Kernel-based identification of asymptotically stable continuous-time linear dynamical systems

This paper is concerned with tele‐presence and tele‐operation of autonomous vehicles over the Additive White Gaussian Noise (AWGN) channel. This wireless communication channel is subject to transmission noise and transmission power constraint. An encoder, decoder and controller are proposed by implementing a novel linearization method for linearizing the nonlinear dynamic systems at operating points. For the linearized systems, the encoder, decoder and controller are implemented that were previously proposed for output tracking as well as stability of linear dynamic systems. Two novel linearization methods are proposed and their satisfactory performances are proved for output tracking as well as stability of nonlinear dynamic system. The first method is based on the fixed linearization rate and the second one is based on the variable (optimal) linearization rate. The decoder that is based on the second method is in fact the extended Kalman filter with the optimal linearization rate. The performances of these two methods are compared with each other and the other proposed methods by implementing them to the problems of the tele‐presence and tele‐operation of autonomous vehicles over the AWGN channel. Their satisfactory performances are illustrated. It is illustrated that the second method has higher computational complexity with slightly better performance and is applicable to a larger class of reference trajectories.

In this paper, the probability of controllability of a class of linear dynamical systems is investigated by applying simple combinatorial reasoning (in the manner of Porter 1972) to the structure of the mode-controllability matrices of systems of this class. The results of this investigation are discussed in relation to the results concerning the probability of stability of linear dynamical systems obtained by Ashby (1952) and Porter (1972).

In many areas of signal, system, and control theory, orthogonal functions play an important role in issues of analysis and design. In this paper, it is shown that there exist orthogonal functions that, in a natural way, are generated by stable linear dynamical systems and that compose an orthonormal basis for the signal space l/sub 2sup n/. To this end, use is made of balanced realizations of inner transfer functions. The orthogonal functions can be considered as generalizations of, for example, the pulse functions, Laguerre functions, and Kautz functions, and give rise to an alternative series expansion of rational transfer functions. It is shown how we can exploit these generalized basis functions to increase the speed of convergence in a series expansion, i.e., to obtain a good approximation by retaining only a finite number of expansion coefficients. Consequences for identification of expansion coefficients are analyzed, and a bound is formulated on the error that is made when approximating a system by a finite number of expansion coefficients.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A biologically plausible model of myelin plasticity demonstrates how oligodendrocytes can selectively adjust conduction delays in axon bundles to allow robust communication between brain regions through long-range synchronization.

In this paper we examine the property of asymptotic stability in several dynamic economic systems, modeled in ordinary differential equation formulations of time parameter t. Asymptotic stability ensures intertemporal equilibrium for the economic quantity the solution stands for, regardless of what the initial conditions happen to be. Existence of economic equilibrium in continuous time models is checked via a Symbolic language, the Xcas program editor. Using stability theorems of differential equations as background a brief overview of symbolic capabilities of free software Xcas is given. We present computational experience with a programming style for stability results of ordinary linear and nonlinear differential equations. Numerical experiments on traditional applications of economic dynamics exhibit the simplicity clarity and brevity of input and output of our computer codes.

In the original paper (K.B. Janiszowski, ibid., vol. 38, no. 8, p. 1313-16, 1993) there is presented a modification of the Tustin approximation. The author argues that the justification of this modification, by means of three examples, is not convincing, because the choice of the examples is questionable and some calculations are not sufficiently accurate. It is shown that some good properties of the proposed modification can be justified by using the Tustin approximation of a continuous-time (CT) model for the discrete-time (DT) system. It is stressed that the proposed modification has only a limited value, since from application point of view the use of CT models is more reasonable. As the conclusion the DT controller design procedure by using CT methods is proposed. >

Given a stable linear time-invariant dynamical system x·= Ax, it is shown that there exists a related stable family of dynamical systems x·=A(k)x. The Lyapunov stability criterion remains valid for all linear operators A(k)=DkA of this family.

System identification in closed-loop has been of considerable interest in the last two decades. Most of the existing methods have been developed for discrete-time models. In this paper, various instrumental variable-based methods are proposed for identifying continuous-time models of systems operating in closed-loop. The accuracy of these methods is also investigated leading to the definition of the optimal IV estimator which gives minimum variance. As this needs the exact knowledge of the noise model, it cannot be used directly in practice. Several alternatives are therefore proposed to cope with this drawback and illustrated with a simulation example.

