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In this study, the controllability of multi-agent systems with second-order dynamic under discrete-time model, which evolve on two time scales. The authors first characterise the systems by difference equations with a singular perturbation parameter. Then, in order to get rid of the singular perturbation parameter, they split the systems into a slow subsystem and fast subsystem based on the iterative method and approximate approach. Moreover, according to matrix theory, they deduce a lot of necessary and/or sufficient controllability criteria of the systems. In particular, a second-order controllability criterion only depending on the eigenvalues of matrices is proposed, which is more easy-to-use and efficient. A simulation example is lastly given to clarify the validity of all theoretical results.

This paper studies the distributed consensus problem of a new class of multi-agent systems, where each agent is represented by the two-time-scale system. Two fully distributed, ϵ-dependent adaptive...

This paper is concerned with robustly input-to-state stable (ISS) and Robust ISS by feedback of uncertain discrete-time singularly perturbed systems (SPSs) with disturbances. Meanwhile, robust stab...

In this paper, the global asymptotic stability of two-time-scale competitive neural networks(CNNs) with multiple time-varying delays is investigated. By constructing a new e-dependent Lyapunov functional, sufficient conditions for the global asymptotic stability of the concerned systems are established, and an optimization problem is formulated to get the best estimate of the e-bound. Compared with the existing results, the proposed results are more general and less conservative in the sense of determining an upper bound for the time-scale parameter e. Finally, three examples are given to illustrate the advantages of the obtained results.

We analyze a time-varying Mperi/Geo2timeScale/N queueing system. The arrival process is periodic Poisson. The service time of a customer has components in different time scales: length of stay (LOS) in days and departure time (hdis) in hours. This queueing system has been used to study patient flows from the emergency department (ED) to hospital inpatient wards. In that setting, the LOS of a patient is simply the number of days she spends in a ward, and her departure time hdis is the discharge hour on the day of her discharge. We develop a new analytical framework that can perform exact analysis on this novel queueing system. This framework has two steps: first analyze the midnight customer count process and obtain its stationary distribution, then analyze the time-dependent customer count process to compute various performance measures. We also develop approximation tools that can significantly reduce the computational time. In particular, via Stein’s method, we derive explicit expressions to approximate the stationary distribution of the midnight count. We provide error bounds for these approximations and numerically demonstrate that they are remarkably accurate for systems with various sizes and load conditions. Our theoretical and numerical analysis have produced a number of insights that can be used to improve hospital inpatient flow management. We find that the LOS term affects the overnight wait caused by the mismatch between daily arrivals and discharges, whereas the hdis term affects the intraday wait caused by the nonsynchronization between the arrival and discharge time patterns. Thus, reducing LOS or increasing capacity can impact the daily average performance significantly; shifting the discharge timing to earlier times of a day can alleviate the peak congestion in the morning and mainly affects the time-dependent performance. The e-companion is available at https://doi.org/10.1287/opre.2016.1566 .

This paper presents a two-time-scale neurodynamic approach to constrained minimax optimization using two coupled neural networks. One of the recurrent neural networks is used for minimizing the objective function and another is used for maximization. It is shown that the coupled neurodynamic systems operating in two different time scales work well for minimax optimization. The effectiveness and characteristics of the proposed approach are illustrated using several examples. Furthermore, the proposed approach is applied for $H_\infty $ model predictive control.

We study a two-time-scale system of jump-diffusion stochastic differential equations. The main goal is to study the convergence rate of the slow components to the effective dynamics. The convergence established here is in the strong sense, i. e., uniformly in time. For the ergodicity assumptions, we use the existence of a Lyapunov function to control the return times. This assumption is weaker than the one- sided Lipschitz condition, frequently used for deriving rates.

Two-time-scale (TTS) distributions are introduced. For a class of stable systems, it is shown that every TTS distribution has a two-frequency-scale (TFS) Laplace transform. Conversely, it is shown that the impulse response of any stable TFS transfer function, and hence any stable (standard) singularly perturbed system, can be characterized in terms of a stable TTS distribution. A time domain decomposition for TTS distributions is obtained which parallels the slow and fast decomposition of singularly perturbed systems and also the frequency domain decomposition of TFS transfer functions. It is shown that every stable TTS distribution can be decomposed in terms of two simpler distributions represented in two different time scales. A composite distribution is constructed from these two which approximates the TTS distribution arbitrarily closely in the L 1 norm.

