Continuous-time Subsystems Research Articles

Fixed-time synchronization of delayed inertial Cohen–Grossberg neural networks with desynchronizing impulses

This article focuses on achieving fixed-time (FXT) synchronization of inertial Cohen–Grossberg neural networks (ICGNNs) in the presence of time-varying delays and desynchronizing impulsive effects. Firstly, a new lemma is presented to achieve FXT stability of the impulsive systems with destabilizing impulses. The settling-time function is shown to depend on both the parameters of impulsive sequence and continuous-time subsystems. Furthermore, based on the proposed lemma, sufficient conditions are established to achieve FXT synchronization of ICGNNS with desynchronizing impulses by designing a unified controller. Two numerical examples are taken into consideration to verify the efficacy of the proposed theoretical results.

Necessary and sufficient conditions for quadratic stabilizability of switched systems on non-uniform time domains

In this paper, we consider the quadratic stabilizability via state feedback for a particular class of switched systems that evolve on a non-uniform time domain by introducing time scales theory. The system considered switches between a continuous-time subsystem with variable lengths and a discrete-time subsystem with variable discrete step sizes. Necessary and sufficient conditions are derived to guarantee the quadratic stability of this class of switched systems via a switching state feedback law based on the existence of a common positive definite matrix satisfying the quadratic stabilizability condition by considering that the two subsystems are unstable. By state feedback, we mean that the switching among subsystems depends on the system states. Current results for this kind of state switching feedback control are derived only for switched systems evolving on a continuous time domain or a discrete time domain with fixed step’s size. These results are not applicable for the particular class of switched systems where there is a mixing between the continuous and discrete dynamics. This motivates the derivation of a new and more general state feedback control law for switched systems in this work. A numerical example illustrating the results is presented.

Consensus of Matrix-Weighted Hybrid Multiagent Systems.

As we all know, heterogeneity is a very important feature of multiagent systems (MASs). In this article, we examine the consensus control problems of matrix-weighted hybrid MASs, which contain discrete-time and continuous-time dynamic agents. Under fixed and switched undirected networks, three consensus algorithms are proposed for matrix-weighted hybrid MASs. In the three consensus algorithms, the sampled data control method is utilized in the continuous-time subsystem to analyze the convergence of different dynamic agents in the matrix-weighted interaction mode. For the symmetric matrix-weighted fixed and switched multiagent networks, when the sampling period meets certain conditions, the consensus criteria are established via the matrix theory, Lyapunov stability theory, and analysis theory. Moreover, asymmetric matrix-weighted fixed multiagent networks which can be applied to some scenarios with scaled and rotated updates constraints are considered, and consensus criteria are also obtained when the sampling period meets certain conditions. Finally, a few simulation examples are supplied to validate the correctness of the obtained theoretical results.

Second-Order Hybrid Consensus of Multi-Agent Systems With Matrix-Weighted Networks

This article considers a hybrid consensus in the context of second-order multi-agent systems with matrix-weighted networks. A matrix-weighted hybrid consensus controller is built upon the sampled-data method in continuous-time subsystem. For the cases of undirected graph and directed graph, some sufficient and necessary conditions, which depend on the sampling period, coupling gains and the eigenvalues of Laplacian matrix, are derived with the assistance of stability theory and matrix theory. Finally, through simulation comparison, the validity of the obtained results is demonstrated.

Stability of switched stochastic reaction–diffusion systems

As one of important hybrid dynamical systems, switched system has practical applications in some practical systems. Generally, switched system is made up of a family of continuous-time subsystems and discrete switching signals. Affected by environmental disturbance, stochastic switched system should be considered. This paper deals with a class of switched stochastic reaction-diffusion systems (SSRDSs, in short), where the discrete switching signal is a right continuous and piecewise function. The switching instants are stopping times or deterministic times. Criterions on stability in probability and exponential stability in mean square of the trivial solution for SSRDSs are derived by means of Lyapunov functional methods. We propose two examples to verify the obtained theoretical results.

