Mode-dependent Average Dwell Time Research Articles

Asynchronous Switching Control of Discrete Time Delay Linear Switched Systems Based on MDADT

Ideally, switching between subsystems and controllers occurs synchronously. In other words, whenever a subsystem requires switching, its corresponding sub-controller will be promptly activated. However, in reality, due to network delays, system detection, etc., the activation of candidate controllers frequently lags, which causes issues with asynchronous switching between controllers and subsystems. This asynchronous switching problem may affect system performance and even make the system unstable because the state between the subsystem and the controller may be inconsistent, resulting in the controller not being able to control the subsystem correctly. To keep the system stable while using asynchronous switching, this work suggests an asynchronous control technique for a class of discrete linear switching systems with time delay based on the mode-dependent average dwell time (MDADT). First, we construct a state feedback controller and establish a closed-loop system. In the asynchronous and synchronous intervals of subsystems and controllers, different Lyapunov functions are selected, and sufficient conditions for exponential stability and the H∞ performance of the closed-loop system under asynchronous switching are obtained. In addition, using the MDADT switching strategy, the relevant parameters of each subsystem are designed and the corresponding state–feedback controller gain matrix can be obtained. Finally, a switching system with three subsystems is shown. The approach is confirmed by simulating it using the average dwell time (ADT) switching strategy and the MDADT switching strategy separately.

Event-triggered finite-time stabilization of nonlinear switched affine systems under mode-dependent and state-dependent switchings

This paper investigates the event-triggered finite-time stabilization (FTS) problem of nonlinear switched affine systems (NSASs) under mode-dependent and state-dependent switching signals, respectively. Firstly, an event-triggered control (ETC) strategy for NSASs with mode-dependent average dwell time constraint is proposed. Note that the presence of affine terms gives rise to difficulties in the exclusion of Zeno behavior for the widely-adopted triggering mechanism consisting of current state and error information. Therefore, a novel triggering mechanism including affine term threshold is proposed to exclude Zeno behavior. Secondly, an event-triggered impulsive control strategy for NSASs under autonomous state-dependent switching is studied. Some Lyapunov-based criteria and a state-dependent switching law for FTS are presented. Moreover, the established event-based control strategies are applied to FTS of boost converter to illustrate the effectiveness of the proposed results.

Observer-based event-triggered control for continuous-time switched linear parameter-varying systems

This paper researches the interval observer–based event-triggered control of switched linear parameter-varying (LPV) systems, which involve unknown external disturbance and measurement noise. First, we offer an event-triggering condition and a controller which are correlated with state estimations. Then, by analyzing the relationship between switching sequences and sampling sequences, we model the resulting systems as switched time-delay systems. It deserves to note that the mismatches of the switching signal for the controllers and the systems may occur due to the sampling of switching signal. Using the merging switching signal technique and the multiple Lyapunov–Krasovskii functional method, and thinking over both synchronous and asynchronous switching of the systems and the controllers, we acquire relevant conditions which are used to realize the stability of the whole switched LPV closed-loop systems under the mode-dependent average dwell time (MDADT) switching. Next, we give a specific algorithm to design the controller gains. Finally, a numerical example is provided to verify the superiority of the outcomes.

Finite‐time input/output‐to‐state stability of nonlinear stochastic switched time‐varying systems with mode‐dependent average dwell time

AbstractThis article investigates the finite‐time input/output‐to‐state stability (FTIOSS) of stochastic switched nonlinear delay systems (SSNDS). This article extends the well‐known concepts of input/output‐to‐state stability to finite‐time control problems. By using the finite‐time stable function and generalized function, we establish an unified FTIOSS criteron for stochastic switched systems, where both stable and unstable switching signals are considered. Compare with the existing works, the main advantage is that the constructed Lyapunov function (LF) is permitted to own indefinite‐derivative. Meanwhile, the Razumikhin technique and the mode‐dependent average‐dwell time (MDADT) approach are introduced to guarantee the FTIOSS of the system. The efficacy of the obtained results is demonstrated by an example.

Finite-time H∞ control under the Round-Robin protocol for switched linear systems with admissible edge-dependent average dwell time

This article focuses on finite-time [Formula: see text] control under the Round-Robin protocol for switched linear systems with admissible edge-dependent average dwell time. To relieve the bandwidth pressure of the sensor, a Round-Robin protocol is constructed to decide the access rights of each node of the sensor. Under the Round-Robin protocol-based control structure, admissible edge-dependent average dwell time is applied to describe the transition relationship between the modes of the subsystem and release the restrictions of mode-dependent average dwell time. Moreover, the finite-time stability and [Formula: see text] performance of switched system with Round-Robin protocol are analyzed by using multiple Lyapunov function method combined with the admissible edge-dependent average dwell time switching. Sufficient conditions for the solution to finite-time control problem are derived which consider the [Formula: see text] performance index. Finally, the availability of the control synthesis methods is verified by the circuit model of Buck–Boost converter.

