Backstepping design with local optimality matching

In nonlinear H^∞-optimal control design for strict-feedback nonlinear systems, our objective is to construct globally stabilizing control laws to match the optimal control law up to any desired order, and to be inverse optimal with respect to some computable cost functional. Our recursive construction of a cost functional and the corresponding solution to the Hamilton-Jacobi-Isaacs equation employs a new concept of nonlinear Cholesky factorization. When the value function for the system has a nonlinear Cholesky factorization, we show that the backstepping design procedure can be tuned to yield the optimal control law     

不确定非线性时滞系统鲁棒镇定化研究

The systematic recursive design method of the robust stabilizing controller for general uncertain nonlinear time-delay systems is investigated in this paper. A delay-independent state feedback control law can be obtained by recursively constructing Lyapunov-Razumikhin function. It is shown that by some design techniques the obstacle that is intrinsic to the application of the Razumikhin condition can be removed such that the design of the robust stabilizing control law is free of any restriction for the systems.     

不确定非线性时滞系统鲁棒镇定的进一步结果

针对广义的不确定非线性时滞系统，研究了其鲁棒镇定控制器的系统的递归设计方法。通过递归地构造Lyapunov-Razumikhin函数获得了一种独立于延时的状态反馈控制律。证明了通过一些设计技术处理，由Razumikhin 条件的应用所带来的固有的设计障碍是可以被克服的，从而使得系统鲁棒镇定控制器的获得不需要任何对系统的限制条件。     

Controlling chaos using invariant manifolds

An analytic non-linear control method based on the concept of macrovariable control is proposed to stabilize chaotic systems. The system trajectory is attracted to some selected invariant manifold by continuous feedback of system states which can be used as perturbations on an available system parameter or outer-force control. A recursive design procedure is also developed to guarantee the asymptotic stability of the system with saturated small controlling signal. The method is applied to stabilizing two typical chaotic non-linear systems at some equilibrium or periodic orbit.     

Integrator backstepping for rounded controls and control rates

We present a backstepping procedure for the design of globally stabilizing state feedback control laws such that the magnitudes of the control signals and their derivatives are bounded by constants which do not depend on the initial conditions. We accomplish this by propagating such boundedness properties through each step of the recursive design     

Adaptive state-feedback stabilization for a class of high-order nonlinear uncertain systems

For high-order nonlinear uncertain systems, there have been a lot of investigations under a strong assumption that the lower bounds of the unknown control coefficients should be exactly known. In this paper, this assumption is removed and a unified approach is developed to systematically construct a state-feedback adaptive stabilizing control law for a class of high-order nonlinear uncertain systems with unknown control coefficients. By using the method of the so-called adding a power integrator merging with adaptive technique, a recursive design procedure is provided to achieve a smooth adaptive state-feedback control law, which guarantees that the closed-loop system is globally uniformly stable while the original system states globally asymptotically converge to zero. Finally, a simulation example is given to illustrate the correctness of the theoretical results.     

Nonlinear learning control for a class of nonlinear systems

Based on the Lyapunov's direct method, a new learning control design is proposed. The proposed technique can be applied in two ways: it is either the standard backward recursive design or its extension. In the first case, the design yields a class of learning control with a difference learning law, under which the class of nonlinear systems is guaranteed to be asymptotically stable with respect to the number of trials in performing repeated tasks. However, implementation of the difference learning control requires derivative measurement of the state for guaranteed stability and performance, as required by most of the existing linear learning control laws. To overcome this difficulty, the proposed design extends the recursive design by employing a new state transformation and a new Lyapunov function, and it yields a class of learning control with a difference-differential learning law. Compared with the existing design methods most of which are based on linear analysis and design, the extension not only guarantees global stability and good performance but also removes such limitations as derivative measurement, Lipschitz condition, and resetting of initial conditions. In addition, the proposed design does not rely on the property of a system under consideration such as the input–output passivity.     

Design of stabilizing controllers of upper triangular nonlinear time-delay systems

In this paper, it is considered the state feedback controller design for a class of upper triangular nonlinear systems with simultaneous input and state delays. By using the state transformation of nonlinear systems, the problem of designing controller can be converted into that of designing a dynamic parameter, which is dynamically regulated by a dynamic equation. Then, by appraising the nonlinear terms of the given systems, a dynamic equation can be delicately constructed. At last, with the help of Lyapunov stability theorem, it is provided the stability analysis for the closed-loop system consisting of the designed controller and the given systems. Both discrete delays and continuous delays with integral form are considered here. Different from many existing control designs for upper triangular nonlinear systems, neither forwarding recursive nor saturation computation is utilized here, and thus our design procedure is simpler. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.     