A dwell time approach for the stabilization of mixed Continuous/Discrete switched systems

In this paper, we study the stabilization properties of Continuous/Discrete switched systems using the dwell time approaches. The considered system switches between a continuous-time subsystem evolving on time intervals with variable lengths and a discrete-time subsystem with variable discrete step sizes. Since the time domain is non-uniform, and the stability of the discrete-time subsystem with variable discrete step sizes does not depend only on the dynamic of the system, but also on the length of the discrete steps, the usual conditions of dwell time approaches may not be applicable to stabilize this special class of switched systems. Motivated by that, stabilizing dwell time and average dwell time conditions are derived by introducing the time scales theory and numerical examples are proposed to illustrate the effectiveness of the proposed methods.

On the Stabilization of a Network of a Class of SISO Coupled Hybrid Linear Subsystems via Static Linear Output Feedback

This paper deals with the closed-loop stabilization of a network which consists of a set of coupled hybrid single-input single-output (SISO) subsystems. Each hybrid subsystem involves a continuous-time subsystem together with a digital (or, eventually, discrete-time) one being subject to eventual mutual couplings of dynamics and also to discrete delayed dynamics. The stabilizing controller is static and based on linear output feedback. The controller synthesis method is of algebraic type and based on the use of a linear algebraic system, whose unknown is a vector equivalent form of the controller gain matrix, which is obtained from a previous algebraic problem version which is based on the ad hoc use of the matrix Kronecker product of matrices. As a first step of the stabilization, an extended discrete-time system is built by discretizing the continuous parts of the hybrid system and to unify them together with its digital/discrete-time ones. The stabilization study via static linear output feedback contains several parts as follows: (a) stabilizing controller existence and controller synthesis for a predefined targeted closed-loop dynamics, (b) stabilizing controller existence and its synthesis under necessary and sufficient conditions based on the statement of an ad hoc algebraic matrix equation for this problem, (c) achievement of the stabilization objective under either partial or total decentralized control so that the whole controller has only a partial or null information about couplings between the various subsystems and (d) achievement of the objective under small coupling dynamics between subsystems.

Model predictive control of switching continuous‐time systems with stochastic jumps: Application to an electric current source

This paper proposes an extension of the model predictive control framework for switching continuous-time linear systems. The switching times follow a stochastic process with limited statistical information. At each switching time, the controller knows the system state, but it is blind with respect to the switching continuous-time subsystems. In this setting, the paper's main contribution is to show how to compute the model predictive control gain. The paper also illustrates the implications of our approach for applications. The approach was used in practice to control an electric current source that supplied a switching load. The experimental data support the usefulness of our approach.

Interval consensus of switched multiagent systems

This paper studies interval consensus for switched multiagent systems over directed networks, which consist of a continuous-time subsystem and a discrete-time subsystem regulated by a switching rule. Interval consensus refers to a state constrained consensus, where each agent is allowed to propose an acceptable interval to saturate their expressed states and the final consensus state lies in the nonempty intersection of all these intervals. We establish conditions guaranteeing interval consensus for switched multiagent system under arbitrary switching rules. Furthermore, we introduce the scaled interval consensus notion, which allows both the convergence of states to a pre-assigned proportion and the scaled consensus values lying in the desired range. Simulation results are provided to verify the effectiveness of the theoretical results.

Second-Order Consensus for Multiagent Systems With Switched Dynamics.

This article investigates the consensus control problem for second-order multiagent systems with switched dynamics, consisting of a continuous-time subsystem and a discrete-time subsystem. Under a fixed directed topology, two linear control protocols are proposed for achieving consensus. One is that two subsystems use different control inputs, where the continuous-time system uses continuous-time control, and the discrete-time system uses discrete-time control. In order to reach consensus for this kind of control protocol, some necessary and sufficient conditions are derived. The other is to use the same control algorithm for the two subsystems, which is a sampled-data control input. Similar consensus conditions are also obtained. Finally, a few simulation examples are given to verify the theoretical results.

