Class Of Switched Systems Research Articles

Robust sliding mode observer based-simultaneous state and actuator fault estimation for a class of switching systems

Robust sliding mode observer based-simultaneous state and actuator fault estimation for a class of switching systems

Robust Guaranteed Cost Composite Anti-bump $$L_2$$-Gain Control for a Class of Switched Systems Under Mixed State-Dependent Switching

Robust Guaranteed Cost Composite Anti-bump $$L_2$$-Gain Control for a Class of Switched Systems Under Mixed State-Dependent Switching

Truncated stochastically switching processes.

There are a large variety of hybrid stochastic systems that couple a continuous process with some form of stochastic switching mechanism. In many cases the system switches between different discrete internal states according to a finite-state Markov chain, and the continuous dynamics depends on the current internal state. The resulting hybrid stochastic differential equation(hSDE) could describe the evolution of a neuron's membrane potential, the concentration of proteins synthesized by a gene network, or the position of an active particle. Another major class of switching system is a search process with stochastic resetting, where the position of a diffusing or active particle is reset to a fixed position at a random sequence of times. In this case the system switches between a search phase and a reset phase, where the latter may be instantaneous. In this paper, we investigate how the behavior of a stochastically switching system is modified when the maximum number of switching (or reset) events in a given time interval is fixed. This is motivated by the idea that each time the system switches there is an additive energy cost. We first show that in the case of an hSDE, restricting the number of switching events is equivalent to truncating a Volterra series expansion of the particle propagator. Such a truncation significantly modifies the moments of the resulting renormalized propagator. We then investigate how restricting the number of reset events affects the diffusive search for an absorbing target. In particular, truncating a Volterra series expansion of the survival probability, we calculate the splitting probabilities and conditional MFPTs for the particle to be absorbed by the target or exceed a given number of resets, respectively.

Bifurcation Analysis for a Class of Cubic Switching Systems

In this paper, we consider a class of switching systems perturbed by cubic homogeneous polynomials. This class of systems is separated by a straight line: [Formula: see text], and has three equilibria: [Formula: see text] and [Formula: see text] which are in the separation line. A new version of the Gasull–Torregrosa method based on Poincaré return maps is presented, and used to compute the Lyapunov constants. Based on this method, a complete classification on the center conditions is obtained for the studied class of systems. Furthermore, by perturbing the cubic switching integral system with cubic homogeneous polynomials, we show that at least ten small-amplitude limit cycles are obtained around one of the centres. This is a new lower bound for the number of limit cycles bifurcating from a center in such switching systems with cubic homogeneous nonlinearities.

Multi-objective generalized predictive control for switching systems under unknown switching sequences

This paper describes a new generalized predictive control to track and stabilize a class of discrete time switching system. The focus is specifically centered on classes of switching systems characterized by unstable modes, undetermined switching signal, anon-minimumphase, and variable dead-times. To overcome this type of issue, an effective predictive control law is established by solving a dynamic multi-objective optimization function. Control problems are formulated in order to stabilize and regulate the system response around the targeted reference. The theoretical background of the proposed method is inspired by the standard generalized predictive control (GPC), in such a way that all desirable features are retained as possible. As a result, the obtained controller is more efficient in terms of stability and tracking. In fact within the framework of this research, the control problem has been formulated by taking into account behaviors of subsystems as well as the switching phase. The optimization of the problem is established in such a way that the obtained control law will be adapted to system dynamics, regardless of the mode. A number of simulation tests are established to evaluate the performance of the developed method. Four benchmark examples were considered for the simulation tests. Simulation results have shown the potential of the developed strategy to control and stabilize switching systems under unknown switching sequences. For further evaluation, the closed-loop performance of the developed strategy has been compared to that obtained with the Multi-Criteria Predictive Control (MOMPC) method. Comparison results have highlighted the effectiveness of the proposed method in terms of stability and tracking than MOMPC method.

Switching fuzzy modelling and control scheme using T-S fuzzy systems with nonlinear consequent parts

This paper extends the idea of switching T-S fuzzy systems with linear consequent parts to nonlinear ones. Each nonlinear subsystem is exactly represented by a T-S fuzzy system with Lure’ type consequent parts, which allows to model and control wider classes of switching systems and also reduce the computation burden of control synthesis. With the use of a switching fuzzy Lyapunov function, the LMI conditions for asymptotic stability of the system with maximum decay-rate and disturbance attenuation properties under arbitrary switching law are derived. Moreover, several numerical examples are provided to demonstrate the effectiveness of the proposed approaches to reduce the computational burden of control synthesis and improving the closed-loop performance of the system.