This note is concerned with the robust stability problem of uncertain two-time-scale systems, where the only information available for system uncertainties is their norm upper bounds. The stability bound /spl epsiv//sup */ is derived via a state transformation and the constructive use of a Lyapunov function. Finally, examples are given to illustrate the applications of the proposed results.

The present paper has two main purposes. The first is to provide an explicit state-space solution of the robust stabilization problem with respect to the NLCF for two-time scale systems. In this construction only the solutions of the control and of the filtering Riccati equations associated with the slow and with the fast dynamics of the nominal plant are used. These solutions do not depend upon the singular perturbation and therefore all computations are well-conditioned. The second purpose of the paper is to investigate the case when an k -independent robust controller can be used for the robust stabilization of a two-time scale nominal system. Two constructions of such controllers are developed under some additional assumptions. Numerical examples illustrate the theoretical developments.

New regulations for emission control require the improvement of the system composed by spark ignition internal combustion engine and three-way catalytic converter (TWC). In particular, an important problem is to minimize harmful emissions during the transient warm-up phase where the TWC is not working yet and, hence, a large amount of pollutants are emitted in the air. Toward this goal we present a dynamical thermo-chemical TWC model simple enough for the design and test of warm-up control strategies. The model is obtained through an asymptotic approximation of a more detailed model, i.e., by letting the adsorption coefficient between gas and substrate tend to infinity. Further, we present a fast integration algorithm based partly on a “method of lines” space-discretization, partly on the “method of characteristics” for “quasi linear” hyperbolic partial differential equations, the separation being allowed by a two time scale analysis of the system. The model has been identified, through a purposely designed genetic algorithm, and validated on experimental data.

This paper focuses on the synthesis of well-conditioned multivariable robust controllers for a broad class of multi-input multi-output two-time-scale nonlinear systems with time-varying uncertain variables, modeled within the framework of singular perturbations. The proposed controller stabilizes the fast dynamics, guarantees boundedness of trajectories, and ensures that the ultimate discrepancy between the outputs and the external reference inputs in the closed-loop system can be made arbitrarily small by an appropriate choice of controller parameters, provided that the singular perturbation parameter is sufficiently small. The developed control method is tested, through simulations, on a fluidized catalytic cracking reactor.

In this paper a reduced-order model for control design applications of a seventh-order two-time-scale discrete-time model of synchronous machines is developed. The numerical simulation is performed on synchronous machines, and the simulation results obtained using the iterative separation of time-scales provide improved accuracy of the reduced-order models, compared with that of the same obtained via the classical quasi-steady-state (qss) technique.

International audience; This paper addresses the state estimation of two-time scale nonlinear systems with an unknown input multi-observer (UIMO). In order to design such an observer, the nonlinear system presented in a singular perturbed form is transformed into an equivalent multiple model with unmeasurable premise variables (UPV) affected by unknown inputs (UI). Then an observer is built and the stability analysis of the state reconstruction error is performed by using the Lyapunov method that leads to the resolution of linear matrix inequalities (LMIs). The performances of the proposed estimation method are highlighted through the application to a wastewater treatment plant (WWTP) model.

Multi-rate control design of two-time-scale systems is considered via digital redesign method. After the multi-rate control design procedures via singular perturbation theory is reviewed and the relationships between slow and fast subproblems are clarified, the design method via the bi-linear transformation method is investigated. Furthermore, in order to verify the validity of this method, an application to the longitudinal control problem of an aircraft is given.

A decentralized model predictive controller applicable for some systems which exhibit different dynamic characteristics in different channels was presented in this paper. These systems can be regarded as combinations of a fast model and a slow model, the response speeds of which are in two-time scale. Because most practical models used for control are obtained in the form of transfer function matrix by plant tests, a singular perturbation method was firstly used to separate the original transfer function matrix into two models in two-time scale. Then a decentralized model predictive controller was designed based on the two models derived from the original system. And the stability of the control method was proved. Simulations showed that the method was effective.