Event-triggered control for switched systems with both continuous-time and discrete-time subsystems

ABSTRACTIn this paper, we consider the event-triggered control for a class of switched systems which are composed of one continuous-time subsystem and one discrete-time subsystem. The proposed event-triggered mechanism adopts the form of periodic triggering, which combines the advantages of periodic control and event-triggered control. Consequently, Zeno behaviour can be essentially eliminated. A criterion is presented to ensure the exponential stability of the closed-loop switched systems. In addition, we extend the above result to the case of the switched system with multiple continuous-time and discrete-time subsystems and the case of observer-based control. Finally, a numerical example is provided to illustrate the theoretical results.

Stability of Wide-Area Power System Controls With Intermittent Information Transmission

This paper investigates the stability problem of wide-area damping controllers with intermittent information transmission. Due to the interruption in communication links between remote measurements and damping controller or from the damping controller to the damping actuators, the closed-loop system might become unstable. The instability is strongly related to the duration of interruption of information transmission. To estimate instability, this paper formulates the problem as continuous/discrete-time switched system and the stability conditions are derived using time-scale theory. This method allows us to handle continuous and discrete dynamics as two pieces of the same framework, such that the system will switch between a continuous-time subsystem (when the communication occurs without any interruption) and a discrete-time subsystem (when the communication fails). The contribution is to estimate the maximum allowable value of the time of interruption of information transmission that does not violate the exponential stability of the closed-loop system. The findings are useful in specifying the minimum requirements for communication infrastructure and the time to activate remedial action schemes. Simulations are performed based on both linear and nonlinear systems to validate the theoretical development.

Stability analysis of a class of switched nonlinear systems using the time scale theory

This paper investigates stability for a class of switched nonlinear systems evolving on a non-uniform time domain. The studied class of systems switch between a nonlinear continuous-time and a nonlinear discrete-time subsystem. This problem is formulated using time scale theory where the latter is formed by a union of disjoint intervals with variable lengths and variable gaps. Using Gronwall’s inequality and properties of the time scale exponential function, sufficient conditions are derived to ensure exponential stability. The results can be applied to cases where the continuous-time subsystem or the discrete-time subsystem is not necessarily stable, and the state matrices of each subsystem are not necessarily pairwise commuting. To illustrate the effectiveness of the proposed scheme, the consensus problem for general linear multi-agent systems under intermittent information transmissions is studied under this framework.

Containment Control for General Second-Order Multiagent Systems With Switched Dynamics.

This paper investigates the distributed containment control problem for a class of general second-order multiagent systems with switched dynamics, which is composed of a continuous-time (CT) subsystem and a discrete-time (DT) subsystem. For this switched multiagent system under fixed directed topology, a distributed containment control protocol is proposed for each follower based on the relative local measurements of neighboring followers and leaders. Some necessary and sufficient conditions are derived under the condition that the network topology contains a directed spanning forest, and these conditions ensure that the general second-order containment control problem can be solved under arbitrary CT-DT switching. If the general second-order system is reduced to the double integrator system, some simpler containment conditions are presented. Furthermore, the similar results are also obtained under switching directed topology. Finally, some simulation examples are presented to show the efficiency of the theoretical results.

Stability of switched systems on non-uniform time domains with non commuting matrices

The time scale theory is introduced to study the stability of a class of switched linear systems on non-uniform time domains, where the dynamical system commutes between a continuous-time linear subsystem and a discrete-time linear subsystem during a certain period of time. Without assuming that matrices are pairwise commuting, some conditions are derived to guarantee the exponential stability of the switched system by considering that the continuous-time subsystem is stable and the discrete-time subsystem can be stable or unstable. Some examples show the effectiveness of the proposed scheme.