Iterative Learning Control Design of Switched Systems With Markovian Jump Parameters via Fuzzy Approach

In this paper, based on Takagi-Sugeno (T-S) approach the work is concerned with the iterative learning control (ILC) problem for a class of switched systems with data packet dropouts. The designed scheme is described by a class of Markovian switching systems with transition probabilities which are time-variant in a network environment. The links of network communications between controller-to-actuator (C/A) and sensor-to-controller (S/C) are unreliable. In terms of the construction of two-dimensional (2D) T-S model, a novel composite strategy of 2D fuzzy iterative learning output feedback control is proposed. The sufficient conditions on stochastic stability are obtained by the 2D Lyapunov stability theory. Furthermore, the dynamics of the closed-loop are guaranteed to be stochastically stable and the desired $H_{\infty }$ performance is also provided. The solutions of the ILC controller are derived by the application of the cone complementarity linearisation (CCL) procedure. Finally, a numerical simulation is illustrated to show the validity of the design.

Limit Cycles and Invariant Curves in a Class of Switching Systems with Degree Four

In this paper, a class of switching systems which have an invariant conicx2+cy2=1,c∈R, is investigated. Half attracting invariant conicx2+cy2=1,c∈R, is found in switching systems. The coexistence of small-amplitude limit cycles, large amplitude limit cycles, and invariant algebraic curves under perturbations of the coefficients of the systems is proved.

Systems with Partially Freezed Components

We study a particular class of switching systems called systems with partially freezed components. Fix an autonomous system of differential equations and consider a family of systems obtained from it by replacing some of components of the right-hand side by zeros (thus, “freezing” some components of a solution). We obtain the flow of a system with partially freezed components by fixing a sequence of switching times and of the corresponding sets of “active” components (i.e., the components that are not “freezed”). Such a sequence is called a freezing sequence. Systems with partially freezed components appear, for example, in the study of generalized Turing machines. In this paper, we are mostly interested in stability properties of such systems; our main goal is to relate such properties to properties of the generating system and freezing sequences.

Constructing Chaotic Systems from a Class of Switching Systems

This paper aims to develop an approach for constructing chaotic systems from a class of linear continuous-time switching systems. First, the Shilnikov criterion is analyzed and extended to the switching systems. Then some kinds of “swing planes” are provided via a heteroclinic loop design, which act as switching planes to chaotify the systems. Furthermore, a numerical example is presented to validate the proposed principle and implementation scheme. The theoretical analysis and numerical simulation have demonstrated the feasibility and effectiveness of the developed techniques.

On Necessary and Sufficient Conditions for Mode Observability of a Class of State Dependant Switched Systems

In this paper we give necessary and sufficient conditions for the mode observability of a class of switched systems, where the switching signal is state dependant. The switching conditions are given by an affine partition of the space Rn. This is a partition where the hyperplane not necessarily crosses through zero. The mode observability conditions are obtained as a result of an algebraic analysis of the so called joint observability matrix. A characterization of the sets where these conditions are fulfilled is also obtained. This characterization is given by translations of the hyperplane generating the partition. The results are illustrated by some examples for specific cases including a mechanical switched system.

Bifurcation of limit cycles at infinity in a class of switching systems

In this paper, we present a method to compute focal values and periodic constants at infinity of a class of switching systems and apply it to study a cubic system. We prove that such a cubic system can have 7 limit cycles in the sufficiently small neighborhood of infinity. Moreover, we consider a quintic switching system to obtain 14 limit cycles at infinity, while continuous quintic systems can have only 11 limit cycles in the sufficiently small neighborhood of infinity. This indicates that switching systems or discontinuous systems can exhibit more complex dynamics compared to smooth systems.

Limit cycles in a class of switching system with a degenerate singular point

Although switching systems have been investigated intensively, there are few results about limit cycles bifurcated from switching systems with degenerate singular point. In this paper, a method to compute focal values for degenerate critical point of switching systems was proposed. Furthermore, we studied a quartic system in order to illustrate the efficiency of our method.

Design for Generating Chaos from a Class of Switching Linear Systems

In this paper, a systematic design approach based on event driven method is investigated for a class of switching systems, and the switching control system is able to generate chaos at will from linear systems under the designed switching rules. To gain this target, structures of a class of linear switching systems are analyzed pro perly, as a consequence of analysis, the corresponding criteria is obtained to judge the existence for this class of switching systems to generate chaos. Then, based on the analysis of structure, feedback controllers designing procedure of some non-autonomous switching systems is deduced step by step. Two numerical examples are given to illustrate the generated chaotic dynamic behavior of the systems, and the validity of main results is also verified by the simulations. Finally, a circuit is provided to show the potential applications of the approac h in engineering.

Stochastic maximum principle for nonlinear optimal control problem of switching systems

The contribution of this paper is to present a stochastic maximum principle for an optimal control problem of switching systems. It presents necessary conditions of optimality for a broad class of switching systems, in which the dynamic of the constituent processes takes the form of stochastic differential equations. The restrictions on the transitions for the system are described through functional equality constraints on the end of each subsystem.