Recursive Observer Design, Homogeneous Approximation, and Nonsmooth Output Feedback Stabilization of Nonlinear Systems

We present a nonsmooth output feedback framework for local and/or global stabilization of a class of nonlinear systems that are not smoothly stabilizable nor uniformly observable. A systematic design method is presented for the construction of stabilizing, dynamic output compensators that are nonsmooth but HÖlder continuous. A new ingredient of the proposed output feedback control scheme is the introduction of a recursive observer design algorithm, making it possible to construct a reduced-order observer step-by-step, in a naturally augmented manner. Such a nonsmooth design leads to a number of new results on output feedback stabilization of nonlinear systems. One of them is the global stabilizability of a chain of odd power integrators by HÖlder continuous output feedback. The other one is the local stabilization using nonsmooth output feedback for a wide class of nonlinear systems in the Hessenberg form studied in a previous paper, where global stabilizability by nonsmooth state feedback was already proved to be possible.     

Global set‐point tracking control for a class of nonlinear systems with iISS inverse dynamics

In this paper, we consider the problem of global set‐point tracking control for a class of nonlinear systems with dynamic uncertainty. Unlike the existing works, the investigated system is with the integral input‐to‐state stable (iISS) inverse dynamics and more general uncertain nonlinearities. By using a recursive design method, a partial‐state feedback controller is designed. The tuning function technique is applied in this procedure to avoid the overparametrization. It is shown that the developed control procedure could guarantee that the tracking error is driven to the origin and the other signals are bounded. In addition, it can also reduce to a linear or even a classical PI control law under some sufficient conditions. Simulation results are illustrated to show the effectiveness of the proposed algorithm. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

一类带不确定输入动态非线性系统的输出反馈鲁棒镇定

研究一类带不确定输入动态非线性系统的输出反馈鲁棒镇定问题.通过在高增益观测器引入新的设计参数,改进了通常的高增益反馈控制的设计方法.在输入动态满足零相对阶最小相位的假设下,基于非分离设计原则给出了动态输出反馈控制器的设计方法,所设计的控制器实现了对任意可允许不确定输入动态的全局鲁棒镇定.     

Adaptive control for a class of large scale non-linear systems

The design of stabilizing controllers for multi-input multi-output (MIMO) non-linear plants with unknown non-linearities is a challenging problem. The inability to identify the non-linearities on-line or off-line accurately motivates the design of stabilizing controllers based on approximations or on approximate estimates of the plant non-linearities. However, the design of a centralized controller for large scale non-linear systems is often complex due to the high dimensionality and difficulty to implement in real time. In this paper a decentralized-like non-linear adaptive control algorithm is designed and analysed for a class of large scale non-linear systems with unknown non-linearities. The controller guarantees closed loop semi-global stability and convergence of the tracking error to a small residual set whose size can be specified a priori provided the neglected in the control design non-linear interconnections are small relative to the modelled non-linear parts. A procedure for choosing the various design parameters to guarantee that the tracking error bound will converge to within the specified a priori bound is presented. Even though the proposed controller is not purely decentralized it does reduce computations and makes the control design easier than a corresponding centralized approach.     

A new approach to adaptive control design without overparametrization for a class of uncertain nonlinear systems

This paper considers the globally stabilizing adaptive controller design for a class of more general uncertain high-order nonlinear systems with unknown control coefficients.Although the existing literature has solved the problem,for n-dimensional systems,the existing methods need at least n + 1 dynamic updating laws for the unknown parameters to construct the stabilizing adaptive controller;that is,the dimension of the dynamic compensator is not less than n + 1,and therefore,there exists serious overparame...     

一类不确定非线性系统无过参数自适应控制设计新方法

文中研究了一类控制系数未知的更一般高阶不确定非线性系统的全局稳定自适应控制设计问题.尽管现有文献已解决了该问题,但对于n维系统,现有构造稳定自适应控制的方法至少需要设计n+1个未知参数的动态调节律,即动态补偿器的维数至少为n+1,存在较为严重的过参数问题.文中通过定义新的需动态调节的未知参数,运用增加幂积分和有关自适应技术,成功地解决了已有方法中的过参数问题,给出了构造只含有一个参数调节律的稳定自适应控制设计新方法.仿真算例验证了文中所给方法的有效性.     

