Multiple Lyapunov Function Approach Research Articles

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.

Stability of stochastic systems with semi-Markovian switching and impulses

The aim of this paper is to investigate the stochastic asymptotic stability of semi-Markov switched systems with mixed impulses. A novel definition of average impulse gain is given to estimate the intensity of the mixed impulses. Based on the multiple Lyapunov function approach and average impulse interval method, we provide sufficient conditions on the stochastic asymptotic stability for the semi-Markov switched system with impulses. Moreover, the influence of impulses on the system is estimated by applying the average impulse gain and average impulse interval method, which are not only suitable for synchronous impulses but also for asynchronous impulses. The theoretical results are demonstrated by two examples.

A Novel Asynchronous Sliding Mode Design for Switched Systems under Input–Output Finite-Time Stability

In this work, the input–output finite-time stability (IO-FTS) of a class of continuous-time switched systems characterized by uncertainties and subjected to external disturbances is studied under asynchronous switching by means of the sliding mode control (SMC) method. The IO-FTS poses a finite-time constraint problem, which involves addressing two main issues: firstly, ensuring that the state trajectory of the switched system reaches the given sliding mode surface within the specified time, and secondly, achieving IO-FTS for the closed-loop switched system during asynchronous switching. To address these issues, we apply a partitioning strategy and construct asynchronous sliding mode controllers with adjustable parameters to ensure the reachability of the system’s state trajectory within a finite time. Subsequently, we employ a multiple Lyapunov function (MLF) approach to provide sufficient conditions that ensure IO-FTS during the whole phase [0,T] for the resulting switched system. Additionally, we analyze the asynchronous characteristics concerning the reachability phase of the designed sliding surface, considering the system’s switching properties. Finally, we demonstrate the efficacy of the proposed approach with a numerical example.

Finite‐time observer‐based fault detection with nonfragile control design for switched nonlinear networked systems with time‐delays

AbstractThe strategy of observer‐based nonfragile control and fault‐detection over finite‐time horizon has been examined for a class of uncertain switched nonlinear networked control systems (NNCSs) contingent with time varying delays inferred by the networks from sensor to controller and controller to actuator. Also, in this study, an observer‐based fault detection control has been designed for the NNCSs. By making use of fault detection control as residual generator, the conveyed fault detection problem is then transformed into attenuation problem. By employing multiple Lyapunov function and average dwell time (ADT) approach, sufficient conditions in terms of linear matrix inequalities (LMIs) ensures the finite‐time boundedness (FTB) criterion of the resulting switched NNCSs with a prescribed disturbance attenuation. Subsequently, the preferred LMIs constraints realizes the controller and observer gains. Finally, two numerical examples are proffered to showcase the efficacity of the proposed technique.

Neural-Network-Based Adaptive Constrained Control for Switched Systems Under State-Dependent Switching Law.

This article addresses the adaptive tracking control problem for switched uncertain nonlinear systems with state constraints via the multiple Lyapunov function approach. The system functions are considered unknown and approximated by radial basis function neural networks (RBFNNs). For the state constraint problem, the barrier Lyapunov functions (BLFs) are chosen to ensure the satisfaction of the constrained properties. Moreover, a state-dependent switching law is designed, which does not require stability for individual subsystems. Then, using the backstepping technique, an adaptive NN controller is constructed such that all signals in the resulting system are bounded, the system output can track the reference signal to a compact set, and the constraint conditions for states are not violated under the designed state-dependent switching signal. Finally, simulation results show the effectiveness of the proposed method.

Bumpless transfer control for switched linear systems with bump induced event-triggered mechanism

Event-triggered control with bumpless transfer for a class of switched linear systems is investigated. The description of event-triggered bumpless transfer (ETBT) performance can restrict the bumpy amplitude at both switching and triggering moments. In order to restrict the bump of the controller with event-triggering, we propose a novel event-triggered mechanism depending on the control bump. A positive lower bound on the event-triggering intervals is estimated. By using multiple Lyapunov functions (MLFs) approach, a sufficient condition is obtained to ensure global asymptotical stability and bumpless transfer performance for switched linear systems with bumpless transfer induced event-triggered strategy. The controller for subsystems, the switching law and the event-triggered scheme are simultaneously acquired by solving linear matrix inequalities (LMIs). Finally, the validity of the designed approach is confirmed through a switched RLC circuit and a numerical example.

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

This paper proposes a new concept of binary -dependent average dwell time, which describes different types of switching signals by the different grouping function 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.

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.

