Mode-dependent Average Dwell Time Approach Research Articles

Stability of highly nonlinear stochastic systems with non-random switching signals and multiple delays

The situation of multiple delays often occur in hybrid stochastic systems. In this paper, multiple time-varying delays are considered for highly nonlinear switching stochastic systems. The function of time-varying delays is differentiable, and its derivative is a positive constant less than 1. By the Lyapunov functional method and the mode-dependent average dwell time approach, existence and uniqueness of solution, asymptotic stability and pth moment exponential stability for highly nonlinear switching stochastic multiple delays systems are obtained. Finally, an example is afforded to explicate the effectiveness our theoretical analysis results.

Reliable finite-frequency H ∞ control for switched systems with actuator faults and mode-dependent average dwell time

This paper deals with the reliable finite-frequency H ∞ control problem for switched systems with actuator faults and mode-dependent average dwell time (MDADT). The objective of designing reliable controllers is to guarantee the stability and robustness of the closed-loop system in the case of actuator faults. The actuator fault is solved using the convex combination method. A finite-frequency H ∞ performance index is first defined in the frequency domain, and then a finite-frequency performance condition is derived by the generalised Kalman-Yakubovi c ˘ -Popov (GKYP) lemma. Combined with the MDADT approach and linear matrix inequality technology, a sufficient condition for the existence of a set of reliable finite-frequency H ∞ controllers is derived. As a comparison, a sufficient condition is also given for the existence of a set of standard finite-frequency H ∞ controllers. Finally, the effectiveness and feasibility of the proposed method are verified using a tilt-rotor aircraft. In addition, simulations and comparisons show that the designed reliable controller can stabilise the system even if actuator faults occur.

Realizing asynchronous finite-time robust tracking control of switched flight vehicles by using nonfragile deep reinforcement learning.

In this study, a novel nonfragile deep reinforcement learning (DRL) method was proposed to realize the finite-time control of switched unmanned flight vehicles. Control accuracy, robustness, and intelligence were enhanced in the proposed control scheme by combining conventional robust control and DRL characteristics. In the proposed control strategy, the tracking controller consists of a dynamics-based controller and a learning-based controller. The conventional robust control approach for the nominal system was used for realizing a dynamics-based baseline tracking controller. The learning-based controller based on DRL was developed to compensate model uncertainties and enhance transient control accuracy. The multiple Lyapunov function approach and mode-dependent average dwell time approach were combined to analyze the finite-time stability of flight vehicles with asynchronous switching. The linear matrix inequalities technique was used to determine the solutions of dynamics-based controllers. Online optimization was formulated as a Markov decision process. The adaptive deep deterministic policy gradient algorithm was adopted to improve efficiency and convergence. In this algorithm, the actor-critic structure was used and adaptive hyperparameters were introduced. Unlike the conventional DRL algorithm, nonfragile control theory and adaptive reward function were used in the proposed algorithm to achieve excellent stability and training efficiency. We demonstrated the effectiveness of the presented algorithm through comparative simulations.

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.

Asynchronous Nonfragile Guaranteed Cost Control for Impulsive Switched Fuzzy Systems With Quantizations and Its Applications

This article investigates the nonfragile guaranteed cost (GC) control problem of discrete-time impulsive switched Takagi–Sugeno (T–S) fuzzy systems with input quantization and asynchronous switching. The model-dependent dynamic quantizers are applied to obtain the quantized input signal. To deeply study the GC performance analysis and GC control problems in the presence of quantization, asynchronous switching, and impulses, a novel piecewise cost function containing the quantized input instead of normal input is applied in this article. By using the mode-dependent average dwell time approach and introducing a class of Lyapunov-like functions allowing to increase during the asynchronous period, new sufficient conditions are established to guarantee the asymptotical stability with the GC performance index for the impulsive switched T–S fuzzy systems with quantized control input and asynchronous switching. Then, new design conditions about the nonfragile GC controllers and dynamic quantizers of impulsive switched T–S fuzzy systems are obtained in the form of linear matrix inequalities. Finally, a numerical example and a practical example are provided.

Dynamic output feedback [formula omitted] control of switched affine systems: An event-triggered mechanism

This work focuses on the dynamic output feedback L∞ control for switched affine systems with dwell time constraints. The presence of affine terms leads to the absence of a common equilibrium point and further makes it more difficult to design dynamic output feedback controllers and avoid the triggering Zeno behavior. To save resources and eliminate the effects of affine terms, first, an improved event-triggered condition with a constant and output information is provided. It is proved that the proposed triggering condition can prevent Zeno behavior from happening by obtaining a minimal inter-event interval. Then construct a novel dynamic output feedback switched affine controller, which skillfully adopts the mode-dependent average dwell time approach with Lyapunov stability theory to obtain a more rigorous and complete control strategy. It not only accommodates the unavailable state information and network transmission restrictions, but also achieves the practical stability of the closed-loop system while ensuring the L∞ performance from external disturbance to the output. Finally, the efficiency of the proposed algorithm is illustrated by simulating the buck-boost DC–DC converter.

