Asynchronously Switched Research Articles

Finite-time stabilization for discrete-time switched stochastic linear systems under asynchronous switching

This paper deals with the problem of state feedback stabilization with finite-time stochastic stability for a class of discrete-time switched stochastic linear systems under asynchronous switching. The attention is focused on designing the feedback controller that guarantees the finite-time stochastic stability of the dynamic system. The finite-time stochastic stability definition of discrete-time switched stochastic systems is introduced. The asynchronous switching idea originates from the fact that switching instants of the controllers lag behind or exceed those of subsystems. On the basis of the average dwell time method and multiple Lyapunov functions approach, a finite-time stochastic stability condition is established. Then, an asynchronously switched controller is designed and the corresponding switching law is derived to guarantee the considered system be finite-time stochastically stable. Two numerical examples are provided to show the effectiveness of the developed results.

Finite‐Time H∞ State Estimation for Discrete‐Time Switched Control Systems Under Asynchronous Switching

ABSTRACTThe Luenberger observer technique has long been used for reliable state estimation of feedback control systems. In this paper it is employed for asynchronously switched control systems. The theory of finite‐time stability (FTS) and finite‐time boundedness (FTB) is incorporated, which is a relatively new concept offering open and challenging problems, especially in the field of robust state estimation for switched control systems. Many real‐world systems are supposed to run for a fixed interval of time and hence the design of finite‐time state observers has more significance from the point of view of many engineering applications. This investigation considers asynchronous switching between observer and physical systems, which accounts for inherent delays in practical applications caused by measurement and sensing mechanisms, and crafts a more practical and accurate design method. Furthermore, performance index which is a vital technique for robust system design against external disturbances is integrated in the design procedure.

Asynchronously switched control of discrete impulsive switched systems with time delays

This paper is concerned with the stabilization problem for a class of uncertain discrete impulsive switched delay systems under asynchronous switching. The so-called asynchronous switching means that the switches between the candidate controllers and system modes are asynchronous. By using the average dwell time (ADT) approach, sufficient conditions for the existence of an asynchronously switched controller is derived such that the resulting closed-loop system is exponentially stable. The desired controller gains and the admissible switching signals are obtained in terms of a set of matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed method.

ℋ ∞ control for asynchronously switched linear parameter‐varying systems with mode‐dependent average dwell time

This study is concerned with the stability, l 2 -gain analysis and ℋ ∞ control for a class of discrete-time switched linear parameter-varying systems with both mode-dependent average dwell time (MDADT) and asynchronous switching, where `asynchronous' means the switching of controllers has a lag to the switching of system modes. The l 2 -gain for general switched systems with MDADT in non-linear setting is firstly derived. Based on the obtained results, the problem of asynchronous ℋ ∞ control for the studied systems is formulated under the framework of MDADT switching logic, and the conditions for the existence of admissible asynchronous ℋ ∞ controllers are deduced in the form of parameterised linear matrix inequalities. A numerical example is provided to verify the effectiveness of the acquired results.

Asynchronous finite-time [formula omitted] control for switched linear systems via mode-dependent dynamic state-feedback

This paper concerns the asynchronous finite-time H∞ control problem for a class of switched linear systems with time-varying disturbances. The asynchronous switching means that the switchings between the candidate controllers and system modes are asynchronous. By using the Average Dwell Time (ADT) and Multiple Lyapunov Functions (MLFs) technologies, some sufficient conditions which can guarantee that the corresponding closed-loop system is finite-time bounded with a prescribed H∞ performance index via asynchronously switched control, are derived for the switched linear systems. Unlike the traditional Lyapunov asymptotic stability, there is no requirement of negative definiteness (or semidefiniteness) on the derivative of Lyapunov-like function. Moreover, a set of mode-dependent dynamic state feedback controllers are designed. Finally, two examples are provided to verify the efficiency of the proposed method.

Exponential stability of time-delay feedback switched systems in the presence of asynchronous switching

This paper studies the asynchronously switched state time-delay feedback control problem for a class of switched linear systems with average dwell time. Using extended multiple Lyapunov-like functional, we first investigate the stability of a class of switched time-delay nonlinear systems with average dwell time. Then, based on this result, sufficient conditions for exponential stability are developed for time-delay feedback switched linear systems in the presence of asynchronous switching, where “asynchronous” means the switching of the controllers has a lag to the switching of subsystems. These conditions are provided in terms of linear matrix inequalities (LMIs). A numerical example is presented to illustrate the developed results.