Improved Controller Design with Two Gain-scaling Factors for Global Asymptotic Stabilization of Nonlinear Systems via Matrix Inequality Approach

In this paper, we consider a problem of global asymptotic stabilization for nonlinear systems with the perturbed nonlinearity. We provide a stabilizing controller with two gain-scaling factors and a new controller design method with matrix inequality approach. In particular, we provide a new procedure for selecting gain-scaling factors which are associated with stabilizing the closed-loop system. As a result, our proposed control method widens the class of considered nonlinear systems and yields better control performance over the existing methods. Via several comparison examples, we illustrate the improved features of the proposed control method over the existing ones.

     

Immersion and invariance: a new tool for stabilization and adaptive control of nonlinear systems

A new method to design asymptotically stabilizing and adaptive control laws for nonlinear systems is presented. The method relies upon the notions of system immersion and manifold invariance and, in principle, does not require the knowledge of a (control) Lyapunov function. The construction of the stabilizing control laws resembles the procedure used in nonlinear regulator theory to derive the (invariant) output zeroing manifold and its friend. The method is well suited in situations where we know a stabilizing controller of a nominal reduced order model, which we would like to robustify with respect to higher order dynamics. This is achieved by designing a control law that asymptotically immerses the full system dynamics into the reduced order one. We also show that in adaptive control problems the method yields stabilizing schemes that counter the effect of the uncertain parameters adopting a robustness perspective. Our construction does not invoke certainty equivalence, nor requires a linear parameterization, furthermore, viewed from a Lyapunov perspective, it provides a procedure to add cross terms between the parameter estimates and the plant states. Finally, it is shown that the proposed approach is directly applicable to systems in feedback and feedforward form, yielding new stabilizing control laws. We illustrate the method with several academic and practical examples, including a mechanical system with flexibility modes, an electromechanical system with parasitic actuator dynamics and an adaptive nonlinearly parameterized visual servoing application.     

Constructive Lyapunov stabilization of nonlinear cascade systems

We present a global stabilization procedure for nonlinear cascade and feedforward systems which extends the existing stabilization results. Our main tool is the construction of a Lyapunov function for a class of (globally stable) uncontrolled cascade systems. This construction serves as a basis for a recursive controller design for cascade and feedforward systems. We give conditions for continuous differentiability of the Lyapunov function and the resulting control law and propose methods for their exact and approximate computation     

一类高阶非线性不确定系统自适应稳定控制

研究了一类高阶非线性不确定性系统的自适应稳定控制设计问题.因该系统的非线性程度高,其控制系数不等同、符号已知、但数值未知,故在此之前其稳定控制设计问题没有得到解决.本文应用自适应技术,结合设计参数的适当选取,从而得到了设计该类非线性系统状态反馈稳定控制器的新方法,并基于反推技术,给出了稳定控制器的设计步骤.所设计的状态反馈控制器使得闭环系统的状态全局渐近收敛于零,其余闭环信号一致有界.最后通过一个仿真例子说明了控制设计方法的有效性.     

Robust control of nonlinear systems by estimating time variantuncertainties

In this paper, robust control design is considered for nonlinear systems with time-variant uncertainties. Instead of assuming that the bounding function on uncertainties is either known or parameterizable in terms of unknown constants, uncertainties or their bounding functions are estimated. It is shown that bounded uncertainties from a known or partially known exo-system can be estimated as a part of a globally stabilizing robust control. The proposed method extends the existing results of adaptive robust control, and it makes robust control more applicable by requiring less information on uncertainties     

Adaptive output feedback control for a class of planar nonlinear systems

This paper is concerned with the problem of global adaptive stabilization by output feedback for a class of planar nonlinear systems with uncertain control coefficient and unknown growth rate. The control coefficient is not supposed to have known upper bound, and this relaxes the corresponding requirement in the existing literature (see e.g. 1 , 2 . First, by the universal control method, an observer is constructed based on the dynamic high‐gain K‐filters. Then, the control design procedure is developed to obtain the stabilizing controller and dynamic compensator for the uncertainties in the control coefficient. It is shown that the global stability of the closed‐loop system can be guaranteed by the appropriate choice of the design parameters. A simulation example is also provided to illustrate the correctness of the theoretical results. © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society.