Consensus of nonlinear MAS via double nonidentical mode-dependent event-triggered switching control

This paper investigates the global exponential consensus almost surely (GEC a.s.) of nonlinear multi-agent system (MAS) with switching topology via double nonidentical mode-dependent event-triggering mechanisms (ETMs). Considering the activated probability of switching modes, the transition probability (TP) and mode-dependent average dwell time (MDADT) are combined to propose a more practical switching rule. To save communication resources as much as possible, a set of nonidentical mode-dependent ETMs are designed, where the ETMs of each node are nonidentical and the ETM for controller-actuator (C-A) channel is designed on the basis of ETM for sensor-controller (S-C) channel. By designing a new Lyapunov-Krasovskii functional (LKF), sufficient conditions are derived to ensure the GEC a.s. of nonlinear MAS and the control gains are obtained by solving linear matrix inequalities (LMIs). Usually, the increment coefficient of LKF at switching instant must be larger than one, which will lead to conservatism. Our results remove this constraint condition and do not require each mode of the consensus error system to be stable. A numerical example is provided to demonstrate the effectiveness and feasibility of the theoretical analysis.

Finite-time stability and asynchronous H∞ control for highly nonlinear hybrid stochastic systems

In this paper, the pth moment finite-time stochastic stability (p-MFTS stability) and asynchronous H∞ control for highly nonlinear hybrid stochastic systems (HNHSSs) are investigated. Firstly, the definition of p-MSFT stability for HNHSSs is proposed, and the stability criteria are given by the mode-dependent average dwell time (MDADT) method. Secondly, the asynchronous H∞ controller is designed to ensure that HNHSSs are pth moment finite-time stochastically stabilizable (p-MFTS stabilizable) and satisfy H∞ performance. When designing the asynchronous H∞ controller, deterministic asynchrony and stochastic asynchrony are considered simultaneously. Moreover, since the coefficients of HNHSSs have highly nonlinear structures without satisfying the linear growth condition (LGC), the Lyapunov function U and the operator LU are bounded by polynomials of degree higher than p, which means that weaker conditions of p-MFTS stability are proposed. Finally, examples are presented to illustrate the availability of the results.

Robust exponential stability analysis of switched systems under switching boundary mismatch

AbstractSwitching boundary is an integral part of the switched system, but the existing literature on switched systems does not focus on the system under switching boundary mismatch. In this article, the switching boundary mismatch is considered, and the control strategy based on observation algorithm is designed for the state dependent switched system. By implementing the proposed strategy, the system can realize robust exponential stability and track the desired trajectory. Since the switching boundary mismatch is unmeasurable, an observation algorithm is designed. Combining the observation algorithm and iterative learning control law, the new control strategy can be derived. According to the Lyapunov stability theory and mode dependent average dwell time method, the robust exponential stability conditions of the closed‐loop system based on linear matrix inequalities are given. The mode dependent average dwell time of each subsystem can be solved simultaneously. Finally, simulations have been taken to verify the designed strategy can render the closed‐loop system achieve robust exponential stability and can track the desired trajectory.

Event-triggered dynamic output feedback control of switched cyber-physical systems with stochastic cyber attacks

This article is concerned with the problem of event-triggered dynamic output feedback control for switched cyber-physical systems subject to stochastic cyber attacks. Two kinds of stochastic cyber attacks obeyed the Bernoulli distribution are taken into account, and a switched stochastic system is derived. An event-triggered strategy is adopted to reduce unnecessary communication and save system resources, and then an event-triggered–based dynamic output feedback controller is designed. The sufficient conditions for the mean-square exponential stability of the switched stochastic system are given by taking advantage of the mode-dependent average dwell time method and the multiple Lyapunov functional technique. Finally, the validity of the proposed theoretical results is verified by two examples.

Stability criteria of switched systems with a binary -dependent average dwell time approach

ABSTRACT This paper proposes a new concept of binary -dependent average dwell time, which describes different types of switching signals by the different grouping function B ϝ for switched systems. Then, combing with the improved multiple Lyapunov function approach, the issues of stability and stabilisation for switched linear systems under the proposed strategy are investigated for the first time, which unify the classical average dwell time (ADT), mode dependent ADT, edge dependent ADT, and Φ dependent ADT, and are more flexible and practical than other existing criteria. Finally, a numerical example is given to illustrate the effectiveness of the obtained results.