Admissible edge-dependent finite-time ℋ∞ filtering for discrete-time switched systems with average dwell time

Considering that the property of finite-time convergence is of great significance for practical filters, this article is focused on the finite-time ℋ∞ filtering for discrete-time switched systems with average dwell time. Different from the case of the general mode-dependent switching, the information of the admissible switching edge is fully exploited to derive more preferable filtering scheme. In order to further reduce the design conservatism, the multiple discontinuous Lyapunov function approach, which incorporates the concept of admissible edge-dependent average dwell time, is used to analyze the finite-time stability and ℋ∞ performance of the filtering error system. This approach assigns each subsystem of the error system with a discontinuous function rather than a continuous one, so it is less conservative compared to the conventional multiple Lyapunov function approach. First, the finite-time boundedness and ℋ∞ performance is analyzed for general switched nonlinear systems with admissible edge-dependent average dwell time. Then, a sufficient condition of the finite-time boundedness and ℋ∞ performance is derived for the filtering error system based on the obtained criterion. Subsequently, an admissible edge-dependent finite-time filtering scheme is proposed for the underlying system in terms of linear matrix inequalities. Finally, the proposed filter design scheme is applied to a DC–DC power converter circuit, and its effectiveness and superiority are verified by the simulation results.

Stability analysis of delayed fractional-order switched systems

This paper discusses stability of delayed fractional-order switched systems. First, two useful propositions are proposed based on Razumikhin approach together with properties of fractional calculus and analytical techniques, which can well solve the difficulties caused by distributed and discrete delays and fractional-order derivatives. Then, with the help of multiple Lyapunov function approach and dwell time technique, an effective way is developed to overcome the trouble caused by switching rules. A delay-dependent dwell time is derived to guarantee asymptotic stability under the hypothesis that each subsystem of delayed fractional-order switched systems is asymptotically stable. Finally, two illustrative examples further clarify the obtained conclusions.

Intermittent Pinning Synchronization for Directed Networks With Switching Technique

This research concerns the pinning synchronization of directed networks from the perspective of switched systems. Some vertices are appropriately selected to be pinned in accordance with an aperiodically intermittent pinning (AIP) strategy. The resultant synchronization error systems are then regarded as switching between two different connection topologies. Under the proposed novel piecewise time-dependent multiple Lyapunov function (PTDMLF) approach, the corresponding synchronization conditions with less conservativeness are formulated. Finally, the provided Chua’s circuit model substantiate the superiority and applicability of the theoretical results.

Stability analysis for highly nonlinear switched stochastic systems with time-varying delays

In this paper, we examine the stability of highly nonlinear switched stochastic systems (SSSs) with time-varying delays, where the switching time instants are deterministic rather than stochastic. Herein, the boundedness of the global solution is first proven for highly nonlinear SSSs via the average dwell time (ADT) method and multiple Lyapunov function (MLF) approach. Then, the stability criteria for qth moment exponential stability and almost surely exponential stability are presented. The main difficulty lies in the presence of switching and time-varying delay terms, which prevents the validation of existing methods. New inequality techniques have been developed to counteract the effects of switching signals and time-varying delays. Finally, an example is provided to verify the effectiveness of the results.

A Multiple Lyapunov Functions Approach for Formation Tracking Control

This paper proposes a leader-follower formation tracking control problem of autonomous unmanned systems with switching directed topologies, where the leader is dynamic. It is considered that the followers have only access to the leader's position. The distributed observer is designed to estimate the velocity of the leader for each follower. Based on the estimated states, this paper presents a distributed formation tracking control algorithm. Using multiple Lyapunov functions (MLFs) stability is ensured. For dealing with switching topologies, the average dwell time (ADT) concept has been used, which relaxes the traditional dwell time restriction for switching topologies. Finally, a numerical simulation demonstrates the theory's effectiveness.

Adaptive tracking control of switched cyber-physical systems with cyberattacks

This study investigates the problem of adaptive tracking control for switched cyber-physical systems against cyberattacks. A tracking signal is generated using an exogenous system. An adaptive tracking controller is designed to compensate for the attacks and then stabilize the studied systems. A switching signal is constructed using the mode-dependent average dwell time (MDADT) method. By using the multiple Lyapunov function approach, which is associated with the adaptive estimated signal, the closed-loop error systems with cyberattacks are asymptotically stable under the designed adaptive tracking controller and MDADT switching signal, and the system states can asymptotically track the reference signal. Finally, two examples are provided to validate the theoretical results.

