Time-varying Dynamical Systems Research Articles

带有随机发生非线性的时变动态系统非脆弱递归状态估计

带有随机发生非线性的时变动态系统非脆弱递归状态估计

Moment Analysis of Linear Time-Varying Dynamical Systems with Renewal Transitions

Stochastic dynamics of several systems can be modeled via piecewise-deterministic time evolution of the state, interspersed by random discrete events. Within this general class of systems, we consi...

Optimal Control Strategy of Multi-Stage Pharmaceutical

Abstract The fermentation production process is the basis for ensuring product quality in pharmaceutical production. There are many variable parameters such as temperature, number of revolutions and PH value in the fermentation production process, therefore, it is difficult to describe the complex problems through precise mathematical models. Since the process has to go through four different steps, each of which is a nonlinear time-varying dynamic system, the four steps constitute a large dynamic system, and the global modeling accuracy cannot be guaranteed; and the optimization problem of the nonlinear time-varying dynamic system is also a problem. In order to solve the above problems, the paper proposes to use the BP (Back Propagation）neural network modeling method to screen the input variables of the system with large effect on the basis of the actual production data of a pharmaceutical factory. Then, based on the process parameters of the fermentation and the output of the product quality index, a multi-stage mapping model based on LSSVM (Least Squares Support Vector Machine) was established. Finally, the PSO (Particle Swarm Optimization) algorithm is used to optimize the parameters of the model.The simulation results show that the model obtained by parameter optimization can achieve better prediction results.

Differential-Geometric-Control Formulation of Flapping Flight Multi-body Dynamics

Flapping flight dynamics is quite an intricate problem that is typically represented by a multi-body, multi-scale, nonlinear, time-varying dynamical system. The unduly simple modeling and analysis of such dynamics in the literature has long obstructed the discovery of some of the fascinating mechanisms that these flapping-wing creatures possess. Neglecting the wing inertial effects and directly averaging the dynamics over the flapping cycle are two major simplifying assumptions that have been extensively used in the literature of flapping flight balance and stability analysis. By relaxing these assumptions and formulating the multi-body dynamics of flapping-wing micro-air-vehicles in a differential-geometric-control framework, we reveal a vibrational stabilization mechanism that greatly contributes to the body pitch stabilization. The discovered vibrational stabilization mechanism is induced by the interaction between the fast oscillatory aerodynamic loads on the wings and the relatively slow body motion. This stabilization mechanism provides an artificial stiffness (i.e., spring action) to the body rotation around its pitch axis. Such a spring action is similar to that of Kapitsa pendulum where the unstable inverted pendulum is stabilized through applying fast-enough periodic forcing. Such a phenomenon cannot be captured using the overly simplified modeling and analysis of flapping flight dynamics.

A Bayesian estimator of operational modal parameters for linear time-varying mechanical systems based on functional series vector TAR model

Operational modal analysis of time-varying mechanical dynamic systems is a useful but challenging task. This paper presents a Bayesian estimator for modal parameters of linear time-varying mechanical dynamic systems in the framework of the functional-series vector time-dependent autoregressive (FS-VTAR) model with output-only measurements. The proposed Bayesian estimator cannot only give the modal parameters with the estimation of mean value, but also supplies the uncertainty with the creditable interval estimation. A series of numerical examples have illustrated the advantages of the proposed Bayesian estimator against the overestimate, the better performance for the short data and the capability of supplying uncertainty of estimates. An experimental example validates the proposed estimator further.

Synchronization in a temporal multiplex neuronal hypernetwork

Synchronization in time-varying complex dynamical systems has been explored in a variety of different coupling topologies during the last two decades. In most of the previous cases, the basic time-varying coupling topologies were considered to be a single interaction between the nodes or in a monolayer configuration, although in many real situations the types of interactions are more than one or in the form of multilayer. In this work, we study the synchronization in multiplex neuronal network, which evolves with time, and each layer consists of more than one interaction function. Specifically, we consider a neuronal hypernetwork at each layer in which neurons are communicated with each other via electrical and chemical synapses simultaneously and independently. The network corresponding to the electrical gap junctional coupling form a small-world network while the connection associated with the chemical synaptic interaction forms a unidirectional random network. Then intralayer connections are allowed to switch stochastically over time with a characteristic rewiring frequency, whereas interlayer connections via electrical synapses are time invariant. We explore the intralayer and interlayer neuronal synchrony in such network and analytically derive the necessary stability conditions for synchrony using master stability function approach, and excellently match with our numerical findings. Interestingly, we find that the higher frequency of switching links in the intralayer enhances both intralayer and interlayer synchrony and conferring larger windows of synchrony. We also analyze the robustness of these synchronization states with respect to initial conditions using the basin stability framework. Furthermore we find that rapidly changing networks take much less time to reach synchronization state. Lastly, we inspect the dynamical robustness of interlayer synchronization against stochastic demultiplexing of each replica, with analytical justification.