Robust predictive control of perturbed switched linear systems with stable and unstable subsystems in the presence of uncertainties

In this article, robust model predictive control is proposed for discrete-time switched linear systems in the presence of external disturbances, model uncertainties and constraints on the states and input. To solve the problem, a mode-dependent average dwell time switching strategy is constructed in controller design procedure, with less limitations than the existing average dwell time switching. Using some mathematical tools, the model predictive control problem is turned into a feasible linear matrix inequality. The control algorithm is presented via two theorems, and the stability analysis is analytically presented, based on multiple Lyapunov function method. Compared with the previous studies, the underlying switched system may consist of stable and unstable subsystems, perturbed by model uncertainties and external disturbances. The simulation results are also given to study the effectiveness of the proposed robust model predictive control algorithm, from a comparison viewpoint.

Finite-Time Control Synthesis for Discrete Fuzzy Switched Singularly Perturbed Systems

This brief addresses the synthesis for a class of discrete fuzzy switched singularly perturbed systems (SPSs) in finite time. Different from Lyapunov stability, finite-time stability (FTS) is set up to analyze the transient performance, where the state remains within the upper thresholds for a given finite-time interval. In the face of singular perturbation, a singular-perturbation-parameter-dependent Lyapunov function is firstly introduced for fuzzy switched SPSs in the sense of finite time. Inspired by the mode-dependent average dwell time (MDADT) switching rule, a developed FTS is constructed to eliminate an ill-conditioned issue owing to a singularly perturbed parameter. Furthermore, a new fuzzy control strategy is proposed to satisfy the predefined FTS. Finally, the feasibility of the main results is proved using an inverted pendulum model.

Stabilization of Switched Logical Networks: Asynchronous Switching Control

This brief deliberates on the stabilization of switched logical networks (SLNs) under the asynchronous switching controller. The studied system takes into account the asynchronous switching phenomenon that the operating subsystem does not match the controller mode caused by non-ideal conditions. Our purpose is to find suitable conditions under which the SLN achieves stabilization under the asynchronous switching controller. By combining the Lyapunov method of logical networks and the mode-dependent average dwell time method, a sufficient criterion is first put forward for the stabilization of SLNs under the asynchronous switching controller. Furthermore, the obtained results are extended to the stabilization of SLNs with logical switching. An example of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$lac$ </tex-math></inline-formula> operon in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$E.~coli$ </tex-math></inline-formula> is finally given to validate the addressed results.

Event-Triggered Adaptive Output-Feedback Control of Switched Stochastic Nonlinear Systems With Actuator Failures: A Modified MDADT Method.

This article investigates the adaptive event-triggered output-feedback control problem for a class of switched stochastic nonlinear systems with actuator faults. In the existing works, the developed results on adaptive control for switched stochastic nonlinear systems are almost based on the average dwell-time method, and how to construct a desired adaptive controller in the frame of the mode-dependent average dwell time (MDADT) remains a control dilemma. By presenting a general adaptive control rule based on the MDADT, this article implements the adaptive output-feedback control for the switched stochastic system under interest. In the process of controller design, fuzzy-logic systems, a flexible approximator, are utilized to approximate the unknown nonlinear functions. The dynamic surface design approach is employed to avoid taking derivatives of the constructed virtual controls to decrease the difficulty of complex calculation greatly. Meanwhile, a switched observer is designed to estimate the unknown states. In the frame of backstepping design, an event-triggered-based adaptive output-feedback controller is constructed such that all signals existing in the closed-loop system are ultimately bounded under a class of switching signals with MDADT property. Finally, the simulation results show the validity of the proposed control strategy.

Stabilization of Switched Linear Neutral Systems With Time-Scheduled Feedback Control Strategy

This article is concerned with the stabilization of continuous-time switched linear neutral systems with tighter bounds on mode-dependent average dwell time. By introducing a novel time-scheduled control strategy, a switching-signal-based multiple discontinuous Lyapunov function (SMDLF) is constructed for continuous-time switched linear neutral systems, where the discontinuous points of the Lyapunov function during each mode-running interval are dynamically adjusted according to the actual system switching signal. First, sufficient criteria are established for global uniform exponential stability (GUES) of switched nonlinear systems. Then, based on the constructed SMDLF, we derive less conservative stability conditions for switched linear neutral systems. Furthermore, a set of time-dependent state feedback controllers are designed to guarantee the GUES of the underlying system. In the end, a simulation example with comparison results is provided to verify the effectiveness and advantages of the presented approach.

