一类非线性系统的微分平滑反步自适应输出反馈控制

研究了一类含不确定参数且存在未知扰动的严反馈非线性系统输出反馈控制问题,设计了一种新型的反步递推(Backstepping)自适应控制器.为实现输出反馈,设计过程引入了虚拟的全维状态观测器.由于Backstepping的虚拟控制量与未知参数逼近值及其高阶导数有关,为此通过微分平滑算法对原系统进行相应的动态扩展.在稳定性分析中,利用Lyapunov定理,得到了系统全局一致有界稳定的条件,并求出系统的稳态跟踪误差.最后给出的仿真算例验证了本文方法的有效性和可行性.     

Constrained anti-disturbance control for a quadrotor based on differential flatness

The classical control design based on linearised model is widely used in practice even to those inherently nonlinear systems. Although linear design techniques are relatively mature and enjoy the simple structure in implementations, they can be prone to misbehaviour and failure when the system state is far away from the operating point. To avoid the drawbacks and exploit the advantages of linear design methods while tackling the system nonlinearity, a hybrid control structure is developed in this paper. First, the model predictive control is used to impose states and inputs constraints on the linearised model, which makes the linearisation satisfy the small-perturbation requirement and reduces the bound of linearisation error. On the other hand, a combination of disturbance observer-based control and H_∞ control, called composite hierarchical anti-disturbance control, is constructed for the linear model to provide robustness against multiple disturbances. The constrained reference states and inputs generated by the outer-loop model predictive controller are asymptotically tracked by the inner-loop composite anti-disturbance controller. To demonstrate the performance of the proposed framework, a case study on quadrotor is conducted.     

The geometry,controllability, and flatness property of the n-bar system

We propose a kinematic model of a system moving in an (m?+?1)-dimensional euclidean space and consisting of n rigid bars attached successively to each other and subject to the nonholonomic constraints that the instantaneous velocity of the source point of each bar is parallel to that bar. We prove that the associated control system is controllable and feedback equivalent to the m-chained form around any regular configuration. As a consequence, we deduce that the n-bar system is flat and show that the Cartesian position of the source point of the last (from the top) bar is a flat output. The n-bar system is a natural generalisation of the n-trailer system and we provide a comparison of flatness properties of both systems.     

Necessary and sufficient conditions of risk‐sensitive optimal control and differential games for stochastic differential delayed equations

In this paper, we consider risk‐sensitive optimal control and differential games for stochastic differential delayed equations driven by Brownian motion. The problems are related to robust stochastic optimization with delay due to the inherent feature of the risk‐sensitive objective functional. For both problems, by using the logarithmic transformation of the associated risk‐neutral problem, the necessary and sufficient conditions for the risk‐sensitive maximum principle are obtained. We show that these conditions are characterized in terms of the variational inequality and the coupled anticipated backward stochastic differential equations (ABSDEs). The coupled ABSDEs consist of the first‐order adjoint equation and an additional scalar ABSDE, where the latter is induced due to the nonsmooth nonlinear transformation of the adjoint process of the associated risk‐neutral problem. For applications, we consider the risk‐sensitive linear‐quadratic control and game problems with delay, and the optimal consumption and production game, for which we obtain explicit optimal solutions.     

On singularities of flat affine systems with n states and n−1 controls

We study the set of intrinsic singularities of flat affine systems with n?1 controls and n states using the notion of Lie‐Bäcklund atlas, previously introduced by the authors. For this purpose, we prove two easily computable sufficient conditions to construct flat outputs as a set of independent first integrals of distributions of vector fields: the first one in a generic case, namely, in a neighborhood of a point where the n?1 control vector fields are independent and the second one at a degenerate point where p?1 control vector fields are dependent of the n?p others, with p>1. After introducing the Γ‐accessibility rank condition, we show that the set of intrinsic singularities includes the set of points where the system does not satisfy this rank condition and is included in the set where a distribution of vector fields introduced in the generic case is singular. We conclude this analysis by three examples of apparent singularities of flat systems in generic and nongeneric degenerate cases.     

