional systems and provide a way to construct an ISS-Lyapunov function for an entire interconnection, if ISS-Lyapunov functions for subsystems are known and the small-gain condition is satisfied. We illustrate the theory on examples of linear and semilinear reaction-diffusion equations.     

A Lyapunov-based small-gain theorem for interconnected switched systems

Stability of an interconnected system consisting of two switched systems is investigated in the scenario where in both switched systems there may exist some subsystems that are not input-to-state stable (non-ISS). We show that, providing the switching signals neither switch too frequently nor activate non-ISS subsystems for too long, a small-gain theorem can be used to conclude global asymptotic stability (GAS) of the interconnected system. For each switched system, with the constraints on the switching signal being modeled by an auxiliary timer, a correspondent hybrid system is defined to enable the construction of a hybrid ISS Lyapunov function. Apart from justifying the ISS property of their corresponding switched systems, these hybrid ISS Lyapunov functions are then combined to establish a Lyapunov-type small-gain condition which guarantees that the interconnected system is globally asymptotically stable.     

Input-to-state stability and gain computation for networked control systems

This paper studies the stability problem for networked control systems. A general result, called network gain theorem, is introduced to determine the input-to-state stability (ISS) for interconnected nonlinear systems. We show how this result generalises the previously known small gain theorem and cyclic small gain theorem for ISS. For the case of linear networked systems, a complete characterisation of the stability condition is provided, together with two distributed algorithms for computing the network gain: the classical Jacobi iterations and a message-passing algorithm. For the case of nonlinear networked systems, characterisation of the ISS condition can be done using M-functions, and Jacobi iterations can be used to compute the network gain.     

Nonlinear small-gain theorems for discrete-time feedback systems and applications

We derive in this work a local nonlinear small-gain theorem in the framework of input-to-state stability for discrete time systems. Our primary objective is to show that, as in the continuous-time context, these discrete-time nonlinear small-gain theorems are very effective in stability analysis and synthesis for various classes of discrete-time control systems. Two converse Lyapunov theorems for discrete exponential stability are developed to assist these applications. New results in stability and stabilization presented in this paper are significant extensions of previous work by other authors (IEEE Trans. Automat. Control 38 (1993) 1398; 39 (1994) 2340; 33 (1988) 1082).     

Input-to-state stability analysis for interconnected difference equations with delay

Input-to-state stability (ISS) of interconnected systems with each subsystem described by a difference equation subject to an external disturbance is considered. Furthermore, special attention is given to time delay, which gives rise to two relevant problems: (i) ISS of interconnected systems with interconnection delays, which arise in the paths connecting the subsystems, and (ii) ISS of interconnected systems with local delays, which arise in the dynamics of the subsystems. The fact that a difference equation with delay is equivalent to an interconnected system without delay is the crux of the proposed framework. Based on this fact and small-gain arguments, it is demonstrated that interconnection delays do not affect the stability of an interconnected system if a delay-independent small-gain condition holds. Furthermore, also using small-gain arguments, ISS for interconnected systems with local delays is established via the Razumikhin method as well as the Krasovskii approach. A combination of the results for interconnected systems with interconnection delays and local delays, respectively, provides a framework for ISS analysis of general interconnected systems with delay. Thus, a scalable ISS analysis method is obtained for large-scale interconnections of difference equations with delay.     

A degree of flexibility in Lyapunov inequalities for establishing input-to-state stability of interconnected systems

In this paper, a novel approach to constructing flexible Lyapunov inequalities is developed for establishing Input-to-State Stability (ISS) of interconnection of nonlinear time-varying systems. It aims at a useful tool for using nonlinear small-gain conditions by allowing some flexibility in Lyapunov inequalities each subsystem is to satisfy. In the application of the ISS small-gain “theorem”, achieving a Lyapunov inequality conforming to a nonlinear small-gain “condition” is not a straightforward task. The proposed technique provides us with many Lyapunov inequalities with which a single trade-off condition between subsystems gains can establish the ISS property of the interconnected system. Proofs are based on explicit construction of Lyapunov functions.     

Mean-square small gain theorem for stochastic control:discrete-time case

This paper presents a small gain theorem in the mean square sense for multiple (interconnected) linear systems with multiplicative noises. The small-gain theorem is proposed in terms of the spectral radius of a matrix, whose elements are the squares of H₂ norms of the involved transfer functions. Both robust stability and performance conditions are characterized by the new small-gain theorem