Fast Kalman-like optimal FIR filter for time-variant systems with improved robustness

In this paper, a fast Kalman-like iterative OFIR algorithm is proposed for discrete-time filtering of linear time-varying dynamic systems. The batch OFIR filter is re-derived in an alternative way to show that this filter is unique for such systems. A computationally efficient fast iterative form is found for the OFIR filter using recursions. It is shown that each recursion has the Kalman filter (KF) predictor/corrector format with initial conditions specified via measurements on a horizon of N nearest past points. In this regard, the KF is considered as a special case of the iterative OFIR filtering algorithm when N goes to infinity. Applications are given for the 3-state target tracking and three-degree-of-freedom (DOF) hover system. It has been shown experimentally that the proposed iterative OFIR algorithm operates much faster than the batch OFIR filter and has the computational complexity acceptable for real-time applications. It has also been demonstrated by simulations that an increase in the number of the states results in better robustness of the OFIR filter against temporary model uncertainties and in higher immunity against errors in the noise statistics.

Decentralized robust control of a hydraulic driven parallel manipulator based on disturbance estimation

Since the parallel robot manipulator is a nonlinear, coupling and time-varying dynamic system, it is difficult to synthesize a controller based on the dynamic model by using a centralized control method. Considering each driving unit as a subsystem and treating the coupling interconnection terms between the joints as a time-varying external disturbance of the driving unit, this paper presents a decentralized robust controller with extended state observer (ESO) in joint-space to implement the high-precision trajectory tracking of the robot manipulator. By constructing two extended state observers, not only matched uncertainties but also unmatched uncertainties can be estimated and then compensated in a feed-forward way. Consequently, high-gain feedback is avoided. In addition, the feedback robust laws ensure the global robustness of the proposed controller. Furthermore, the stability of the system is verified by constructing the Lyapunov function. The simulation results show that the proposed controller can estimate both matched and unmatched uncertainties of the driving unit accurately, and the system possesses high trajectory tracking performance and strong robustness.

On finite-time consensus objectives in time-varying interconnected discrete linear dynamic systems under internal and external delays

This article formulates the properties of achievable consensus of linear interconnected discrete systems with multiple internal and external point delays. The formulation is stated in an algebraic generic context as the ability of achievement of (a non-necessarily zero) finite-time common error between the various subsystems. The consensus signals are generically defined so that they can be, in general, distinct of the output or state components. However, the consensus signals of all the interconnected subsystems have the same dimension for coherency reasons. A particular attention is paid to the case of weak interconnection couplings in both the open-loop case and the closed-loop one under, in general, linear output feedback. Some further extensions are given related to consensus over intervals and related to consensus of positive interconnected systems.

An analysis and design for time-varying structures dynamical networks via state constraint impulsive control

ABSTRACTThis paper investigates the problems of exponential stabilisation criterion for time-varying structures dynamical networks via state constraint impulsive control. Two types of state constraint impulsive control schemes are proposed which include fully state constraint and partial state constraint. Combining with convex analysis, inductive method and matrix measure theory, some sufficient conditions are obtained to ensure exponential stabilisation for time-varying structures dynamical systems by using the constrains linear feedback impulsive controllers. Meanwhile, some simulation results are given to validate the effectiveness of the proposed criteria in the end.

Experimental Demonstration of the Vibrational Stabilization Phenomenon in Bio-Inspired Flying Robots

Bio-inspired flying robots (BIFRs) are micro-air-vehicles that use biomimetic actuation (oscillatory flapping wing) for lift, propulsion, and control. The dynamic behavior of these bio-inspired systems is quite intricate to study as it is typically described by a multibody, multi-time-scale, nonlinear, time-varying dynamical system. However, this rich dynamics lead to unconventional stabilization mechanisms whose study essentially necessitates a mathematically rigorous analysis. Our recent efforts using differential geometric control theory revealed a vibrational stabilization mechanism induced on the body pitching due to the interaction between the fast wing flapping dynamics and the slow body dynamics. In this effort, we construct an experimental setup allowing for two degrees of freedom for the body; vertical motion and pitching motion. The objective is to experimentally verify and demonstrate the vibrational stabilization phenomenon in insect flight and its mimicking BIFRs.

Epidemic-Like Stochastic Processes with Time-Varying Behavior

The mathematical analysis of epidemic-like behavior has a rich history, going all the way back to the seminal work of Bernoulli in 1766 [5]. More recently, mathematical models of epidemic-like behavior have received considerable attention in the research literature based on additional motivation from areas such as communication and social networks, cybersecurity systems, and financial markets; see, e.g., [6]. The types of viral behaviors exhibited in many of these applications tend to be characterized by epidemic-like stochastic processes with time-varying parameters [12, 13]. In this paper we consider variants of the classical mathematical model of epidemic-like behavior analyzed by Kurtz [8],[7, Chapter 11], extending the analysis and results to first incorporate time-varying behavior for the infection and cure rates of the model and to then investigate structural properties of the interactions between local (micro) and global (macro) behaviors within the process. Specifically, we start by formally presenting an epidemic-like continuous-time, discretestate stochastic process in which each individual comprising the population can be either in a non-infected state or in an infected state, and where the rate at which the noninfected population is infected and the rate at which the infected population is cured are both functions of time. We established that, under general assumptions on the timevarying processes and under a mean-field scaling with respect to population size n, the stochastic processes converge to a continuous-time, continuous-state time-varying dynamical system. Then we study the stationary behavior of both the original stochastic process and the mean-field limiting dynamical system, and verify that they, in fact, have similar asymptotic behavior with respect to time. In other words, we establish that the following diagram is commutative.