Stability of highly nonlinear neutral stochastic delay systems with non-random switching signals

For the last few decades, many works on stability criteria have been established for neutral stochastic delay systems, which are modeled by stochastic differential delay equations. Some of these works do not involve switching signals, and others contain Markovian switching signals. This paper studies highly nonlinear neutral stochastic delay systems with non-random switching signals. Firstly, the rule of non-random switching signals is imposed. Then, by using the Lyapunov function method and the mode-dependent average dwell time approach, the existence and boundedness of unique global solution is discussed for highly nonlinear neutral stochastic delay systems with non-random switching signals. In addition, without the linear growth condition, asymptotic stability and exponential stability are obtained. In the last part of the article, an illustrative example is provided to show the effectiveness of the obtained results.

Finite-Time Synchronization for Switched Neural Networks via Quantized Feedback Control

This paper is concerned with the problem of finite-time $\mathcal {H}_{\infty }$ synchronization for a class of discrete-time switched neural networks with quantized feedback controllers. First, we take advantage of mode-dependent average dwell time approach and semi-time-dependent (STD) Lyapunov function method to establish new criteria for the finite-time synchronization. Based on the newly developed criteria, a finite-time bounded real lemma is presented and further, the quantized state feedback controller is designed to ensure the finite-time $\mathcal {H}_{\infty }$ synchronization of the underlying neural networks. The conservatism is further reduced by the proposed mode-dependent and STD controller. Finally, we use two illustrative examples to show the effectiveness and superiority of the results obtained in this paper.

A generalized mode-dependent average dwell time approach to stability analysis of positive switched systems with two subsystems

The stability problem for positive switched systems with two subsystems is investigated with an improved mode-dependent average dwell time (MDADT) scheme. By utilizing system positivity and the new scheme, the stability conditions of the considered system are addressed. The proposed switching law is more applicable in practice than the average dwell time (ADT) and MDADT schemes with certain conditions, and those existing methods can be regarded as some special cases of the theoretical findings in the paper. Then, the new stability criteria are extended to non-autonomous systems. Finally, two simulation examples with some comparisons to the classical results are given to illustrate the advantages of our obtained results.

Finite-Time Stability of Discrete Linear Singular Switched Positive Systems with Time-Delay by a Mode-Dependent Average Dwell Time Approach

Finite-Time Stability of Discrete Linear Singular Switched Positive Systems with Time-Delay by a Mode-Dependent Average Dwell Time Approach

Event-Triggered Output Regulation for Networked Flight Control System Based on an Asynchronous Switched System Approach

In this article, the event-triggered output regulation problem is investigated for a networked flight control system with a switched system approach. By properly scheduling triggered times of periodic sampling associated with continuous event-triggering and switching instants of each subsystem, an alternate event-triggered mechanism based on the subsystem model is proposed to transmit the triggered information to the candidate controller. Since the subsystem may switch between two adjacent events while the corresponding controller does not switch, asynchronous switching may occur. Meanwhile, an event-triggered switching signal caused by asynchronous switching is designed with the mode-dependent average dwell time approach and event-triggered instants. By constructing multiple Lyapunov functions in the framework of the input delay approach and designing an error feedback controller, the sufficient condition for event-triggered asynchronous output regulation problem is solved. Finally, the proposed methods are proved to be effective by the F-18 aircraft model.

Stability of highly non‐linear switched stochastic systems

It is well known that the linear growth condition is an important assumption for the stochastic differential system, which can ensure that the solution of the stochastic system will not explode at a finite time. However, there exist a lot of highly non-linear stochastic differential systems, which do not satisfy the linear growth condition, i.e. their coefficients cannot be bounded by a linear function. In this study, the existence of the unique global solution is first proved for highly non-linear switched stochastic systems with non-random switching signals, where the linear growth condition is not required anymore. In addition, by using the mode-dependent average dwell time approach and the Lyapunov functions method, the p th moment exponential stability is presented for highly non-linear switched stochastic systems with both stable and unstable subsystems. An illustrative example is provided to show the effectiveness of the developed theoretical results.

Switching Stabilization for Type-2 Fuzzy Systems With Network-Induced Packet Losses.

This paper is concerned with the stabilization problem of type-2 fuzzy systems with network-induced packet losses. By regarding the packet lost process as an unstable mode of a switched system, the stability of the system is then guaranteed with the aid of the mode-dependent average dwell time approach in the sense of the slow and fast switching. The discrete-time multiple discontinuous Lyapunov function is also utilized for the analysis. Two sufficient conditions regarding the stability and the stabilization of the system are proposed. The state-feedback matrices can be then calculated from the conditions to ensure the criterion that the packet-loss rate is no larger than a specific constant. Two practical examples are given to illustrate the feasibility and effectiveness of the proposed method.