International audience; The aim here is to study two-time-scale models and their associated parameter identification. When it is possible to consider two well-separated time scales, and when the fast component of the applied loading is periodic, a periodic time homogenization scheme, similar to what exists in space homogenization, can be used to derive a homogenized model. A parameter identification process for this latter is then proposed, consisting in homogenizing with respect to time a classical identification strategy based on the use of adjoint state formulations; it is then applied to an academic example showing the benefits of such a strategy.

Output feedback design of discrete-time decentralized systems with slow and fast modes is considered. Conditions for the complete separation of slow and fast subsystems are given. The slow and fast subsystem outputs, which are obtained by applying the slow and fast subcontrollers to the corresponding subsystems, will be shown to approximate those of the original system. Also, the composite control, when being applied to the original system, will place the eigenvalues sufficiently close to the desired locations.

Output feedback control of linear time-invariant singularly perturbed systems is studied. The set of all compensators that stabilize a singularly perturbed system while preserving its two-time-scale structure is parameterized. The parameterization is used to show that any two-frequency-scale stabilizing compensator can be asymptotically approximated by a compensator designed via a sequential procedure. In this procedure, a fast (high-frequency) compensator is designed first to stabilize the fast model of the system. Then, a strictly proper slow (low-frequency) compensator is designed to stabilize a modified slow model. The parallel connection of the two compensators forms a two-frequency-scale stabilizing compensator for the singularly perturbed system.

The block processing technique is applied to a class of two-time-scale linear discrete-time systems. Block state-space structures for slow and fast subsystems have been obtained. Based upon these models, blocked slow and fast controls are designed. In addition, an extra control is designed to exactly compensate for the effects of the parasitics.

The design of stabilizing feedback control of singularly perturbed diserete-time systems is decomposed into the design of slow and fast controllers which are combined to form the composite control. Composite control strategies are developed for the case of single rate measurements (all variables are measured at the same rate) as well as for the case of multirate measurements (slow variables are measured at a rate slower than that of fast variables).

Linear shift-invariant discrete-time systems satisfying the two time scale property-are considered. Conditions for a complete separation of slow and fast subsystems are given. Subsystem regulator problems are investigated and the controllability property of the system is established based on the subsystem controllability properties. A subsystem controller design method is proposed depending on the separability of the slow and fast controls.

Linear shift-invariant discrete-time systems satisfying the two-time-scale property are considered. A transformation matrix is formed and applied to the system to separate its slow and fast modes. Two subsystems are then defined, one for the slow modes and the other for the fast modes. An eigenvalue placement technique is proposed that will place the eigenvalues of the closed loop sub-systems at desired locations. The composite controller will also be formed for the original system.

The design of a state feedback controller for a two-time-scale discrete-time system is considered via a two-stage design approach. After discrete-time modelling via slow and fast sampling rates has been discussed, state feedback design approaches for the fast sampling model (i.e. the two-stage design approach and the direct approach) are studied, and the relation between them is clarified. Following these results, the eigenvalue assignment and the stabilizing problems are investigated.

For a class of nonlinear singularly perturbed systems, feedback stabilizing and near-optimal controls are designed using two separate lower order subsystems. The two-time-scale properties greatly simplify the stability analysis and the nonlinear controller design. Two electric machine examples (a dc motor and a synchronous generator) illustrate the proposed design procedure.

A linear, shift-invariant discrete system exhibiting two-time-scale (slow and fast) character is addressed. An iterative algorithm based on linear programming for the computation of time-optimal control is presented by decoupling the original system into slow and fast subsystems. It is found that the computation time and storage capacity for the computation of time-optimal control of the slow and fast subsystems is less than that required for the original system. A numerical example is provided to illustrate the proposed algorithm.

Two-time-scale decoupling is adopted to obtain slow and fast subsystems. Based on these subsystems, a multirate composite control strategy is derived. It is shown how a recently presented multirate scheme can be modified to handle slow, nonzero mean disturbances, by introducing time incremental models. The improvements with the given multirate control law are illustrated by an example. >

International audience; The aim of this paper is to study two-time-scale nonlinear transient models and their associated parameter identification. When it is possible to consider two well-separated time scales, and when the fast component of the applied loading is periodic, a periodic time homogenization scheme, similar to what exists in space homogenization, can be used to derive a homogenized model. A parameter identification process for this latter is then proposed, and applied to an academic example, which allows to show the benefits of such a strategy.