Linear Continuous Time Research Articles

Distributed Model-Based Event-Triggered Leader–Follower Consensus Control for Linear Continuous-Time Multiagent Systems

This article investigates the event-triggered leader-follower consensus control problem for linear continuous-time multiagent systems (MASs). A new consensus protocol and an event-triggered communication (ETC) strategy based on a closed-loop state estimator are designed. The closed-looped state estimator renders us more accurate state estimations, therefore the triggering times can be decreased while maintaining control performance. We show that the consensus of MASs can be achieved by employing the proposed control scheme. In addition, the Zeno-phenomena can be excluded. As a practical application, our method is successfully applied to the vehicle platoon control. The effectiveness is further verified by simulations conducted on the Prescan platform.

Singularity Excitations and Initial Value Problem in Continuous LTI Systems

A modern challenge in electrical engineering education is to keep the math at a sufficient level, with a goal to find an optimal balance between calculus competence and operative skills needed for real-life technical applications. It is not uncommon that some gaps emerge during this quest, which makes it difficult for undergraduates to entirely understand topics related on prior knowledge. This paper aims to draw attention to several important moments concerning total response of Continuous Linear Time Invariant systems, which are superficially or incorrectly explained in many textbooks, and to offer logical arrangement which can be easily understood and accepted by students. The base of discussion relies on classical calculus background, particularly on Picard’s theorem on existence and uniqueness. This theorem is rarely mentioned in signals and systems textbooks. However, mathematical models of many types of signals don’t satisfy the condition for continuity, which can easily produce difficulties in the learning process. It is shown that some reported disagreements and issues related to initial conditions, can be easily cleared out by using the smooth transition from classical calculus to mathematics used in system theory. It is also shown that the classical method is always the primary tool, even for determining the impulse response, while the impulse response is unnecessary or sufficient to determine the total system response, regardless of whether the convolution integral is used.

Fault Detection in Hydroelectric Generating Units with Trigonometric Filters

A procedure based on trigonometric filters is proposed for parameter identification in a hydroelectric power generating unit approximated by a Multi Input - Single Output linear continuous-time varying system. First the discrete cosine transform is used as an interpolation filter and secondly an integral transform based on a Fourier kernel is applied to obtain a discrete-time model. Then a recursive least squares algorithm is performed to estimate abrupt changes of parameters and thus detect faults in the power plant. The whole method is successfully applied to a scenario fed with real sampled data featured by a poor excitation.

Stability of Linear Continuous-Time Systems With Stochastically Switching Delays

Necessary and sufficient conditions for the stability of linear continuous-time systems with stochastically switching delays are presented in this paper. It is assumed that the delay random paths are piece-wise constant functions of time where a finite number of values may be taken by the delay. The stability is assessed in terms of the second moment of the state vector of the system. The solution operators of individual linear systems with constant delays, chosen from the set of all possible delay values, are extended to form new augmented operators. Then for proper formulation of the second moment in continuous time, tensor products of the augmented solution operators are used. Finally the finite-dimensional versions of the stability conditions, that can be obtained using various time discretization techniques, are presented. Some examples are provided that demonstrate how the stability conditions can be used to assess the stability of linear systems with stochastic delay.

Preview control for a class of linear stochastic systems with multiplicative noise

ABSTRACT In this paper, the preview control problem for a class of linear continuous time stochastic systems with multiplicative noise is studied based on the augmented error system method. First, a deterministic assistant system is introduced, and the original system is translated to the assistant system. Then, the integrator is employed to ensure the output of the closed-loop system tracking the reference signal accurately. Second, the augmented error system, which includes integrator vector, control vector and reference signal, is constructed based on the system after translation. As a result, the tracking problem is transformed into the optimal control problem of the augmented error system, and the optimal control input is obtained by the dynamic programming method. This control input is regarded as the preview controller of the original system. For a linear stochastic system with multiplicative noise, the difficulty being unable to construct an augmented error system by the derivation method is solved in this paper. And, the existence and uniqueness solution of the Riccati equation corresponding to the stochastic augmented error system is discussed. The numerical simulations show that the preview controller designed in this paper is very effective.

A Simple Simulation Approach for the Estimation of Convergence and Performance of Fully Adaptive Equalization in High-Speed Serial Interfaces

We propose a simple approach to simulate the convergence and the performance of high-speed serial interfaces with adaptive equalization. Such a method uses as input the pulse response of the channel (printed circuit board and cables, plus package/socket) that is then modified by adaptive techniques implementing feed-forward, decision-feedback, and linear-continuous time equalization. Probabilistic considerations are used in this novel method to estimate the evolution during time of the LMS loop and the resulting evolution of the eye diagram. Sample results are reported for a realistic link operating at 20 Gb/s.