Controllability and observability of switched multi-agent systems

ABSTRACTThis paper considers controllability and observability of switched multi-agent systems, which are composed of continuous-time and discrete-time subsystems. First, a controllability criterion is established in terms of the system matrices. Then, by virtue of the concepts of the invariant subspace and the controllable state set, a method is proposed to construct the switching sequence to ensure controllability of switched multi-agent systems, and a necessary and sufficient condition is obtained for controllability. Moreover, a necessary controllability condition is derived in terms of eigenvectors of the Laplican matrix. With respect to observability, two necessary and sufficient algebraic conditions are obtained. Finally, simulation examples are provided to illustrate the theoretical results.

Parameter estimation of the fractional‐order Hammerstein–Wiener model using simplified refined instrumental variable fractional‐order continuous time

This study proposes a direct parameter estimation approach from observed input–output data of a stochastic single-input–single-output fractional-order continuous-time Hammerstein–Wiener model by extending a well known iterative simplified refined instrumental variable method. The method is an extension of the simplified refined instrumental variable method developed for the linear fractional-order continuous-time system, denoted. The advantage of this novel extension, compared with published methods, is that the static output non-linearity of the Wiener model part does not need to be invertible. The input and output static non-linear functions are represented by a sum of the known basis functions. The proposed approach estimates the parameters of the linear fractional-order continuous-time subsystem and the input and output static non-linear functions from the sampled input–output data by considering the system to be a multi-input–single-output linear fractional-order continuous-time model. These extra inputs represent the basis functions of the static input and output non-linearity, where the output basis functions are simulated according to the previous estimates of the fractional-order linear subsystem and the static input non-linear function at every iteration. It is also possible to estimate the classical integer-order model counterparts as a special case. Subsequently, the proposed extension to the simplified refined instrumental variable method is considered in the classical integer-order continuous-time Hammerstein–Wiener case. In this paper, a Monte Carlo simulation analysis is applied for demonstrating the performance of the proposed approach to estimate the parameters of a fractional-order Hammerstein–Wiener output model.

Factored performance functions and decision making in continuous time Bayesian networks

The continuous time Bayesian network (CTBN) is a probabilistic graphical model that enables reasoning about complex, interdependent, and continuous-time subsystems. The model uses nodes to denote subsystems and arcs to denote conditional dependence. This dependence manifests in how the dynamics of a subsystem changes based on the current states of its parents in the network. While the original CTBN definition allows users to specify the dynamics of how the system evolves, users might also want to place value expressions over the dynamics of the model in the form of performance functions. We formalize these performance functions for the CTBN and show how they can be factored in the same way as the network, allowing what we argue is a more intuitive and explicit representation. For cases in which a performance function must involve multiple nodes, we show how to augment the structure of the CTBN to account for the performance interaction while maintaining the factorization of a single performance function for each node. We introduce the notion of optimization for CTBNs, and show how a family of performance functions can be used as the evaluation criteria for a multi-objective optimization procedure.

Consensus of switched multi-agent systems with random networks

ABSTRACTThis paper studies the consensus problem of the switched multi-agent system composed of continuous-time and discrete-time subsystems. Communication among agents is modelled as a random network where the existence of any information channel is probabilistic and independent of other channels. Then, some necessary and sufficient conditions are presented for solving average consensus of the switched multi-agent system under arbitrary switching. Furthermore, we show that the average consensus in different sense (mean square, almost surely and in probability, respectively) are equivalent. Finally, simulations are provided to illustrate the effectiveness of our theoretical results.

Multiobjective control system controllers design based on switching and applications

Many systems operate in an uncertain environment of limitations such as temperature, pressure, and physical acceleration/deceleration limitation, etc. Whatever the linear or nonlinear control system design methods are, the aircraft engine will encounter limitations on some occasions. So the aircraft engine control system consists of a family of continuous-time subsystems and switches from one to another depending on various environmental factors (see Figure 1). When the system switches from one subcontrol loop to another, the stability of the system is the basic performance that must be considered. The traditional control method is to switch slowly to avoid the dangers. Therefore, there is much space to improve the dynamic performance of the control system.