Stabilization of discrete-time positive switched linear systems: A nonzero elements chain method

This article studies the stability problem of discrete-time positive switched linear systems by introducing a nonzero elements chain method. Compared to existing works, the highlight of this article is reflected in the inclusiveness of the subsystem, that is, each subsystem is allowed to be stable, marginally stable or even unstable. Some sufficient conditions depending on the characteristics of system matrices and the time-dependent switching signals are established, so as to guarantee the exponential stability of positive switched linear systems. In addition, the main result is extended to the case of time-varying delay. At last, the superiority of the obtained results is well verified by numerical examples.     

Wiener models of direction-dependent dynamic systems

Analysis of systems with direction-dependent dynamics is currently limited to cases in which the dynamics in the two directions of the output are first order; results for such systems have been published for both pseudo-random maximum-length binary (MLB) and inverse-repeat maximum-length binary (IR-MLB) inputs. These relatively limited analytical results make it useful to examine alternative ways of modelling such systems and in this paper, Wiener models are considered for this purpose. Methods for optimising the Wiener model parameters by matching the system and model cross-correlation functions, outputs, and discrete Fourier transforms of the outputs are considered, and the results are compared. These methods are also applied to a first-order direction-dependent system with a maximum-length ternary (MLT) input, for which no analytical results are currently available, and to a second-order system with an IR-MLB input.     

On the observability of linear motion quantities in navigation systems

Navigation systems are a key element in a large variety of mobile platforms, where the correct knowledge of their position and attitude is essential in most applications. This paper focuses on the observability of linear motion quantities (position, linear velocity, linear acceleration, and accelerometer bias). It presents necessary and sufficient conditions, with a clear physical insight, for the observability of these variables in 3-D. The analysis provided is based on kinematic models, which are exact and intrinsic to the motion of a rigid-body, and different cases are presented depending on the assumptions made on the sensor suite that is available on-board.     

State-dependent parameter modelling and identification of stochastic non-linear sampled-data systems

State-dependent parameter representations of stochastic non-linear sampled-data systems are studied. Velocity-based linearization is used to construct state-dependent parameter models which have a nominally linear structure but whose parameters can be characterized as functions of past outputs and inputs. For stochastic systems state-dependent parameter ARMAX (quasi-ARMAX) representations are obtained. The models are identified from input–output data using feedforward neural networks to represent the model parameters as functions of past inputs and outputs. Simulated examples are presented to illustrate the usefulness of the proposed approach for the modelling and identification of non-linear stochastic sampled-data systems.     

Extended least-correlation estimates for errors-in-variables non-linear models

This paper introduces a method of parameter estimation working on errors-in-variables polynomial non-linear models in which all measurements are corrupted by noise. The first step is to develop the linear regression models which are equivalent to polynomial non-linear systems. A main idea is to extend the parameter vector by even-order components of noise and to augment the regression vector by appropriate constants or measurements. Applying the method of least correlation, which has a capability to cope with errors-in-variables linear models, to the equivalent model with extended parameters and augmented regressors yields an extended least-correlation estimator. Analysis shows that, for non-linear systems with third or lower order polynomials, the parameters estimated by the proposed method asymptotically converge to the true values. Numerical examples also support analytical results. Applications of the approach to Volterra models, Hammerstein models and Weiner non-linear systems are included.     

Stabilization of uncertain linear distributed delay systems with dissipativity constraints

This paper examines the problem of stabilizing linear distributed delay systems with nonlinear distributed delay kernels and dissipativity constraints. Specifically, the nonlinear distributed kernel includes functions such as polynomials, trigonometric and exponential functions. By constructing a Liapunov–Krasovskii functional related to the distributed kernels, sufficient conditions for the existence of a state feedback controller which stabilizes the uncertain distributed delay systems with dissipativity constraints are given in terms of linear matrix inequalities (LMIs). In contrast to existing methods, the proposed scenario is less conservative or requiring less number of decision variables based on the application of a new derived integral inequality. Finally, numerical examples are presented to demonstrate the validity and effectiveness of the proposed methodology.     

线性广义系统的区间观测器设计

本文研究了连续时间线性广义系统的区间观测器设计问题.首先根据正系统的稳定性判据提出了一种基于线性矩阵不等式的广义区间观测器直接设计法,然后通过引入更多的设计自由度进一步放宽了区间观测器的设计条件,扩大了设计方法的适用范围.所提出的设计方法无需坐标变换,是一种直接设计方法.最后,通过两个仿真算例验证了所提出方法的有效性.     

Regularizations of linear time varying singular systems

Singular systems of differential equations arising in reduced-order models are often regularized by the introduction of small parameters. The types of regularization used for linear time invariant systems need not work on linear time varying systems. This paper gives examples and discusses this behavior. Conditions under which the standard type of regularization works are developed.     

On strong controllability for planar affine nonlinear systems

Different to linear systems, a controllable nonlinear system does not generally imply that it is strongly controllable. This paper will investigate the strong controllability of planar affine nonlinear systems and obtain its necessary and sufficient condition by introducing the variation function of the control curve. These conditions are imposed on the system structure only. In addition, we also point out that, for a class of polynomial systems, their strong controllability is equivalent to their controllability. Finally, some examples are given to show the application of our results.     

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.     