Design of Switching Controller for Connected Vehicles Platooning With Intermittent Communication via Mode-Dependent Average Dwell-Time Approach

In real life, due to the influence of environment and physical equipments, C-V2X wireless communication network connection is prone to be intermittent. When intermittent communication occurs, the vehicle cannot make correct control decisions because it cannot receive the required information from neighboring vehicles, which will lead to the deterioration of the performance of the vehicle platoon. Considering the intermittent information connection of the leading vehicle through C-V2X communication network, a robust control method is proposed to realize vehicle platoon control. The platoon control strategy of a connected vehicle system is designed based on the mode-dependent average dwell time (MDADT) method. The designed strategy has better performance in reducing conservatism and improving flexibility, by comparison with the average dwell time (ADT) method. Moreover, based on the designed switching strategy, the sufficient conditions for the platoon control system to meet the exponential stability and exponential <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{2}$ </tex-math></inline-formula> performance are analyzed, and then, the linear matrix inequalities for solving the controller gain are given. Furthermore, the designed method has an advantage in applying to a variety of communication topologies. Finally, the effectiveness of the proposed robust control method in the case of intermittent communication in leading vehicle’s information transmission is verified by simulation.

Finite-time adaptive control for uncertain switched port-controlled Hamiltonian systems

In this paper, the finite-time boundedness (FTB) and H∞ control are discussed for a class of uncertain switched port-controlled Hamiltonian (PCH) systems via adaptive control strategies. In view of the mode-dependent matching principle, the energy-based multiple Lyapunov functions method and the mode-dependent average dwell time (MDADT) approach, sufficient conditions on the FTB are obtained for uncertain switched PCH systems by employing a set of adaptive mode-dependent state feedback controllers. Furthermore, to solve the finite-time H∞ control for the system under consideration, a new set of mode-dependent state feedback controllers are designed to restrain both the structured uncertainties and disturbances, and sufficient conditions on the H∞ control problem are derived for the system under a new MDADT scheme. Finally, the numerical simulations are presented to illustrate the effectiveness of the proposed finite-time adaptive control methods.

Stability and Stabilization of Polynomial Fuzzy-Model-Based Switched Nonlinear Systems Under MDADT Switching Signal

This article proposes a novel Lyapunov stability analysis for a class of switched nonlinear systems under the mode-dependent average dwell time (MDADT) switching signals. For the first time, a polynomial fuzzy model is used to describe the nonlinearity of the switched systems instead of a Takagi–Sugeno fuzzy model, which can represent a wider range of nonlinear plants. As existing advanced results are relatively conservative and lead to that tighter bounds on the dwell time are not easy to be obtained, therefore, the stability analysis for switched systems is still quite challenging. In this article, to tackle this problem, by developing a polynomial multiple Lyapunov function (MLF) approach and exploring the feature of the membership functions, relaxed stability conditions are derived for the switched polynomial fuzzy-model-based control systems. In particular, the polynomial MLF is guaranteed radially unbounded by a two-step procedure, making traditional quadratic MLF a specific case, thereby improved stability conditions can be established in the form of sum-of-squares. Moreover, the new algorithm for multivariate Chebyshev membership functions based on linear programming is proposed to introduce the information of membership functions and further relax the stability conditions to obtain tighter bounds on MDADT. Finally, a simulation example demonstrates the effectiveness of the developed techniques.

Stabilization of discrete-time positive switched T-S fuzzy systems subject to actuator saturation

&lt;abstract&gt;&lt;p&gt;The stabilization of discrete-time positive switched Takagi-Sugeno (T-S) fuzzy systems with actuator saturation is investigated in this paper. It is assumed that the switched subsystems are partially stabilizable. Based on the convex hull technique (CHT) and parallel distribution compensation (PDC) algorithm, a saturated fuzzy controller and slow-fast combined mode-dependent average dwell time (MDADT) switching signal are co-designed and sufficient conditions for the positivity and stability of closed-loop positive switched T-S fuzzy systems (PSTSFSs) are developed, which can be reduced to the ones under the case where all switched subsystems are stabilizable. Moreover, the largest attraction domain estimation (ADE) is given for PSTSFSs by formulating an optimization problem. Finally, the designed control scheme is applied to two illustrative examples to verify its availability and superiority.&lt;/p&gt;&lt;/abstract&gt;

Stability of nonlinear positive semi-Markovian jump systems with mode-dependent delay subject to mode-dependent average dwell time

This article concentrates on the stability of nonlinear positive semi-Markovian jump systems (NPSMJSs) with mode-dependent delay, where the transition rate functions depend on both the sojourn-times and the average dwell time (ADT) switching. By resorting to linear programming (LP) approach, sufficient conditions for stochastic exponential stability of mode-dependent delay for NPSMJSs are developed. In addition, we obtain the $ L_{1}- $gian performance analysis. Finally, two numerical examples are proposed to illustrate the advantages of the theoretical results.