Class Of Time-varying Systems Research Articles

On Methodology for Solving Control Problems of One Class of Time-varying Systems

On Methodology for Solving Control Problems of One Class of Time-varying Systems

Probabilistic-constrained distributed fusion filtering for a class of time-varying systems over sensor networks: a torus-event-triggering mechanism

This paper investigates the problem of distributed fusion over sensor networks with probabilistic constraints and stochastic perturbations. In order to save the bandwidth resources, a new event-triggering mechanism (ETM), called torus-event-triggering mechanism (TETM), is utilised for data transmission. Compared with the traditional ETMs, the TETM has two thresholds, which will not only discard the sampling data smaller than the lower threshold but also hold back the packet larger than the upper threshold. The main purpose of this paper is to design a time-varying distributed fusion filter such that: (1) the probability of the filtering error falling in a given ellipsoid domain is greater than a specified value and (2) the ellipsoidal set is minimised in the sense of matrix norm at each time point. To achieve the above-mentioned purpose, sufficient conditions are given to obtain the global fusion with the help of the recursive linear matrix inequality technique. The desired local filter parameters are then computed by solving an optimisation problem with some inequality constraints. Finally, a numerical simulation is given to illustrate the effectiveness and applicability of the proposed distributed fusion strategy.

Finite-time control of uncertain time-varying systems in p-normal form

Abstract This paper addresses a finite-time regulation problem for time-varying nonlinear systems in p-normal form. This class of time-varying systems includes a well-known lower-triangular system and a chain of power integrator systems as special cases. No growth condition on time-varying uncertainties is imposed. The control law can guarantee that all closed-loop trajectories are bounded and well defined. Furthermore, all states converge to zero in finite time.

Novel approach to attitude stabilization of satellite using geomagnetic Lorentz forces

A satellite in a circular Earth orbit is under consideration. The three–axis stabilization of the satellite in orbital coordinate system with the attitude control system using moments of Lorentz forces is studied. The linearized mathematical model of this system is time-varying linear system. Unlike the earlier works on this problem, we propose the novel rigorous approach based on the fact that the considered linearized system belongs to a certain class of time-varying systems. Systems of this class can be reduced to time-invariant systems of larger order. For obtained time-invariant system, controllability is analyzed, and the optimal stabilization algorithm based on the LQR method is constructed. The results of numerical simulation demonstrate the efficiency of the proposed approach.

Time-Variant Frequency Response Function Measurement of Multivariate Time-Variant Systems Operating in Feedback

The classical time-invariance assumption is often not (exactly) met in real-life applications. As a natural extension of the frequency response function (FRF), the time-variant FRF (TV-FRF) provides quick insight into the complex dynamics of time-variant systems. Recently, a procedure has been proposed to estimate nonparametrically the TV-FRF from known input, noisy output measurements of time-variant systems operating in open loop. However, in many applications, feedback is present either due to an explicit control action or due to the interaction between a nonideal actuator and the system under test. The extension of the open-loop approach to noisy input, noisy output measurements of time-variant systems operating in closed loop requires the deconvolution of the time-variant impulse response of the cascade of two time-variant systems. In this paper, this nontrivial problem is solved for a particular class of time-variant systems. The robustness of the approach with respect to the system assumption is demonstrated via simulations and measurements on an electronic circuit.

Minimum-energy control for time-varying systems with multiple state and input delays

This paper considers the minimum-energy control problem for a class of time-varying systems with multiple state and input delays. First, a state transform matrix is presented. By using the transform matrix, a system with multiple state and input delays is converted to a formal equivalent one without delay. Then, the optimal problem of the novel system is solved by using the maximum principle. Analytical expressions of the optimal control law and optimal performance are given by two formulas with respect to the state transform matrix. At last, an algorithm is given to solve the analytical expression of the state transform matrix. Simulation results show that the design algorithm is efficient and easy to implement.

Robust Observer-Based Output Feedback Control for Time-Varying Systems

In this paper, we study the robust output feedback control for a class of time-varying systems where the observer is used to estimate the system states and a learning scheme is also proposed to learn the time-varying parameters. A regulator control problem is pursued with known time-varying bounds. It is shown that to estimate the system states asymptotically only part of the time-varying function need to be learned, not necessarily all the time-varying parameters. The designed output feedback closed-loop control system guarantees a robust norm bound performance measure and uniformly asymptotic stability based on quadratic stability.

Robust Control Design Based-On Integral Sliding-Mode Control

This paper proposes a robust control design based-on integral sliding-mode and H2–norm performance criterion to handle a class of time-varying systems with perturbations including non-linearities and disturbances. The stabilization problems for such systems are studied: integral slid-ing-mode is designated to completely nullify the matched perturbations and, in the meantime, elim-inate the reaching phase to the sliding surface, while H2–norm is a robust linear control measured for system on the sliding surface. In addition to the integral sliding mode control, the contribution of the paper is to implement a parameter-dependent Lyapunov function for H2–norm robust linear control that the overall designed system is less conservative for the system with both matched and unmatched perturbations.