A moving horizon approach to a noncontinuum state estimation

Many problems of academic and industrial interests such as operating mode switching, feed quality change, process fault diagnosis and phase change analysis in a chemical process either take a noncontinuum form or can be represented by a discrete-valued state and be readily solved. In this study, a noncontinuum state estimator, which is based on a moving horizon method for a class of switching system that follows a hidden Markov model, is developed. A new approach to arrival cost development and constraints handling in moving horizon estimation of noncontinuum state are discussed. The effectiveness of the proposed method is illustrated by considering mode estimation problems in a simulated leakage detection system as well as a continuous stirred tank reactor.

Discussion on: “Suboptimal switching control consistency analysis for discrete-time switched linear systems”

The past 20 years has seen a huge number of papers produced in the area of switched and hybrid systems. The principal focus of these papers has been to produce conditions under which stability can be guaranteed, either in the case of arbitrary switching, or in the case of constrained switching, where one constrains the switching through state constraints, or through limits on the rate of switching. Some important topics have, however, rather disappointingly, been the subject of far less study. These include the discretization of switched systems, the design of systems where constraints are fixed rather than a design variable, and the design of switched systems with performance guarantees (to name but a few). A major contribution of the paper under discussion is that it falls into the latter category, and provides results that are likely to be of interest, not only to the academic community, but also to practicing engineers. Following similar work in the context of continuous-time switched linear systems [1], the authors introduce the concept of consistency for the discrete-time counterpart. More specifically, a given switching strategy is consistent if it improves the performance of the closed loop system when compared with any of the isolated subsystems. The performance of the controlled system is evaluated in terms of input–output H2 and H∞ indexes, which are defined in such a way that whenever the switching policy is constant, then the indices coincide with the conventional definition for the single subsystem. Section 3 constitutes the main part of the paper. The authors present two theorems that guarantee the existence of a consistent switching function; the first based on conditions on the Hi matrices, and the second based on even other conditions on the class of switching systems considered. In both cases the use of Lyapunov–Metzler inequalities is heavily employed. Note in the discussion following both of these theorems, the investigation of strict consistency involves the formulation of a non-convex search that would almost certainly be

Bounds and invariant sets for a class of switching systems with delayed-state-dependent perturbations

We present a novel method to compute componentwise transient bounds, componentwise ultimate bounds, and invariant regions for a class of switching continuous-time linear systems with perturbation bounds that may depend nonlinearly on a delayed state. The main advantage of the method is its componentwise nature, i.e. the fact that it allows each component of the perturbation vector to have an independent bound and that the bounds and sets obtained are also given componentwise. This componentwise method does not employ a norm for bounding either the perturbation or state vectors, avoids the need for scaling the different state vector components in order to obtain useful results, and may also reduce conservativeness in some cases. The present paper builds upon and extends to switching systems with delayed-state-dependent perturbations previous results by the authors. In this sense, the contribution is three-fold: the derivation of the aforementioned extension; the elucidation of the precise relationship between the class of switching linear systems to which the proposed method can be applied and those that admit a common quadratic Lyapunov function (a question that was left open in our previous work); and the derivation of a technique to compute a common quadratic Lyapunov function for switching linear systems with perturbations bounded componentwise by affine functions of the absolute value of the state vector components. In this latter case, we also show how our componentwise method can be combined with standard techniques in order to derive bounds possibly tighter than those corresponding to either method applied individually.

Stabilization and tracking for switching linear systems under unknown switching sequences

This paper describes recent progress in the study of switching linear systems i.e. linear systems whose dynamics can switch among a family of possible configurations/modes. The attention is focused on those classes of switching systems governed by unknown switching sequences. For this case, we address the problem of devising suitable control actions able to stabilize the plant and regulate its output about a desired reference trajectory. The approach considered in this paper consists in designing a suitable family of feedback controllers and a mode-estimator that at any time determines which candidate controller has to be placed in the feedback loop on the grounds of a real-time estimate of the current plant mode. It is shown that, even if a correct reconstruction of the plant mode from the measured data is not always possible, under certain conditions, exponential stability of the closed-loop can be guaranteed for any slow-on-the-average plant switching sequence.

Remarks on the stabilizability of integrator switching systems

SUMMARYIn this work, a class of switching systems known as integrator is studied. Such systems have the feature of being very simple and allow us to gain insight on the effect that the switching sequence has on system stability. Three problems are analyzed. First, the practical stabilizability problem under system uncertainty is studied. Confinement regions are explicitly computed, and switching sequences based on the nominal behavior of the systems are derived. Second, the practical stabilizability problem using output feedback is solved; in this case, sufficient conditions are proposed. Finally, by joining both results, sufficient conditions for practical stabilizability of uncertain systems under output feedback are given. The results are illustrated with examples and some extensions for uncertain linear system and event‐based switching are given. Copyright © 2012 John Wiley & Sons, Ltd.