Regional averaged controllability for hyperbolic parameter dependent systems

The purpose of this paper is to extend the notion of regional controllability for hyperbolic parameter dependent systems. The key idea is the characterization of the textit{averaged regional control} with minimal energy. This control steers the state average (with respect to such a parameter) towards the desired state only on a given part of the system evolution domain. In this paper, we give the precis definition and the properties of this new concept. Then, we use an approach based on an extension of the Hilbert uniqueness method devoted to the calculation of the control in two different cases: zone control and pointwise control.     

Redesign of adaptive observers for improved parameter identification in nonlinear systems

We propose a method for redesigning adaptive observers for nonlinear systems. The redesign uses an adaptive law that is based on delayed observers. This increases the computational burden, but gives significantly better parameter identification and robustness properties. In particular, given that a special persistency of excitation condition is satisfied, we prove uniform global asymptotic stability and semi-global exponential stability of the origin of the state and parameter estimation error, and give explicit lower bounds on the convergence rate of both the state and parameter estimation error dynamics. For initial conditions with a known upper bound, we prove tunable exponential convergence rate. To illustrate the use of the proposed method, we apply it to estimate the unmeasured flow rate and the uncertain friction parameters in a model of a managed pressure drilling system. The simulation results clearly show the improved performance of the redesigned adaptive observer compared to a traditional design.     

一类非线性系统镇定问题的分层控制方法

通过利用分层控制设计方法,研究了一类仿射非线性系统的镇定问题.为了镇定这类系统,分层方法构建了一个简单的抽象系统,然后根据抽象系统的控制律求得原始系统的控制律.最后,一个四维仿射非线性系统的仿真例子说明了这种方法的有效性.     

Recursive estimation in piecewise affine systems using parameter identifiers and concurrent learning

Piecewise affine systems constitute a popular framework for the approximation of non-linear systems and the modelling of hybrid systems. This paper addresses the recursive subsystem estimation in continuous-time piecewise affine systems. Parameter identifiers are extended from continuous-time state-space models to piecewise linear and piecewise affine systems. The convergence rate of the presented identifiers is improved further using concurrent learning, which makes concurrent use of current and recorded measurements. In concurrent learning, assumptions on persistence of excitation are replaced by the less restrictive linear independence of the recorded data. The introduction of memory, however, reduces the tracking ability of concurrent learning because errors in the recorded measurements prevent convergence to the true parameters. In order to overcome this limitation, an algorithm is proposed to detect and remove erroneous measurements at run-time and thereby restore the tracking ability. Detailed examples are included to validate the proposed methods numerically.     

On global controllability of affine nonlinear systems with a triangular-like structure

In this paper, we investigate a class of affine nonlinear systems with a triangular-like structure and present its necessary and sufficient condition for global controllability, by using the techniques developed by Sun Yimin and Guo Lei recently. Furthermore, we will give two examples to illustrate its application.     

Well-posed problem of nonlinear singular distributed parameter systems and nonlinear GE-semigroup

According to the well-posed problem of nonlinear singular distributed parameter systems, first of all, the nonlinear GE-semigroup induced by a continuous （possibly nonlinear） operator is introduced in Banach space, which is a generalization of GE-semigroup （i.e., generalized operator semigroup）, and the properties of nonlinear GE-semigroup are discussed; and then the existence, uniqueness and constructive expression for the strong solution of nonlinear singular distributed parameter system are discussed by nonlinear GE-semigroup; at last, the exponential stability of nonlinear singular distributed parameter system is studied by using nonlinear GE-semigroup, functional analysis and operator theory in Banach space.     

Output regulation of nonlinear output feedback systems with exponential parameter convergence

This paper revisits the global robust output regulation (GROR) problem of nonlinear output feedback systems with uncertain exosystems by error output feedback control. The problem was conventionally tackled by employing a linear canonical internal model and as a result, suitable adaptive stabilization has to be done for the augmented system to achieve output regulation. Distinguished from that, a novel nonlinear internal model approach is developed in the present study that successfully converts the GROR problem into a robust non-adaptive stabilization problem for the augmented system. The feature of the new approach is two-fold. On one hand, stabilization of augmented system is disentangled from any extra adaptive control law and thus the procedure is simplified. On the other hand, it leads to explicit strict Lyapunov characterization for the closed-loop system and consequently assures exponential parameter convergence.     