Stabilization Control for Linear Continuous-Time Mean-Field Systems

This paper investigates the stabilization and control problems for linear continuous-time mean-field systems (MFS). Under standard assumptions, necessary and sufficient conditions to stabilize the mean-field systems in the mean square sense are explored for the first time. It is shown that, under the assumption of exact detectability (exact observability), the mean-field system is stabilizable if and only if a coupled algebraic Riccati equation (ARE) admits a unique positive semi-definite solution (positive definite solution), which coincides with the classical stabilization results for standard deterministic systems and stochastic systems. One of the key techniques in the paper is the obtained solution to the forward and backward stochastic differential equation (FBSDE) associated with the maximum principle for an optimal control problem. Actually, with the analytical FBSDE solution, a necessary and sufficient solvability condition of the optimal control, under mild conditions, is derived. Accordingly, the stabilization condition is presented by defining an Lyaponuv functional via the solution to the FBSDE and the optimal cost function. It is worth of pointing out that the presented results are different from the previous works for stabilization and also different from the works on optimal control.

Nash Tracking Game with Preview by State Feedback for Linear Continuous-Time Markovian Jump Systems

Nash Tracking Game with Preview by State Feedback for Linear Continuous-Time Markovian Jump Systems

Nash Tracking Game with Preview by State Feedback for Linear Continuous-Time Systems

In this paper, we study Nash tracking game problems with preview for linear continuous-time systems over finite time intervals. We introduce cross-coupled differential Riccati equations (CDREs) to give solutions of the tracking problems with multi-players. Corresponding to the coupled properties of the CDREs, the forms of preview compensator dynamics are cross-coupled. In this paper, we focus on the derivation of the necessary conditions for the solvability of the tracking problems by variational approach.

Exact Discrete Representations of Linear Continuous Time Models with Mixed Frequency Data

The time aggregation of vector linear processes containing (i) mixed stock‐flow data and (ii) aggregated at mixed frequencies, is explored, focusing on a method to translate the parameters of the underlying continuous time model into those of an equivalent model of the observed data. Based on manipulations of a general state‐space form, the results may be used to model multiple frequencies or aggregation schemes. Estimation of the continuous time parameters via the ARMA representation of the observable data vector is discussed and demonstrated in an application to model stock price and dividend data. Simulation evidence suggests that these estimators have superior properties to the traditional approach of concentrating the data to a single low frequency.

Fault Detection of continuous time linear switched systems using combination of Bond Graph method and switching observer

In this paper, a new Fault Detection (FD) scheme based on combination of switching observer and Bond Graph (BG) method for linear continuous time switched systems with Average Dwell Time (ADT) approach is proposed. The proposed scheme is a BG-based two-stage FD system in which the compact state space representation and Global Analytical Redundancy Relations (GARRs) are derived based on the BG model. In the first stage, a switched observer is designed considering disturbance attenuation level, fault sensitivity and rapid fault detection criteria by solving a weighted Linear Matrix Inequality (LMI) optimization problem. Next, a new form of GARRs which is based on output estimation error of the observer and is called Error-based Global Analytical Redundancy Relations (EGARRs) is developed to combine the observer and BG method. The output estimation errors from the observer, which are adequately sensitive to faults and simultaneously the effects of disturbances are attenuated therein, are given to the EGARRs to generate the residuals of the FD system. The proposed method may be used for fault detection of switched linear systems with ADT based on the BG model of the system. Finally, two case studies including a two-tank system and a buck converter-driven DC motor are considered to show the efficiency and real-time implementation of the proposed method.

Selection of a Relaxation Function to Describe the Dissipative α-Relaxation Process in Latex Polymers

Discrete relaxation times D(τ) in latex polymers are calculated using the phenomenological model of a standard linear body and continuous relaxation time spectra H(τ) involving the Kohlrausch function in the temperature range from –150 to +250°C. The higher relaxation inhomogeneity of the modified polymers confirms the previously obtained experimental data on its estimates across the width of the continuous spectrum of relaxation times with the involvement of dependence λ/λmax = f {(Т – Тmax)/Тmax}.

Partial Feedback Linearizing Model Predictive Controllers for Multiple Photovoltaic Units Connected to Grids through a Point of Common Coupling

In this paper, partial feedback linearizing model predictive controllers are designed for grid-connected systems comprising multiple photovoltaic (PV) units where these units are connected through a point of common coupling (PCC). The proposed controllers are designed for voltage source inverters (VSIs) based on comprehensive dynamical models of grid-connected PV systems with the proposed topology. The proposed partial feedback linearization scheme decouples multiple PV units in the forms of several reduced-order subsystems and enables linear controller design through the linear continuous-time receding horizon model predictive control scheme. The proposed partial feedback linearization scheme also considers dynamic interactions among multiple PV units as external noises or disturbances and decouples these noises. This paper includes the noise decoupling capability of the partial feedback linearization for grid-connected PV systems with multiple PV units which are connected through a PCC. Simulation results clearly demonstrate the effectiveness of the proposed scheme under different operating conditions as compared to an existing proportional integral controller.

