Average Dwell-time Condition Research Articles

Set‐membership estimation of switched LPV systems: Application to fault/disturbance estimation

SummaryThis paper proposes a set‐membership state estimation method for Switched Linear Parameter Varying (SLPV) systems subject to unknown but bounded parametric uncertainties, disturbances and noises. A zonotopic outer approximation of the state estimation domain is computed at every time iteration. The size of this zonotope is designed to be convergent and bounded by satisfying ‐radius‐based and Average Dwell Time (ADT) conditions that are formulated in the Linear Matrix Inequality (LMI) framework. An extension of the state estimation method is presented to address the fault/disturbance estimation problem for SLPV systems. By using the state augmentation technique, the fault/disturbance estimation problem is transformed into a state estimation problem of the generated augmented descriptor switched LPV system. An application to vehicle lateral dynamics fault estimation is used for assessment purposes. Simulation results demonstrate the effectiveness of the proposed algorithm and highlight its advantages over the existing methods.

On exponential stability in [formula omitted]th moment of neutral Markov switched stochastic time-delay systems

In this article, the problem of the pth moment exponential stability is be investigated for neutral Markov switched stochastic time-delay systems. By virtue of inequalities based on the state-dependent multiple Lyapunov functions, we propose adequate conditions for the p-ES of Markov switched neutral stochastic differential delay equation applying properties for the stationary distribution of Markov switched process. For a class of neutral Markov switched stochastic time delay systems with impulse, several new criteria for pth moment exponential stability is obtained using the impulse average dwell-time condition, the integral transformation inequality, and stochastic analysis theory. The results extend and improve the related results from the existing literature. Some examples are provided to illustrate the validity of our derived results.

Adaptive Fault-Tolerant Control for Nonlinear MASs Under Actuator Faults and DoS Attacks

In this article, we study the adaptive fault-tolerant control (FTC) for multiagent systems (MASs) under denial-of-service (DoS) attacks and actuator faults. The mixed connectivity-maintained/broken attack containing both connectivity-maintained and connectivity-broken attacks is considered, which results that the MASs are with switching topologies. Also, characteristics of DoS attacks, such as durations and frequencies of attacks, make it more difficult to design fault-tolerant controllers and analyze the stability for MASs with node faults. A novel FTC strategy is presented to compensate for node faults. Then, by using the Lyapunov stability analysis, an average dwell-time condition is presented for the bounded synchronization of MASs under DoS attacks. An example of nonlinear forced pendulum systems is proposed to verify the proposed approach.

Delays-Based Distributed Bipartite Consensus Control of Nonlinear Multiagent Systems With Switching Signed Topologies

This paper explores the distributed leader-following bipartite consensus control issue for nonlinear multiagent systems under switching signed topologies and communication delays. It is permitted that the signed topologies are switched with an average dwell-time condition, and the delays are modeled as the time-varying functions. In the permission, we develop a new dynamic output feedback control-based distributed bipartite consensus method. First, we put forward the delays-dependent distributed switched compensators to the followers, adopting the relevant output information, which are applied to asymptotically estimate the leader-following tracking errors and provide the control signals. Then, we construct the distributed output feedback switched controllers with the linear structure for all followers, which are dependent on the compensators. By utilizing the Lyapunov-Krasovskii functional analysis method, we verify that our proposed controllers can render the agents gaining the bipartite consensus if the switching signal of signed topologies fulfills an average dwell-time condition. Finally, two examples are executed in the simulation to confirm the validity of the given control strategy.

Finite/fixed-time input-to-state stability of impulsive nonlinear systems

In this paper, we investigate the finite-time and fixed-time input-to-state stability of impulsive nonlinear systems involving hybrid impulses which have time-dependent multiple jump maps. Under unified average dwell-time conditions, several criteria for finite-time and fixed-time input-to-state stability are established by virtue of the Lyapunov function with linear rate and nonlinear rate of jump maps. It shows that, when the finite/fixed-time input-to-state stable continuous systems are subject to hybrid impulses, the finite-time and fixed-time input-to-state stability can be ascertained under the requirement that the accumulative effect of hybrid impulses is non-destabilizing or the accumulative effect of hybrid impulses is destabilizing and the impulses are not activated too frequently. Finally, the effectiveness of theoretical results is verified by two numerical examples and an application example about an axisymmetric circular spacecraft.