On Iterative Learning Control for Remote Control Systems with Packet Losses

The problem of iterative learning control (ILC) is considered for a class of time-varying systems with random packet dropouts. It is assumed that an ILC scheme is implemented via a remote control system and that packet dropout occurs during the packet transmission between the ILC controller and the actuator of remote plant. The packet dropout is viewed as a binary switching sequence which is subject to the Bernoulli distribution. In order to eliminate the effect of packet dropouts on the convergence property of output error, the hold-input scheme is adopted to compensate the packet dropout at the actuator. It is shown that the hold-input scheme with average ILC can achieve asymptotical convergence along the iteration axis for discrete time-varying linear system. Numerical examples are provided to show the effectiveness of the proposed method.

The stability of a specific class of mechanical systems

A special class of mechanical systems is considered, the linearized equations of which either belong to the class of time-varying systems, reducible to stationary systems using constructive Lyapunov transformations or to systems close to these. A method of decomposing of the matrices of a system, which differs from the traditional method, is proposed for investigating of the stability of motion. It is shown that the conclusions concerning the stability are more complete in the case of this decomposition of the system matrix. A number of problems on the stability of motion of various mechanical systems is considered as examples.

ISSUES IN OPTIMAL CONTROL OF DYNAMIC DISCRETE-EVENT SYSTEMS

We define the notion of Dynamic Discrete-Event Systems, a class of time-varying systems, and present a simple approach to optimal control of such systems. More specifically, we use limited-lookahead online control and an algorithm which tries to maximize the benefit of the executed sequences of events, while at the same time ensuring that unwanted (illegal) sequences are avoided. We use examples to illustrate the different types of problems that can arise if such control is used, for example, overspecialization and failure to take advantage of available resources. These issues are used to formulate a list of desirable properties for a new algorithm that optimizes the control of dynamic systems.

Logarithmic integrals and system dynamics: an analogue of Bode's sensitivity integral for continuous-time, time-varying systems

A new time-domain interpretation of Bode's integral is presented. This allows for a generalization to the class of time-varying systems which possess an exponential dichotomy. It is shown that the sensitivity function is constrained, on average, by the spectral values in the dichotomy spectrum of the antistable component of the open-loop dynamics.

On the 45° -Region and the uniform asymptotic stability of classes of second order parameter-varying and switched systems

In this paper we present sufficient conditions for the stability of a number of classes of time-varying systems. These results are of interest for two reasons. Firstly, the conditions presented take the form of matrix pencil eigenvalue criteria, and are therefore co-ordinate independent and easily verifiable. Secondly, we show a direct relationship between the form of our criteria, and the choice of Lyapunov function used to demonstrate stability (quadratic or unic). These results indicate the importance of the region of the complex plane known as the 45°-Region.

A Recursive Algorithm for Identification of Linear Time-Varying Lumped Systems via Hermite Polynomials

The paper presents a recursive algorithm for identification of parameters of a class of time-varying systems via Hermite polynomials. Hermite polynomials belong to the class of complete set of orthogonal polynomials. They possess very useful properties for developing recursive algorithms. These operational and recurrent properties of Hermite polynomials have been used to obtain an algorithm for estimating the parameters from input-output data. Monte-Carlo results show that consistent estimates can be obtained when the measurement noise is white. Higher variance, however, for noise in the simulation has resulted in higher bias.

Stabilization of uncertain dynamic systems including state delay

The authors consider a class of time-varying systems with time-varying state delay and uncertain input and parameters. They present sufficient conditions on the open loop to obtain an arbitrary-degree closed-loop stability. They construct a min-max controller from knowledge of the upper bound of the delay. >

Application of routh approximant method for reducing the order of a class of time-varying systems

A class of time-varying systems is considered for simplification, and a method is proposed to approximate a high-order time-varying system by a time-invariant lower dimensional system.

Decoupling of linear time-varying systems with time delays in the control variables or state variables

Sufficient conditions for decoupling by state feedback are developed for several classes of time-varying systems which contain time delays. The sufficient conditions are constructive in nature since they can be used to design the decoupler. Two numerical examples are included to illustrate the design procedure.

Minimal realization of a class of time-varying dynamical systems

An algorithm for the irreducible realization of a class of time-varying systems is proposed. The procedure results in a Jordon canonical form minimal realization. This class of time-varying systems has been of recent interest in the study of linear time-varying systems.

Passivity and Positive Reality†

Abstract This paper servos to define a function space representation of the concepts of passivity and positive reality. Linear time-varying differential systems are utilized as a vehicle for bringing these abstract concepts to a concrete form. Necessary conditions and sufficient conditions are then established in terms of the system parameters to ensure the aforementioned concepts. In the course of this study, earlier results of Silverman (1968) are extended to cover a larger class of time-varying systems.

On a class of time-varying systems

A class of time-varying systems whose matrices satisfy a certain matrix Riccati equation is discussed. For this class, the state transition matrix can be found in closed form.