Some new sufficient conditions for graphs to have fractional k-factors

Let G be a graph, and k a positive integer. Let h: E(G)→[0, 1] be a function. If ∑ _{e? x} h(e)=k holds for any x∈V(G), then we call G[F _h ] a fractional k-factor of G with indicator function h, where F _h ={e∈E(G):h(e)>0}. In this paper, we prove some results on the existence of a fractional k-factor in a simple graph depending on δ(G) and α(G). Furthermore, we show that the results are best possible in some sense.     

On some sufficient conditions for optimality of the pursuit time in the differential game with multiple pursuers

Consideration was given to the problem of optimal pursuit of one object by multiple objects. The player’s moves obey the ordinary differential equations. Geometrical constraints are imposed on the player controls. Sufficient conditions were obtained for optimality of the pursuit time, and the optimal player strategies were constructed.     

The asymptotic properties of the suppressed functional differential system by Brownian noise under regime switching

In the previous work by Wu et al., it was shown that the polynomial Brownian noise may suppress the potential explosion of the nonlinear system without the linear growth condition or the one-sided linear growth condition and the linear Brownian noise may stabilise this suppressed system. This paper is a continuation of our previous article and considers the asymptotic properties of the suppressed functional differential system under regime switching. These asymptotic properties show that the suppressed functional differential system by polynomial Brownian noise will grow with at most polynomial speed.     

Performance assessment of control systems in rolling mills – application to strip thickness and flatness control

This contribution takes the control performance monitoring (CPM) technology into a new industrial area, the metal processing, where not much work has been done before. It is shown how to explore not yet discovered opportunities for controller performance improvement in this industrially interesting field, where special aspects have to be considered. This includes online vs. batch-wise performance evaluation, time-based vs. length-based assessment, and oscillation diagnosis. The paper presents two industrial case studies of the performance evaluation of control systems in a tandem cold rolling mill: (1) a feedforward/feedback strip thickness controller; and (2) an internal model control of the strip flatness. Routine operating data are analysed to obtain the performance monitoring metrics in terms of minimum variance index, oscillation index, and to suggest improvement measures. A monitoring tool for calculating and displaying the performance indices has been developed, and tailored to the applications in this field. The results indicate that tuning the feedback thickness controller is suggested to better handle entry thickness disturbances for specific coils. The performance of the flatness controller is found to be satisfactory, thus no actions are needed.     

On sufficient conditions for the stability of interval matrices

We investigate the Hurwitz and Schur stability of interval matrices using Lyapunov's second method and interval analysis techniques. Previous results require a check of the definiteness of 2^{n(n − 1)/2} concerns of a certain interval matrix. The present results require a check of the definiteness of only 2^{n − 1} corners.     

DHNN优化设计新方法及在板形模式识别的应用

基于离散Hopfield神经网络(DHNN)的联想记忆能力,提出了随机扰动优化设计DHNN的新方法.该方法降低了DHNN对权值矩阵的苛刻要求,避免进入伪稳定点;并将其用于板形模式识别,采用勒让德多项式表示常见的6种板形基模式,不需大量的测试样本来训练网络,是一种更简单、实用的板形模式识别新方法,为实现板形控制提供依据,仿真结果证明了这种方法的可行性     

Legendre wavelets method for approximate solution of fractional-order differential equations under multi-point boundary conditions

In this paper, Legendre wavelet collocation method is applied for numerical solutions of the fractional-order differential equations subject to multi-point boundary conditions. The explicit formula of fractional integral of a single Legendre wavelet is derived from the definition by means of the shifted Legendre polynomial. The proposed method is very convenient for solving fractional-order multi-point boundary conditions, since the boundary conditions are taken into account automatically. The main characteristic behind this approach is that it reduces equations to those of solving a system of algebraic equations which greatly simplifies the problem. Several numerical examples are solved to demonstrate the validity and applicability of the presented method.     