Leader-Following Consensus Control for Uncertain Feedforward Stochastic Nonlinear Multiagent Systems.

This article addresses the leader-following consensus problem of feedforward stochastic nonlinear multiagent systems with switching topologies. Output information for all agents, except for state information, can be acquired based on sensor measurement. Moreover, the stochastic disturbances from external unpredictable environments are considered on all agent systems with a feedforward structure. In these conditions, we propose a novel consensus scheme with a simple design procedure. First, for each follower, we construct a dynamic gain-based switched compensator using its output and its neighbor agents' outputs to provide feedback control signals. Then, for each follower, we develop a compensator-based distributed controller that is not directly associated with the topology switching signal such that it has a first derivative and antishake. Thereafter, by means of the Lyapunov stability theory, we verify that the leader-following consensus can be acquired asymptotically in probability under the controllers' action if the topology switching signal fulfills an average dwell time condition. Finally, the feasibility of the control algorithm is checked via numerical simulation.

Stochastic input-to-state stability for stochastic complex dynamical control networks with impulsive perturbation

In this paper, stochastic input-to-state stability (SISS) for stochastic complex dynamical control networks with impulsive perturbation (SCDCNIP) is investigated. An appropriate global Lyapunov function is developed which is closely related to topology of SCDCNIP and dynamical behaviors of every node system of SCDCNIP. Some sufficient criteria are given to guarantee SCDCNIP to meet SISS by imposing the average dwell-time (ADT) condition and reverse average dwell-time (RADT) condition. Moreover, as an application of our theoretical results, typical stochastic coupled oscillators with impulsive perturbation (SCOIP) are studied. Finally, some numerical simulation results are provided to verify the correctness and validity of our results.

Robust tracking for functional electrical stimulation cycling with unknown time-varying input delays: A switched systems approach.

Motorized functional electrical stimulation (FES) cycling has been demonstrated to have numerous health benefits for individuals suffering from neurological disorders. FES-cycling is usually designed to track the desired trajectories in real time. However, there are input delays between the exertion of the stimulation and the corresponding muscle contraction that potentially destabilize the system and undermine training efforts. Meanwhile, muscle fatigue gives rise to a time-varying input delay and decreased force. Moreover, switching between FES and motor control can be chattering and destabilizing owing to the high frequency. This article constructs Lyapunov-Krasovskii functionals to analyze the stability and robustness of the nonlinear cycling system with time-varying input delay. A new average dwell time condition is then provided to ensure the input-to-state stability of the considered systems. Finally, numerical simulations are illustrated to verify the effectiveness of the developed controller.

Impulsive cluster synchronization for complex dynamical networks with packet loss and parameters mismatch

This paper investigates the cluster synchronization (CS) for a class of complex dynamical networks (CDNs) with parameters mismatch to the selected cluster pattern. An impulsive control strategy with multiple control gains is proposed. Particularly, the possible packet loss phenomenon in control input is fully considered, and it is characterized by a series of impulse packet loss rate (iPLR) conditions. In terms of the reverse average dwell time (rADT) condition and the average impulse gain method, some sufficient conditions guaranteing that all the nodes of CDNs can be synchronized to their cluster sets are derived, from which the constraint relationships among rate coefficients, impulsive control law, and iPLR can be revealed. Finally, an example is given to illustrate the correctiveness of our results.

ADT-based adaptive back-stepping control for the switched non-affine nonlinear system with uncertain parameters

The adaptive back-stepping control issue for the switched non-affine nonlinear system with the uncertain parameter is addressed in this paper. Inspired by the “extended state” conception, the integral item is first employed in the original switched nonlinear system to generate an augmented switched non-affine nonlinear system. Then, the non-affine structures in the system dynamics are adopted to devise the virtual controls directly, and the dynamic surface control is integrated to eliminate the “explosion of complexity” caused by the back-stepping design. Furthermore, the estimation of switched unknown parameter is achieved by the continuous variable, and the individual Lyapunov functions including the estimation errors are constructed for each subsystem. Combined with the multiple Lyapunov functions methods, the uniformly ultimately bounded of the closed-loop switched system could be ensured under any switching law, which satisfies the average dwell time condition. Furthermore, system tracking errors would converge to the neighborhood of the zero. Finally, numerical simulations demonstrate the validity of proposed control approaches.