A Stackelberg strategy for continuous-time mixed H2/H∞ control problem with time delay

This paper is concerned with the mixed H2/H∞ control with linear continuous time system and time delay. To deal with this, we presents a Stackelberg strategy by treating the control input and the disturbance as leader and follower, respectively. The leader’s control strategy minimizes the cost function which is in H2 norm and the follower’s control strategy maximizes the cost function which is in H∞ norm. The main technique of this paper is deal with the noncausal relationship of the variables caused by time delay in the control input by introducing two costates to capture the future information and one state to capture the past information. Through theory analyzing, the Stackelberg strategy exists uniquely. Moreover, with the assistance of the extended state space expression, the explicit expression of the strategy is obtained.

Hybrid Optimal Tracking Control for Linear Continuous-Time Systems by Simultaneous Optimization Approach of System States and Mode Distributions

In this paper, we study optimal LQG tracking control problems for linear continuous-time hybrid systems. We adopt an approach to prepare some candidates of mode distributions and minimize value functions at each time for the systems and performance indices. By the approach, system states and mode distributions are simultaneously optimized so that the performance indices are minimized for available information of reference signals. We consider optimization problems for averaged systems and averaged performance indices throughout mode distributions. Finally we give numerical examples and verify that we can obtain both optimal tracking performance and optimal candidate of mode distributions by the algorithm presented in this paper.

Structural detectability analysis of cyber attacks for power grids via graph theory

Cyber-physical systems are pervasive in every walk of life. The safety performances of these systems are threatened by external malicious attacks and unforeseen failures. In terms of grid structural characteristics and graph theory, this study proposes a new framework to solve the problem of structural vulnerability which is caused by undetectable attacks in power grids. Based on the linear continuous-time descriptor system model, the digraph associated with structural matrix model for power grid is introduced in detail. To analyse the attack detectability in digraph, a series of basic properties are proposed about digraphs of structural power grids. Then an algorithm is proposed for obtaining the positions of the detection outputs to ensure left-invertible and observability for grid systems. In addition, an algorithm for judging whether there exists a structural vulnerability for the arrangement of the attack inputs and outputs of power grids is proposed, by which one can find disjoint paths if there exists structural vulnerability. Finally, some examples are shown to verify the effectiveness of the proposed algorithms.

A Result on Almost Sure Stability of Linear Continuous-Time Markovian Switching Systems

This work investigates the almost sure stability for linear Markovian switching systems in continuous time by using Lyapunov function method. The distribution of switching points is combined into constructing the Lyapunov function, which gives rise to the fluctuation in bounding the transient phase over the time interval confined between two successive switching points due to the randomness of their locations. Showing that the influence of the accumulated fluctuations, by averaging it out, will be negligible, is the key step in proving our stability result. Illustrative examples are included to show the effectiveness of the theoretical result.

Hybrid Optimal Tracking Control with Preview for Linear Continuous-Time Systems by Simultaneous Optimization Approach of System States and Mode Distributions

Hybrid Optimal Tracking Control with Preview for Linear Continuous-Time Systems by Simultaneous Optimization Approach of System States and Mode Distributions

On the Asymptotic Hyperstability of Linear Time-Invariant Continuous-Time Systems under a Class of Controllers Satisfying Discrete-Time Popov’s Inequality

This paper is concerned with the property of asymptotic hyperstability of a continuous-time linear system under a class of continuous-time nonlinear and perhaps time-varying feedback controllers belonging to a certain class with two main characteristics; namely, (a) it satisfies discrete-type Popov’s inequality at sampling instants and (b) the control law within the intersample period is generated based on its value at sampling instants being modulated by two design weighting auxiliary functions. The closed-loop continuous-time system is proved to be asymptotically hyperstable, under some explicit conditions on such weighting functions, provided that the discrete feed-forward transfer function is strictly positive real.

Analysis of Positive Linear Continuous–Time Systems Using the Conformable Derivative

Abstract Positive linear continuous-time systems are analyzed via conformable fractional calculus. A solution to a fractional linear system is derived. Necessary and sufficient conditions for the positivity of linear systems are established. Necessary and sufficient conditions for the asymptotic stability of positive linear systems are also given. The solutions of positive fractional linear systems based on the Caputo and conformable definitions are compared.