Positive impulsive observer design of fractional-order positive switched systems with mode-dependent average dwell time

This paper investigates the positive impulsive observer design of fractional-order positive switched systems with mode-dependent average dwell time (MDADT). By using the MDADT approach and the Lyapunov–Krasovskii functional technique, sufficient conditions are obtained to ensure the error system is globally exponentially stable. An algorithm is proposed to design the observer gain matrices via linear programming. Finally, two examples are provided to illustrate the effectiveness of the proposed method.

Guaranteed Cost Finite-Time Control for Positive Switched Linear Systems with Time-Varying Delays

This paper considers the guaranteed cost finite-time control for positive switched linear systems with time-varying delays. The definition of guaranteed cost finite-time boundedness is firstly given. Then, by using the mode-dependent average dwell time approach, a static output feedback law and a state feedback control law are constructed, respectively, and sufficient conditions are obtained to guarantee that the closed-loop system is guaranteed cost finite-time boundedness. Such conditions can be easily solved by linear programming. Finally, an example is given to illustrate the effectiveness of the proposed method.

Finite-Time Stability of Discrete Switched Singular Positive Systems

The finite-time stability problem of discrete switched singular positive systems (DSSPSs) is investigated in this paper. First, the concept of finite-time stability for DSSPSs is proposed, and a necessary and sufficient condition of finite-time stability for DSSPSs under arbitrary switching is obtained. Second, based on the mode-dependent average dwell time approach, by constructing the quasi-linear Lyapunov function, a sufficient stability criterion of finite-time stability for DSSPSs is derived in terms of a set of linear matrix inequalities. Finally, a numerical example is given to show the effectiveness of the proposed techniques.

Stability analysis of switched cellular neural networks: A mode-dependent average dwell time approach

This paper addresses the exponential stability of switched cellular neural networks by using the mode-dependent average dwell time (MDADT) approach. This method is quite different from the traditional average dwell time (ADT) method in permitting each subsystem to have its own average dwell time. Detailed investigations have been carried out for two cases. One is that all subsystems are stable and the other is that stable subsystems coexist with unstable subsystems. By employing Lyapunov functionals, linear matrix inequalities (LMIs), Jessen-type inequality, Wirtinger-based inequality, reciprocally convex approach, we derived some novel and less conservative conditions on exponential stability of the networks. Comparing to ADT, the proposed MDADT show that the minimal dwell time of each subsystem is smaller and the switched system stabilizes faster. The obtained results extend and improve some existing ones. Moreover, the validness and effectiveness of these results are demonstrated through numerical simulations.

An MDADT-Based Approach forL2-Gain Analysis of Discrete-Time Switched Delay Systems

We study theL2-gain analysis problem for a class of discrete-time switched systems with time-varying delays. A mode-dependent average dwell time (MDADT) approach is applied to analyze theL2-gain performance for these discrete-time switched delay systems. Combining a multiple Lyapunov functional method with the MDADT approach, sufficient conditions expressed in form of a set of feasible linear matrix inequalities (LMIs) are established to guarantee theL2-gain performance. Finally, a numerical example will be provided to demonstrate the validity and usefulness of the obtained results.

Reliable guaranteed‐cost control of delta operator switched systems with actuator faults: mode‐dependent average dwell‐time approach

This study deals with the reliable guaranteed-cost control problem for a class of delta operator switched linear systems, in terms of mode-dependent average dwell-time (MDADT) approach. Firstly, based on MDADT approach, asymptotical and exponential stabilities of delta operator non-linear switched systems are analysed. Then, the reliable controller and the minimum MDADT are designed to stabilise the considered delta operator linear switched system with actuator faults and to determine an upper bound of the given cost function. A flight control switched system is given to show the validity and potential of the proposed method.

Semi-periodically intermittent control for synchronization of switched complex networks: a mode-dependent average dwell time approach

In this paper, we study the synchronization problem for switched complex networks with delayed coupling via semi-periodically intermittent control technique and a mode-dependent average dwell time method. The mathematical model of switched complex networks is established, and the networks switch among a finite number of subnetworks in accordance with a switching rule. By applying multiple Lyapunov function method and the mode-dependent average dwell time (MDADT) approach, less conservative synchronization criteria are derived based on a sequence of solvable linear matrix inequalities. Particularly, the conventional synchronization conditions are improved by using semi-periodically intermittent control and MDADT approach. Moreover, delayed coupling may affect the stability of the switched complex networks. In this paper, novel synchronization criteria are derived to deal with the relations between time delay and other parameters appropriately. Finally, a numerical example is provided to demonstrate the effectiveness of the derived theoretical results.