Truncation approximants to probabilistic evolution of ordinary differential equations under initial conditions via bidiagonal evolution matrices: simple case

In this work, we investigate the probabilistic evolution approach (PEA) to ordinary differential equations whose evolution matrices are composed of only two diagonals under certain initial value impositions. We have been able to develop analytic expressions for truncation approximants which can be generated by using finite left uppermost square blocks in the denumerable infinite number of PEA equations and their infinite limits. What we have revealed is the fact that the truncation approximants converge for initial value parameter, values residing at most in a disk centered at the expansion point and excluding the nearest zero(es). The numerical implementations validate this formation.     

On the approximate controllability of semilinear fractional differential systems

Fractional differential equations have wide applications in science and engineering. In this paper, we consider a class of control systems governed by the semilinear fractional differential equations in Hilbert spaces. By using the semigroup theory, the fractional power theory and fixed point strategy, a new set of sufficient conditions are formulated which guarantees the approximate controllability of semilinear fractional differential systems. The results are established under the assumption that the associated linear system is approximately controllable. Further, we extend the result to study the approximate controllability of fractional systems with nonlocal conditions. An example is provided to illustrate the application of the obtained theory.     

On the necessity of the invariance conditions for reach control on polytopes

We study the Reach Control Problem (RCP) to make the solutions of an affine system defined on a polytopic state space reach and exit a prescribed facet of the polytope in finite time without first leaving the polytope. So-called invariance conditions are used to prevent solutions from leaving the polytope through facets which are not designated as the exit facet. These conditions are known to be necessary for solvability of the RCP on polytopes by continuous state feedback. We study whether the invariance conditions are also necessary for solvability of the RCP on polytopes by open-loop controls. We show by way of a counterexample that surprisingly the answer is negative. We identify a suitable class of polytopes for which the invariance conditions remain necessary conditions.     

On the sufficient equivalence conditions of gaussian measures corresponding to homogeneous fields whose spectral densities have real zeros

The sufficient equivalence criteria of probability measures corresponding to Gaussian homogeneous random fields are given in terms of the spectral densities of the fields considered. These criteria are represented in a form taking into account the possibility of vanishing of the mentioned spectral densities. Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 37–48, November–December, 1999.     

旁路开关不停电代路运行的差动保护技术研究

由于光纤通道的飞速发展,光纤差动保护在电力系统的应用越来越广泛,目前220kV线路的两套主保护采用光纤差动保护。220kV线路两套均采用光纤差动保护后,当这些线路需要旁代时,在旁代的操作过程中,需要将两套差动保护退出,线路失去主保护,影响系统的安全运行,否则旁代过程中需导致停运线路,就失去了旁代线路的意义,故研究一种差动保护装置,在线路旁代过程中至少保留一套该种差动保护,不影响整条线路的正常运行。     

The prospects of the SSILP system under new conditions

The problems of the system of standards for scientific-technical information, librarianship and publishing are considered and developments that have permitted the challenging directions of the SSILP system to be determined are described.     

On the stability of a differential Riccati equation for continuous-discrete observers

This article deals with the stability properties of a continuous-discrete Riccati differential equation. The main motivation comes from the theory of Kalman filters for continuous-time nonlinear systems with sampled measurements, where this type of equation often arises. Stability is to be understood in the following sense: under appropriate hypotheses, the solution matrix is always symmetric positive definite and bounded from above and below. No uniformity is expected from the sampling procedure, only an upper bound on the elapsed time between consecutive samples is needed. The exposition consists of two parts. First, the stability properties are proven and second, by means of three examples, it is shown how the article's main result applies.     

滑动与打滑条件下的轮式移动机器人自抗扰跟踪控制

针对具有未知的滑动与打滑的轮式移动机器人(WMR),提出了一种基于自抗扰思想的跟踪控制策略.首先建立了滑动与打滑条件下的轮式移动机器人动力学模型.其次,由反步法设计运动学控制器,基于模型设计线性扩张观测器和动力学控制器,并给出了控制器稳定性分析.最后与积分滑模控制进行了仿真对比,结果表明该控制方法的误差收敛速度更快.观测器能够精确估计滑动与打滑及动力学不确定性对机器人的扰动,提高了轮式移动机器人轨迹跟踪的鲁棒性.