Averaging of nonsmooth systems using dither

It was shown by Zames and Shneydor and later by Mossaheb that a high-frequency dither signal of a quite arbitrary shape can be used to narrow the effective nonlinear sector of Lipschitz continuous feedback systems. In this paper, it is shown that also discontinuous nonlinearities of feedback systems can be narrowed using dither, as long as the amplitude distribution function of the dither is absolutely continuous and has bounded derivative. The averaged system is proven to approximate the dithered system with an error of the order of dither period.     

Feedback stabilization for a class of discontinuous systems driven by integrator

This paper investigates the feedback stabilization problem for a class of discontinuous systems which is characterized by Filippov differential inclusion. Lyapunov-based backstepping design method is generalized with nonsmooth Lyapunov functions to solve the control problem. A set-valued time derivative is introduced first for nonsmooth function along discontinuous vector fields, which enables us to perform Lyapunov-based design with nondifferentiable Lyapunov function. Conditions for designing a virtual control law which is shown nondifferentiable in general in the recursive design problem are proposed. Finally, as a special case, piecewise linear system is discussed to demonstrate the application of the presented design approach.     

ISS properties of nonholonomic vehicles

The paper presents the first result on nonholonomic systems enjoying input to state stability (ISS) properties. Although it is known that smooth stabilizability implies ISS, the converse is not generally true. This leaves the possibility of non-smoothly stabilizable systems being ISS with respect to a particular input, after an appropriate feedback transformation. This is shown to be true for the case of the unicycle with a dynamic extension, in a particular topology induced by a metric appropriate for this type of systems. A feedback control law renders the closed-loop system locally ISS in the particular topology. Potential applications include stability and robustness analysis of formations of mobile robots.     

State and output feedback stabilization of multiple chained systems with discontinuous control

The problem of state and output feedback stabilization of nonholonomic multiple chained systems is addressed and solved using a particular class of discontinuous control laws. The obtained control laws are relatively simple, compared with others existing in the current literature, and guarantee exponential convergence of the closed-loop system. A simulation example, showing the main features of the proposed controllers, is enclosed.     

A nonsmooth IMC method for mechanical systems with backlash

This paper proposes a discrete-time nonsmooth internal model control （NSIMC） approach for mechanical transmission systems described by so-called sandwich system with backlash. In this method, a dynamic compensator is introduced to compensate for the effect of the input linear subsystem. Thus, the sandwich systems with backlash can be simplified as a pseudo-Hammerstein system with backlash. The corresponding NSIMC strategy is designed to control this system. The design procedure of the controller is presented based on the analysis on the robust stability by considering the model errors involved with the effect of backlash as well as the compensated error of the input linear subsystem. Moreover, as the model is switched among the different operating zones, the robust filters are proposed to guarantee the robust stability and satisfactory control performance of the system.     

基于Backstepping 的非仿射非线性系统鲁棒控制

针对一类不确定非仿射非线性系统的跟踪控制问题, 提出一种鲁棒Backstepping 控制策略. 首先, 为利用仿 射非线性方法设计控制器, 给出一种适用于全局的非仿射非线性近似方法; 然后, 设计快速收敛非线性微分器以估计复合干扰和获取虚拟信号的微分, 进而给出不确定非仿射非线性系统的复合控制器, 其中鲁棒项和阻尼项分别用于减少逼近误差和近似方法中动态误差对系统跟踪的影响; 最后, 通过仿真实验验证了所提出方法的有效性.     

On the controllability of piecewise-linear hypersurface systems

This paper investigates the global controllability of piecewise-linear (hypersurface) systems, which are defined as control systems that are subject to affine dynamics on each of the components of a finite polyhedral partition. Various new tools are developed for the study of the problem including a classification of the facets of the polyhedra in the partition. Necessary and sufficient conditions for complete controllability are obtained via the study of a suitably defined controllability connection matrix of polyhedra.     