Sensor fault detection and isolation of an industrial gas turbine using partial adaptive KPCA

In this paper, sensor fault detection and isolation of time-varying nonlinear dynamical systems is studied by utilizing an adaptive kernel principal component analysis (KPCA) solution as a useful method to overcome the weaknesses of conventional KPCA approach in dealing with time-varying dynamical processes. Toward this goal, adaptive Hotelling's T2 is used with KPCA to tackle the time-varying behavior of nonlinear systems. Moreover, for fault isolation, partial adaptive KPCA (AKPCA) is proposed where a set of residual signals is generated based on the structured residual set framework. The simulation studies demonstrate that using the proposed methodology, the occurrence of sensor faults in the nonlinear dynamic model of an aeroderivative gas turbine can be effectively detected and isolated in the presence of component degradation.

基于二维时变符号混沌系统的流密码算法设计

基于二维时变符号混沌系统的流密码算法设计

On the positivity, excitability and transparency properties of a class of time-varying bilinear dynamic systems under multiple point internal and external delays

AbstractThis paper investigates formally the internal and external positivity, together with its excitability and transparency properties, of a class of bilinear time-varying continuous-time dynami...

Heart rate from face videos under realistic conditions for advanced driver monitoring

Abstract The role of physiological signals has a large impact on driver monitoring systems, since it tells something about the human state. This work addresses the recursive probabilistic inference problem in time-varying linear dynamic systems to incorporate invariance into the task of heart rate estimation from face videos under realistic conditions. The invariance encapsulates motion as well as varying illumination conditions in order to accurately estimate vitality parameters from human faces using conventional camera technology. The solution is based on the canonical state space representation of an Itô process and a Wiener velocity model. Empirical results yield to excellent real-time and estimation performance of heart rates in presence of disturbing factors, like rigid head motion, talking, facial expressions and natural illumination conditions making the process of human state estimation from face videos applicable in a much broader sense, pushing the technology towards advanced driver monitoring systems.

A Sparse Multiwavelet-Based Generalized Laguerre–Volterra Model for Identifying Time-Varying Neural Dynamics from Spiking Activities

Modeling of a time-varying dynamical system provides insights into the functions of biological neural networks and contributes to the development of next-generation neural prostheses. In this paper, we have formulated a novel sparse multiwavelet-based generalized Laguerre–Volterra (sMGLV) modeling framework to identify the time-varying neural dynamics from multiple spike train data. First, the significant inputs are selected by using a group least absolute shrinkage and selection operator (LASSO) method, which can capture the sparsity within the neural system. Second, the multiwavelet-based basis function expansion scheme with an efficient forward orthogonal regression (FOR) algorithm aided by mutual information is utilized to rapidly capture the time-varying characteristics from the sparse model. Quantitative simulation results demonstrate that the proposed sMGLV model in this paper outperforms the initial full model and the state-of-the-art modeling methods in tracking performance for various time-varying kernels. Analyses of experimental data show that the proposed sMGLV model can capture the timing of transient changes accurately. The proposed framework will be useful to the study of how, when, and where information transmission processes across brain regions evolve in behavior.

Gap metric computation for time-varying linear systems on finite horizons

It is shown how to compute the aperture, or gap, between the finite-horizon graphs of linear time-varying dynamical systems, given state-space models of the continuous-time input-output maps. The approach involves four quadratic matrix first-order differential equations, three with the symplectic structure of Riccati equations. All four are subject to single-ended boundary conditions. So standard numerical methods can be used to compute the solutions as required. Three of the differential equations, two Riccati and the other not, need to be solved once to construct normalized graph representations, and to test an invertibility condition, respectively. When this invertibility condition is verified, the directed gaps are equal, and the remaining Riccati differential equation is solved repeatedly in a bisection search to determine one of these. Computation of both directed gaps to find the maximum would, by contrast, involve repeatedly solving two such Riccati differential equations, each in a bisection search.

New criterion for asymptotic stability of time-varying dynamical systems

In this paper, we establish some new sufficient conditions for uniform global asymptotic stability for certain classes of nonlinear systems. Lyapunov approach is applied to study exponential stability and stabilization of time-varying systems. Sufficient conditions are obtained based on new nonlinear differential inequalities. Moreover, some examples are treated and an application to control systems is given.

Adaptive Observers with Uncertainty in Loop Tuning for Linear Time-Varying Dynamical Systems

Adaptive Observers with Uncertainty in Loop Tuning for Linear Time-Varying Dynamical Systems