Asynchronously switched control of a class of slowly switched linear systems

The stabilization problem for a class of switched linear systems with average dwell time (ADT) switching is reinvestigated in this paper. State-feedback controllers are designed, which takes the more practical case, asynchronous switching, into account, where the so-called “asynchronous switching” indicates that the switchings between the controllers and the system modes are in the presence of a time delay. By combining the asynchronous switching, an improved stabilization approach is given, and existence conditions of the controllers associated with the corresponding ADT switching are formulated in terms of a set of linear matrix inequalities. A numerical example is given to show the validity and potential of the obtained theoretical results.

Asynchronous fault detection filter design approach for discrete‐time switched linear systems

SUMMARYThis paper is concerned with the problem of the fault detection filter design for discrete‐time switched linear systems with average dwell‐time. The designed fault detection filters are also switched systems, which are assumed to be asynchronously switched with the original switched systems. Improved results on the weighted l2 performance and the H − performance are first given, and the multiple Lyaounov‐like functions during matched period and unmatched period for the running time of one subsystem are used. By the aid of multiple Lyapunov‐like functions combined with Projection Lemma, the FD filters are designed such that the augmented systems under asynchronous switching are exponentially stable, and the residual signal generated by the filters achieves the weighted l2‐gain for disturbances and guarantees the H − performance for faults. Sufficient conditions are formulated by linear matrix inequalities, and the filter gains are characterized in terms of the solution of a convex optimization problem. Finally, examples are provided to demonstrate the effectiveness of the proposed design method. Copyright © 2012 John Wiley & Sons, Ltd.

Stabilisation of a class of switched delay systems with asynchronous switching

This paper investigates the problem of asynchronously switched stabilising control for a class of switched linear systems with time delay. When there exists asynchronous switching between the controllers and the subsystems, based on the average dwell time (ADT) method, a sufficient condition for exponential stability is developed for a class of switching signals. The condition is delay-dependent and is given in terms of linear matrix inequalities (LMIs). A numerical example illustrates the effectiveness of the proposed method.

Asynchronously switched control of switched linear systems with average dwell time

This paper concerns the asynchronously switched control problem for a class of switched linear systems with average dwell time (ADT) in both continuous-time and discrete-time contexts. The so-called asynchronous switching means that the switchings between the candidate controllers and system modes are asynchronous. By further allowing the Lyapunov-like function to increase during the running time of active subsystems, the extended stability results for switched systems with ADT in nonlinear setting are first derived. Then, the asynchronously switched stabilizing control problem for linear cases is solved. Given the increase scale and the decrease scale of the Lyapunov-like function and the maximal delay of asynchronous switching, the minimal ADT for admissible switching signals and the corresponding controller gains are obtained. A numerical example is given to show the validity and potential of the developed results.

Efficient Moving Horizon State and Parameter Estimation for the Varicol SMB Process

Abstract Abstract In this paper, a moving horizon state and parameter estimation (MHE) scheme for the Varicol process is presented. The Varicol process is an extension of the Simulated Moving Bed (SMB) process that realizes non-integer column distributions over the separation zones by an asynchronous switching of the inlet and outlet ports (the ports are shifted individually). These additional degrees of freedom can be used to yield an improvement in economical performance compared to SMB operation. The proposed estimation scheme is based on a rigorous SMB model that incorporates rigorous chromatographic columns and port switching. The absence of model simplifications allows the extension of the estimation scheme to the more complex Varicol process. The goal of the estimation scheme is to reconstruct the full state of the system, i.e. the concentration profiles along all columns, and to identify critical model parameters in the presence of noisy measurements. The estimation is based on measurements of the concentrations of the components at the two outlet ports (which are asynchronously switched from one column to the next) and at one fixed location between two columns. The state estimation scheme utilizes a deterministic model within the prediction horizon. State noise is only considered in the state and in the parameters up to the beginning of the horizon. By applying a multiple-shooting method and a real-time iteration scheme for solving the resulting optimization problem, the computation times are reduced and the scheme can be applied online. A numerical simulation for an enantiomer separation system with nonlinear adsorption isotherm is presented.