A Galerkin discretisation-based identification for parameters in nonlinear mechanical systems

In the paper, a new parameter identification method is proposed for mechanical systems. Based on the idea of Galerkin finite-element method, the displacement over time history is approximated by piecewise linear functions, and the second-order terms in model equation are eliminated by integrating by parts. In this way, the lost function of integration form is derived. Being different with the existing methods, the lost function actually is a quadratic sum of integration over the whole time history. Then for linear or nonlinear systems, the optimisation of the lost function can be applied with traditional least-squares algorithm or the iterative one, respectively. Such method could be used to effectively identify parameters in linear and arbitrary nonlinear mechanical systems. Simulation results show that even under the condition of sparse data or low sampling frequency, this method could still guarantee high accuracy in identifying linear and nonlinear parameters.     

Robust output-feedback control for stochastic nonlinear systems with modeling errors

In this paper,the stabilization problem of a stochastic nonlinear system with modeling errors is considered. An augmented observer is first presented to counteract the unmeasurable states as well as modeling errors.An adaptive output feedback controller is designed such that all signals in the closed-loop system are bounded in probability and the output is regulated to the origin almost surely.     

On tracking control for affine nonlinear systems by sliding mode

The stability problem of output tracking of a bounded time-varying reference by decouplable affine nonlinear systems using sliding mode control is investigated. It is shown that when the error dynamics on the sliding surface is chosen to be linear time-invariant, closed loop stability of systems under the presented sliding mode control can be guaranteed only if the systems are minimum phase.     

Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties

In this paper, we consider discrete time systems with polytopic time varying uncertainty. We look for a class of parameter dependent Lyapunov functions which are quadratic on the system state and depend in a polytopic way on the uncertain parameter. We show that extending the new discrete time stability condition proposed by de Oliveira et al. (Systems Control Lett. 36 (1999) 135.) to the case of time varying uncertainty leads to a necessary and sufficient condition for the computation of such a Lyapunov function. This allows to check asymptotic stability of the system under study. The obtained linear matrix inequalities condition can also be used to cope with the control synthesis problem.     

Controller design for a class of nontriangular nonlinear systems with input dependent growth rate

In this paper, we consider the global control problem for a class of high‐order nonlinear systems in the nontriangular form. Compared with the existing results, the growth rate of the nonlinearities depends on the control input, which cannot be dominated by the traditional constant gain. Under the assumption that the nonlinear terms satisfy the homogeneous growth conditions, a dynamic state‐feedback controller is elaborately designed to stabilize the system based on the adding a power integrator technique and the domination methodology. Moreover, by choosing the dynamic gain appropriately, the assumptions on the nonlinearities can be further relaxed to the polynomial case. Numerical simulations are provided to show the effectiveness of the proposed control laws.     

Stability analysis of linear time-varying systems: Improving conditions by adding more information about parameter variation

In this paper a new Lyapunov function is proposed for stability analysis of linear time-varying systems. This new function carries more information regarding parameter variation leading to less conservative conditions. Using Finsler’s lemma and a suitable form to describe the high-order time-derivatives of the parameters, finite sets of LMIs are obtained which are progressively less conservative as a pair of parameters grow. Previous results can be seen as a special case and numerical examples are carried out for the sake of illustration.     

Classification and stabilizability analysis of bimodal piecewise affine systems

This paper presents a classification of bimodal piecewise affine systems from the viewpoint of well‐posedness. First, we address the feedback well‐posedness problem of a general class of bimodal piecewise affine systems, which is the problem of feedback equivalence to a well‐posed system. Next, based on this result, we classify all feedback well‐posed systems into four classes to address the control problem of piecewise affine systems in a systematic way. As its application, the stabilizability problem with well‐posedness is discussed for each class, and several remarks on stabilizability are given. Copyright © 2002 John Wiley & Sons, Ltd.     