Event-triggered attitude synchronization of multiple rigid body systems with velocity-free measurements

In this paper, an attitude synchronization problem with velocity-free measurements is investigated for multiple rigid body systems under event-triggered mechanism. To avoid the angular velocities in the control design, an auxiliary system is constructed for the indirect asymptotic estimation of angular velocities, which provides the necessary damping for the closed-loop system. The event-triggered attitude protocol is proposed with a clock-based triggering strategy, and the continuous communication and monitoring requirements among rigid bodies are removed. The convergence of synchronization is analyzed based on a positively invariant set contained in SO(3), which inherently avoids the singularity problem or non-uniqueness issue for the attitude representation. Furthermore, based on an invariant-like principle, we extend the topology graph to a switching topology under an average dwell-time condition. A numerical simulation is conducted to show the effectiveness of the proposed control strategy.

A dwell time approach for the stabilization of mixed Continuous/Discrete switched systems

In this paper, we study the stabilization properties of Continuous/Discrete switched systems using the dwell time approaches. The considered system switches between a continuous-time subsystem evolving on time intervals with variable lengths and a discrete-time subsystem with variable discrete step sizes. Since the time domain is non-uniform, and the stability of the discrete-time subsystem with variable discrete step sizes does not depend only on the dynamic of the system, but also on the length of the discrete steps, the usual conditions of dwell time approaches may not be applicable to stabilize this special class of switched systems. Motivated by that, stabilizing dwell time and average dwell time conditions are derived by introducing the time scales theory and numerical examples are proposed to illustrate the effectiveness of the proposed methods.

Improved Input-to-State Stability Analysis of Impulsive Stochastic Systems

This article is concerned with the input-to-state stability (ISS) and stochastic input-to-state stability (SISS) of impulsive stochastic nonlinear systems. By constructing a general SISS-Lyapunov function, which takes the exponential SISS-Lyapunov function as a special case, the ISS criteria are obtained, respectively, for destabilizing and stabilizing impulses. It should be stressed that we impose the average dwell-time (ADT) condition for destabilizing impulses and reverse average dwell-time (RADT) condition for stabilizing impulses to restrain the occurrence of impulses, which extends the fixed dwell-time condition in recent literature. Moreover, the ADT and RADT conditions in this article correspond to the average impulsive interval method in most existing results under the exponential ISS-Lyapunov condition. As a subsequent result, the ISS and SISS of impulsive stochastic interconnected systems on networks are also studied by the Lyapunov method and graph-theoretic technique. Finally, several illustrative examples together with their numerical simulations are provided to demonstrate the theoretical results.

Hierarchical autonomous switching control of a multi-modes omnidirectional mobile robot

Adequate control flexibility and tracking precision of the omnidirectional mobile robot (OMR) are difficult to be guaranteed with a fixed control mode. To address this challenge, this paper presents a modified hierarchical autonomous switching control scheme for an OMR with multiple maneuver-modes, which is capable of switching the alternative modes to adapt to the operational conditions and performing a satisfactory trajectory tracking control. Utilizing a hierarchical switching signal, the design begins by formulating a hybrid discrete OMR system with multiple subsystems cascading to its alternative kinematic states. Under the integrated system constraints, a new hierarchical switched fractional-order receding horizon control is presented to offer more adjusting flexibilities, which constructs a novel fractional-order cost function and then derives a numerical solvable solution. Meanwhile, with a Lyapunov-principle-based supervisory variable, an autonomous switching law is proposed so that the preferred subsystem can be selected to enhance the moving maneuverability. Under certain average dwell time conditions, the asymptotic stability of the resultant system is guaranteed. Finally, comparative experiments implemented on the real-world scenarios are provided to demonstrate the superior tracking performance and enhanced robustness of the proposed hierarchical autonomous switching control method as compared to traditional control schemes.

Hybrid state observer‐based event‐triggered control for switched linear systems with quantized input

The paper investigates the design of hybrid state observer-based event-triggered controller for switched linear systems subject to quantized input and unknown but bounded additional disturbance and measurement noise. Firstly, by introducing a hybrid state observer and constructing a mode-dependent event-triggered mechanism, we design event-triggered controller for the considered switched linear systems. Then, by modeling the closed-loop system as an augmented asynchronous switched time-delay system, we deal with the asynchronous control problem caused by the switching between two consecutive trigger instants for the switched linear system. Thirdly, based on merging signal technique and multiple Lyapunov functional method, we obtain the sufficient criteria to guarantee the stability of the switched system when the switching signal meets an average dwell time condition, and further establish the hybrid observer-based event-triggered controller gains. Finally, a simulation example illustrates the validity of the results.