Stabilization of nonholonomic chained systems via nonregular feedback linearization

This paper addresses the problem of feedback stabilization of nonholonomic chained systems within the framework of nonregular feedback linearization. Firstly, the nonsmooth version of nonregular feedback linearization is formulated, and a criterion for nonregular feedback linearization is provided. Then, it is proved that the chained form is linearizable via nonregular feedback control, thus enable us to design feedback control laws using standard techniques for linear systems. The obtained discontinuous control laws guarantee convergence of the closed-loop system with exponential rates. Finally, simulation results are presented to show the effectiveness of the approach.     

非完整移动机器人的反步跟踪控制方法

移动机器人是典型的非完整系统,对其进行运动控制是一个热点且是一项具有挑战性的工作.目前的大部分研究都是基于运动学模型的,而在实际应用中,动力学特性不可忽视.针对轨迹跟踪这一典型控制任务,文中对一种轮式移动机器人进行了动力学建模.利用反步技术,提出了一种控制结构,综合了速度控制器和力矩控制器.该控制律不但能够得到稳定跟踪所需要的速度,而且同时能够计算出驱动移动机器人行进的电机力矩.仿真结果表明,该控制律可以良好地工作.控制结构的通用性保证了其他控制方法拓展的可能性.     

Robust stabilization for nonholonomic systems with state delay and nonlinear drifts

This paper presents a control strategy for stabilization of the nonholonomic control systems with strongly nonlinear drifts and state delay.Applying a novel Lyapunov functional and backstepping recursive method,the design of robust nonlinear state feedback controllers is proposed,which can guarantee the stability of the closed-loop systems.Finally,a numerical example is provided to show the effectiveness of the method.     

Discontinuous exponential stabilization of chained form systems

In this paper a novel approach to exponential stabilization of chained form system is proposed. Provided that the control law fulfills mild assumptions, it is shown that a Brunovsky-like change of coordinates depending on the control transforms any chained form system into a system having a linearly bounded nonlinear part. Using linear tools, it is possible to exponentially stabilize a chained form system for any initial condition outside a submanifold containing the origin. This result is then generalized to global exponential stabilization. The so obtained static discontinuous feedback is bounded for bounded states and exponentially converges to zero along the closed-loop trajectories of the system.     

Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching

A more general class of stochastic nonlinear systems with irreducible homogenous Markovian switching are considered in this paper. As preliminaries, the stability criteria and the existence theorem of strong solutions are first presented by using the inequality of mathematic expectation of a Lyapunov function. The state-feedback controller is designed by regarding Markovian switching as constant such that the closed-loop system has a unique solution, and the equilibrium is asymptotically stable in probability in the large. The output-feedback controller is designed based on a quadratic-plus-quartic-form Lyapunov function such that the closed-loop system has a unique solution with the equilibrium being asymptotically stable in probability in the large in the unbiased case and has a unique bounded-in-probability solution in the biased case.     

Discontinuous control of nonholonomic systems

The problem of asymptotic convergence for a class of nonholonomic control systems via discontinuous control is addressed and solved from a new point of view. It is shown that control laws, which ensures asymptotic (exponential) convergence of the closed-loop system, can be easily designed if the system is described in proper coordinates. In such coordinates, the system is discontinuous. Hence, the problem of local asymptotic stabilization for a class of discontinuous nonholonomic control systems is dealt with and a general procedure to transform a continuous system into a discontinuous one is presented. Moreover, a general strategy to design discontinuous control laws, yielding asymptotic convergence, for a class of nonholonomic control systems is proposed. The enclosed simulation results show the effectiveness of the method.     

Discontinuous control of high-order generalized chained systems

The stabilization problem for nonlinear systems in a generalized high-order chained form is solved by means of discontinuous state feedback control laws. The proposed controllers yield exponential convergence of the states to the origin. Moreover, the design does not require the precise knowledge of the system parameters. The method is applied to an underactuated surface vessel and a mobile robot moving on an uneven surface and its effectiveness is demonstrated through simulations.     