Fully distributed event-triggered time-varying formation control of multi-agent systems subject to mode-switching denial-of-service attacks

In this study, the time-varying state formation control problem for general linear multi-agent systems (MASs) subject to mode-switching denial-of-service (MSDoS) attacks is considered. Based on only the sampled state information of itself and neighboring agents at event-triggered instants, a novel fully distributed event-triggered secure control strategy without continuous communication between agents is delicately designed. Note that the control strategy is implemented in a fully distributed manner, which means that it does not require any global network information. By using the multiple Lyapunov function approach based on edge-dependent average dwell time, this study presents the MASs subject to MSDoS attacks with limited attack frequency and attack width can achieve the specified time-varying state formation structure under the designed control strategy. Furthermore, this study presents that in any finite time, the control strategy does not exhibit Zeno behavior. Finally, the effectiveness and performance of the designed control strategy are validated by a numerical simulation.

Positive consensus for multi-agent systems with average dwell time switching

This paper considers the positive consensus for a class of multi-agent systems (MASs) with average dwell time (ADT) switching. First, sufficient and necessary conditions are derived for preserving the positivity of the closed-loop MASs. Second, the performance analysis of the consensus error system is accomplished by using the multiple Lyapunov functions (MLFs) approach, and an ADT switching technique designs the corresponding controlled switching signal. Then, both leaderless and leader-following positive consensus are achieved. Furthermore, to reduce the computational complexity, a novel leader-following positive consensus criterion is derived in the form of linear programming (LP). Finally, simulation examples are given to illustrate the effectiveness of the proposed method.

Bumpless Transfer of Uncertain Switched System and Its Application to Turbofan Engines

Nonlinear control problems in turbofan engines are challenging. No single nonlinear controller can achieve desired control effects in a full flight envelope, but in the case of multiple controllers, there exist problems in the bumpless transfer between different controllers. To this end, this paper presents a bumpless transfer mechanism for an uncertain switched system based on integral sliding mode control (ISMC), and the mechanism can be used for the speed control of turbofan engines. The uncertain switched system is used to describe the turbofan engine dynamics. Then, the ISMC controller is derived for subsystems of the uncertain switched system. A resetting scheme is introduced for the ISMC controller to ensure the continuity of control inputs during the controller transition, as well as the bumpless transfer. In view of the transient behavior caused by controller switching, the global stability of the switched system is analyzed using the multiple Lyapunov function approach and average dwell time condition. Simulation results validate that the designed resetting scheme can ensure the continuity of control input signals and avoid the instability caused by high-frequency controller switching, and increase the control effectiveness of the proposed ISMC method within the full flight envelope.

Pinning exponential cluster synchronization for fractional-order complex dynamical networks with switching topology and mode-dependent impulses

In this paper, we focus on the global exponential cluster synchronization of switched fractional-order complex dynamical networks (FCDNs) with switching topology and impulses, where the impulse effects are independent or dependent of switched modal. Compared with the literature, impulsive effects can occur not at the mode switched moment, but also at the instants without me AII) with the average dwell time (ADT) and the mode-dependent average impulsive interval (MDAII) with the mode-dependent average dwell time, by adopting multiple Lyapunov functional approach, the inequality analysis technique and pinning control strategy, the global exponential cluster synchronization conditions are achieved. Finally, the validity of theoretical results is verified by two simulation examples.

Finite-time H ∞ control for discrete-time switched systems with admissible edge-dependent average dwell time

This paper is concerned with finite-time control for discrete-time switched linear systems via admissible edge-dependent switching. The admissible edge-dependent average dwell-time (AED–ADT) is employed to identify a class of constrained switching signals for the resulting closed-loop system. Moreover, multiple discontinuous Lyapunov function (MDLF) approach, which is less conservative than the traditional multiple Lyapunov function (MLF) method, is used to analyse the closed-loop stability and performance by incorporating the idea of AED–ADT. By constructing the MDLFs in quadratic forms, a synthesis condition for finite-time bounded control is first proposed, then a synthesis condition for finite-time control is further developed based on the obtained result. Finally, two simulation examples are given to verify the effectiveness and practicability of the presented control synthesis method.

Stability and stabilisation of switched time-varying delay systems: a multiple discontinuous Lyapunov function approach

In this paper, stability and stabilisation of switched time-varying delay systems are investigated. By developing, a multiple discontinuous Lyapunov function approach and using the mode-dependent average dwell time (MDADT) switching signal, sufficient conditions are first proposed to guarantee the exponential stability of the switched system with stable and unstable subsystems where the time-varying delay is considered in the states. Relaxed stability conditions are also obtained by using a form of the Bessel–Legendre inequality. Then stabilisation of the proposed system is presented by designing a sliding mode controller. Sufficient conditions and sufficient relaxed conditions of a reduced-order sliding mode dynamics are derived, and desired sliding surfaces in the form of linear matrix inequalities (LMIs) are also given. The obtained conditions are checked by using the combined genetic algorithm and convex programming techniques. Moreover, some numerical and practical examples are given to illustrate the effectiveness of the obtained theoretical results.