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.

Generalised existence condition and design method for switched nonlinear state-norm estimators

The state-norm estimation problem for the switched nonlinear system under a more generalized type of switching signals is investigated in this paper. The component subsystems consist of input/output-to-state stability (IOSS) and non-IOSS continuous systems simultaneously, whose activation time is lower and upper bounded by mode-dependent time-varying functions, respectively. The considered switching signals satisfy mode-dependent time-varying constraints, whose switching number can grow faster than those with constant average dwell time condition. Then based on multiple IOSS Lyapunov functions method, the existence condition and design method for the switched state-norm estimator are proposed. The obtained results present extensions compared with the existing results, which are applicable for the more general situations. Finally, the effectiveness and improvement of the proposed approach are illustrated by a numerical example.

Leader-following asynchronous consensus for multiagent systems with unknown control and output directions

This paper focuses on the distributed consensus problem for multiagent systems subject to high-order integrator dynamics and unknown control and output directions based on switching topologies. Unlike existing works, both control and output directions are unknown in the systems and delay is considered between the switching of candidate K-filters and that of topologies. In these conditions, we produced a fresh distributed consensus algorithm by the correlative output information. By designing asynchronous switched K-filters and classical K-filters, the state variables of the leader and all followers are reconstructed. Based on the backstepping method and the Nussbaum-type functions, we put forward the distributed controller with K-filters for the follower. Then, we scrupulously prove that all agents can acquire consensus driven by the controller if the switching signal satisfies an average dwell time condition. Finally, the correctness of the algorithm is tested based on a numerical simulation.

Input-to-state stability of impulsive stochastic infinite dimensional systems with Poisson jumps

This paper is concerned with the input-to-state stability (ISS) of mild solutions to a class of impulsive stochastic infinite dimensional systems with Poisson jumps (ISISP). By using a Yosida strong solutions approximation approach for mild solutions of ISISP and the Itô’s formula, several Lyapunov-based sufficient conditions ensuring the ISS of ISISP with stabilizing and destabilizing impulses are established, respectively. The main merits of the sufficient conditions are that (i) the ISS-Lyapunov function can be non-exponential; (ii) average dwell-time condition is imposed to restrict the occurrence frequency of impulses; (iii) the effects of destabilizing or stabilizing impulses can be explicitly shown compared with the existing works about the stability of mild solutions to impulsive stochastic infinite dimensional systems by the fixed point approach. Moreover, when the ISS-Lyapunov function is exponential, we present a more general result which is suitable for destabilizing and stabilizing impulses simultaneously. Finally, examples of stochastic heat equations are provided to illustrate the proposed results.

Exponential stabilization of continuous-time dynamical systems via time and event triggered aperiodic intermittent control

This paper studies the exponential stabilization of continuous-time dynamical systems via aperiodic intermittent controls (APIC). Time-triggered and event-triggered APIC schemes are designed respectively for continuous-time dynamical systems. Under time-triggered APIC (T-APIC), by proposing the notions of (minimum) average control width and using the method of Lyapunov-like function, the exponential stabilization criteria expressed by converse average dwell-time conditions are derived. Based on indices of threshold-value and check-period, the event-triggered APIC (E-APIC) is proposed. E-APIC is state dependent and the algorithm for E-APIC is given to derive criteria of exponential stabilization. Moreover, by introducing control-free index into APIC, an E-APIC with state-based control widths (SCW) is proposed to improve the constraints on control widths in E-APIC and T-APIC. In order to verify performances of the intermittent control schemes including periodic intermittent control (PIC), some discussions are given by using notions of number of control, rate of control, and cost of control. Finally, one example with numerical simulations is given for illustrations. It is shown that both PIC and T-APIC are stronger control schemes than E-APIC and E-APIC with SCW. E-APIC and E-APIC with SCW have better performances than PIC and T-APIC with lower values on rate of control, number of control, and cost of control. And E-APIC with SCW has lowest rate of control and can achieve least total control time.