The Popov criterion for the stability of linear, time-invariant, finite-dimensional systems with a single non-linearity has been generalized by a numbers of authors through a relaxation of the single non-linearity and the finite-dimensional constraints in order to be applicable to a wider range of practical problems. This paper extends these results further by relaxing the time-invariant constraint. It is shown that a covariance condition when satisfied is a sufficient condition for the system output to be bounded and square integrable for zero input conditions.

A Perturbation Approach to Continuous-Time Portfolio Selection Under Stochastic Investment Opportunities

Identification of continuous-time nonlinear systems: The nonlinear difference equation with moving average noise (NDEMA) framework

Networked control systems with probabilistic time-varying delay based on event-triggered non-fragile [formula omitted] control

The research on statistical inference after data-driven model selection can be traced as far back as Koopmans (1949). The intensive research on modern model selection methods for high-dimensional data over the past three decades revived the interest in statistical inference after model selection. In recent years, there has been a surge of articles on statistical inference after model selection and now a rather vast literature exists on this topic. Our manuscript aims at presenting a holistic review of post-model-selection inference in linear regression models, while also incorporating perspectives from high-dimensional inference in these models. We first give a simulated example motivating the necessity for valid statistical inference after model selection. We then provide theoretical insights explaining the phenomena observed in the example. This is done through a literature survey on the post-selection sampling distribution of regression parameter estimators and properties of coverage probabilities of naïve confidence intervals. Categorized according to two types of estimation targets, namely the population- and projection-based regression coefficients, we present a review of recent uncertainty assessment methods. We also discuss possible pros and cons for the confidence intervals constructed by different methods.

본 논문에서는 불확실성을 포함한 연속시간 비선형 동적 시스템에 대한 퍼지 모델 기반 제어기의 지능형 디지털 재설계를 위한 조직적인 방법을 제안한다. 불확실 비선형 시스템을 표현하기 위해 연속시간 불확실 TS 퍼지 모델이 구성되었다. 안정화와 추적을 위한 퍼지 모델 기반 제어기 설계를 위해 EPDC 기법이 이용되었다. 설계된 연속시간 제어기는 지능형 디지털 재설계 기법을 이용함으로써 이산시간 제어기로 전환되었다. 이 새로운 설계 기법은 퍼지 모델 기반 제어 이론과 불확실성을 가진 비선형 동적 시스템에 대한 진보된 디지털 재설계 기법의 통합을 위한 조직적이고, 효과적인 틀을 제공한다. 마지막으로, 단일 링크 유연 로봇 시스템의 모의 실험을 이용해 개발된 설계 방법의 효용성과 실행 가능성을 입증한다. In this paper, we propose a systematic method for intelligent digital redesign of a fuzzy-model-based controller for continuous-time nonlinear dynamical systems which may also contain uncertainties. The continuous-time uncertain TS fuzzy model is first constructed to represent the uncertain nonlinear systems. An extended parallel distributed compensation(EPDC) technique is then used to design a fuzzy-model-based controller for both stabilization and tracking. The designed continuous-time controller is then converted to an equivalent discrete-time controller by using an integrated intelligent digital redesign method. This new design technique provides a systematic and effective framework for integration of the fuzzy-model-based control theory and the advanced digital redesign technique for nonlinear dynamical systems with uncertainties. Finally, The single link flexible-joint robot arm is used as an illustrative example to show the effectiveness and the feasibility of the developed design method.

The application of robust control theory requires models containing unknown, bounded perturbations and unknown, bounded input signals. Model validation is a means of assessing the applicability of a given model with respect to experimental data. This paper develops a theoretical framework, and a computational solution, for the model validation problem in the case where the model, including unknown perturbations and signals, is given in the continuous time domain, yet the experimental datum is a finite, sampled signal. The continuous nature of the unknown components is treated directly with a sampled data lifting theory. This gives results which are valid for any sample period and any datum length. Explicit calculation of whether sufficient data for invalidation has been obtained arises naturally in this framework. A common class of robust control models is treated and leads to a convex matrix optimization problem. A simulation example illustrates the approach.