磁悬浮系统的基于RBF网络的自适应反推控制

针对一类磁悬浮系统,研究了基于RBF网络的自适应反推控制器的设计和分析问题.首先在较弱的条件下,通过引入一监督控制,保证了闭环系统的状态落入一紧集中;然后通过RBF网络的逼近性质和反推设计技术,给出了一种鲁棒自适应控制器的设计;最后利用Lyapunov稳定性理论,严格地分析了这种自适应控制系统的稳定性和跟踪性能.     

TCSC控制的一种新自适应Backstepping方法

针对带有TCSC（Thyristor Controlled Series Compensator）的单机无穷大电力系统,提出一种新的TCSC自适应非线性控制Backstepping方法．该方法不仅保留了系统的非线性特性和对未知参数的实时在线估计,而且突破了经典的确定性等价性原理来设计参数估计器和动态反馈控制器．仿真结果表明,与基于传统自适应Backstepping得到的控制设计相比较,这种新方法在系统响应和自适应速度方面具有更优越的性能,从而为工程应用提供了一种有效的选择．     

On the variable structure control approach with sliding modes to robust finite-time consensus problems: A methodological overview based on nonsmooth analysis

When controlling cyber–physical systems via consensus algorithms, the robustness issue is of paramount importance because of model mismatching and/or disturbances that generally modify the Laplacian flow dynamics associated to the overall network, compromising the possibility to achieve any expected, orchestrated emergent behavior. To face this issue, the Variable Structure Control (VSC) approach has recently been shown to be an effective tool in designing control protocols over networks, providing robustness and often yielding finite-time convergence. Moreover, VSC further enables the decoupling of simultaneous control objectives where reaching a consensus state is only part of a more complex task, for instance as it happens in distributed optimization. Thus motivated, this paper overviews, from a tutorial perspective, some selected recent advances in the application of VSC with Sliding Modes to design robust consensus controllers in both the leader-less and the leader-following settings. Efforts are also made to unify the notation and to discuss the theoretical foundations of the nonsmooth analysis tools at the basis of their design for a wide readership unfamiliar with these problems and formal tools. To this aim, examples supporting the treatment, and numerical simulations, are given and discussed in detail. Finally, hints for future investigations along with some current open problems are provided.     

基于矩阵分解的多变量鲁棒自适应反推控制

针对含有输入未建模动态的一类MIMO系统,在高频增益矩阵的顺序主子式的符号已知的前提下,给出了多变量自适应反推控制器的设计.严格地证明了对一类未建模动态,闭环适应系统的所有信号都是全局一致有界的,且输出渐近收敛于零.     

Backstepping control integrated with Lyapunov-based model predictive control

In this study, backstepping control integrated with Lyapunov-based model predictive control (BS-MPC) is proposed for nonlinear systems in a strict-feedback form. The virtual input of the first step is designed by solving the finite-horizon optimal control problem (FHOCP), and the real input is designed by the backstepping method. BS-MPC guarantees (semiglobal) ultimate boundedness of the closed-loop system when the control is implemented in a zero-order hold manner. When the robustness of BS-MPC is analyzed for uniformly bounded disturbances, the ultimate boundedness of the solution of perturbed system is guaranteed. BS-MPC can provide a better desired value of the virtual input of the first step by solving the FHOCP, resulting in a faster stabilization of the system compared with the backstepping control. In addition, BS-MPC requires less computational load compared with MPC because the dimension of the states considered in the on-line optimization problem of BS-MPC is lower than that of MPC.     

Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings

This paper is concerned with the global stabilization problem for switched nonlinear systems in lower triangular form under arbitrary switchings. Two classes of state feedback controllers and a common Lyapunov function (CLF) are simultaneously constructed by backstepping. The first class uses the common state feedback controller which is independent of switching signals; the other class utilizes individual state feedback controllers for the subsystems. As an extension of the designed method, the global stabilization problem under arbitrary switchings for switched nonlinear systems in nested lower triangular form is also studied. An example is given to show the effectiveness of the proposed method.