Stabilization by means of state space depending switching rules

In this paper we consider switched systems defined by a pair of linear systems , such that there exists a neutrally stable linear combination of the matrices A₁, A₂. Under an additional assumption, we prove that there exists a state space depending switching rule which stabilizes the system in a very general sense. The result is illustrated by some simulations and examples.     

Bounding steady-state availability models with group repair and phase type repair distributions

We propose an algorithm to obtain bounds for the steady-state availability using Markov models in which only a small portion of the state space is generated. The algorithm is applicable to models with group repair and phase type repair distributions and involves the solution of only four linear systems of the size of the generated state space, independently on the number of “return” states. Numerical examples are presented to illustrate the algorithm and compare it with a previous bounding algorithm.     

随机非线性扰动下广义马氏跳变系统的控制器设计

针对实际系统中非线性扰动以一定概率存在的情况, 讨论广义马氏跳变系统的控制问题. 首先, 运用Bernoulli 变量描述系统中非线性扰动的存在与否, 建立相应的数学模型, 得到在上述一般条件下系统的随机容许性与解的存在唯一性条件. 然后, 以LMI 形式给出模态依赖和模态独立控制器的存在条件. 与现有结果相比, 所得结果考虑了非线性扰动的存在概率, 具有较小的保守性. 最后, 通过数值例子验证了所得结果的有效性和优越性.

     

线性时滞系统的相对稳定性分析方法

实际控制过程中,时滞的引入常常导致系统性能的下降,也使得系统的稳定性分析变得困难。从一类具有时滞项的线性时不变( LTI) 系统的特征根求解出发,研究了系统的稳定性分析问题。复平面上系统特征根的位置不仅决定了系统的绝对稳定性,还决定系统的相对稳定性-瞬态性能。由于时滞的引入,系统特征方程变成超越方程,其解的数量为无穷。并提出一种从超越方程实部和虚部系数中提取出双向量并结合二维向量旋转的解决方法,可以准确简洁地求出超越方程在复平面上指定区域边界上的根。最后给出仿真实例表明了算法的正确性和有效性。     

More efficient predictive control

An approach for constrained predictive control of linear systems (or uncertain systems described by polytopic uncertainty models) is presented. The approach consists of (in general non-convex, but often convex) offline optimization, and very efficient online optimization. Two examples, one being a laboratory experiment, compare the approach to existing approaches, revealing both advantages and disadvantages.     

Real-time optimal control and observation

A survey of the results obtained by authors and their coworkers (mainly in 2000–2003) on realization of modern principles of optimal control and observations in real time was made. Optimal control problems and the problems of observation of deterministic systems, problems under the conditions of set-membership uncertainty; perfect and imperfect measurements, feedforward, feedback, and combined loop cases, inertial and inertialess controls; and special and dynamical regulators for indirect control, linear piecewise linear, and nonlinear models are considered consecutively. The presentation focuses mainly on linear models, since the optimal control of nonlinear systems is based on linear or piecewise linear approximations of the initial model. For the realization of the positional solutions of the optimal control and observation problems, fast dual methods taking into account the dynamical nature of the problems being investigated are justified. The application of the results on optimal control in real time for the solution of classical control problems (problems of regulating, stabilizing, tracking, etc.) is discussed. The presentation is accompanied by computational examples.     

Structural indistinguishability between uncontrolled (autonomous) nonlinear analytic systems

In this paper, an approach for analysing the structural indistinguishability between two uncontrolled (or autonomous) analytic systems is presented. The approach involves constructing, if possible, a smooth mapping between the trajectories of two candidate models. If either of the models satisfies an observability criterion, then such a transformation always exists when the models are indistinguishable from their outputs. The approach is illustrated by examples from epidemiology and chemical reaction kinetics. One important outcome is that the susceptible, infectious, recovered (SIR) and SIR with temporary immunity (SIRS) models are shown to be indistinguishable when a proportion of the number of infectives is measured.     

Input addition and leader selection for the controllability of graph-based systems

In this paper, we consider dynamical graph-based models, which are well fitted for the structural analysis of complex systems. A significant amount of work has been devoted to the controllability of such graph based models, e.g. recently for multi-agent systems or complex networks. We study here the controllability through input addition in this framework. We present several variants of this problem depending on the freedom which is left to the designer on the additional inputs. We use a unified framework, which allows us to encompass the different applications and representations (large scale systems, complex communications networks, multi-agent systems, …) and provide convenient graph tools for their analysis. Our contribution is to characterize the structural modifications of the system resulting from an input addition (or a leader selection) and of the mechanisms which lead to controllability. We provide information on the possible location of additional inputs and on the minimal number of inputs to be added for controllability.     

On identification of parallel block-cascade nonlinear models

The class of nonlinear systems studied in this paper is assumed to be modelled by parallel block-cascades. Such models are composed of parallel branches where each branch has a linear block in cascade with a zero-memory nonlinear block followed by another linear block. These types of models are extensively used to represent nonlinear dynamic systems and are known in the literature as Wiener-Hammerstein models. Using a zero-mean stationary white gaussian sequence as an input to such models, a structure identification criterion is developed, utilizing the bispectrum estimate of the output sequence only. The application of this criterion is shown by several simulation examples. Also, impulse response estimation of an example of such a model is considered to show the effectiveness of the proposed identification technique.