约束不确定非线性系统的鲁棒优化镇定

针对状态和输入约束不确定非线性仿射系统,提出一种鲁棒镇定的优化控制器设计方法.基于弱鲁棒控制Lyapunov函数概念,构造一个参数可调控制器.再利用LaSalle定理和逆优化理论,验证该控制器的鲁棒镇定性和逆最优性.进一步,采用滚动优化原理在线计算控制器的可调参数,实现闭环系统的鲁棒优化镇定.最后对一个开环不稳定振荡器系统进行鲁棒优化镇定,其结果验证了文中方法的有效性.     

State‐dependent switching law design with guaranteed dwell time for switched nonlinear systems

In this article, without the help of predesigned dwell time constraints, a new state‐dependent switching law with guaranteed dwell time for switched nonlinear systems is studied. Some sufficient conditions for asymptotic stability of switched nonlinear systems are derived. Also, all the abovementioned conditions can be transformed to a set of sum of squares (SOS) constraints, which can be checked by using the bilinear SOS methodology. Meanwhile, an improved path following method is provided to solve a bilinear SOS problem. Finally, three simulation examples are given to demonstrate the effectiveness of the obtained results.     

Set membership state and parameter estimation for systems described by nonlinear differential equations

This paper investigates the use of guaranteed methods to perform state and parameter estimation for nonlinear continuous-time systems, in a bounded-error context. A state estimator based on a prediction-correction approach is given, where the prediction step consists in a validated integration of an initial value problem for an ordinary differential equation (IVP for ODE) using interval analysis and high-order Taylor models, while the correction step uses a set inversion technique. The state estimator is extended to solve the parameter estimation problem. An illustrative example is presented for each part.     

具有零动态的SISO仿射非线性系统的神经网络自适应跟踪控制

针对具有零动态的SISO仿射非线性系统提出了一种神经网络直接自适应跟踪控制方法.采用梯度下降算法最小化未知理想控制器与神经网络控制器的误差代价函数以获得参数自适应律,控制器中无需另加鲁棒控制项.基于Lyapunov稳定性定理证明了在该控制器的作用下能保证输出跟踪误差及相应闭环系统的所有状态最终一致有界及神经网络参数的收敛性.仿真结果验证了该文方法的有效性.     

A dual‐observer approach for global output feedback stabilization of planar nonlinear systems with output‐dependent growth rates

In this paper, we investigate the problem of global output feedback stabilization for a class of planar nonlinear systems under a more general growth condition, which encompasses both lower‐order and higher‐order state growths with output‐dependent rates. For more accurate estimation, two new observers with nonlinear gains are constructed to estimate the states on the lower‐order and higher‐order scales, respectively. The estimates produced from the dual‐observer are used delicately in the output feedback control law with both lower‐order and higher‐order modes. The overall stability of the system is guaranteed by rigorously choosing these nonlinear gains in the control law and the dual‐observer.     

一类不确定非线性离散时滞系统的鲁棒H∞滤波设计

考虑一类同时带有非线性动态和参数不确定性的离散时滞系统的鲁棒H∞滤波设计问题．假设参数不确定性具有线性分式形式,而非线性动态满足Lipschitz条件,给出滤波器使误差系统鲁棒渐近稳定且达到指定的干扰抑制水平．对参数已知情形,先建立广义有界实引理,然后给出H∞滤波器的存在条件,证明了H∞滤波器的存在性可归结为线性矩阵不等式的可解性,基于线性矩阵不等式给出了H∞滤波器的综合方法和步骤．对参数不确定性情形,通过引进标度参数,将不确定非线性离散时滞系统的鲁棒H∞滤波问题转化为确定系统的H∞滤波设计．最后给出仿真例子验证所得结果的有效性．