Piecewise Lyapunov Function Method Research Articles

Finite-time bumpless transfer control problem for switched LPV systems with guaranteed switching frequency

For the switched linear parameter-varying (LPV) systems, the finite-time bumpless transfer control (FTBTC) issue is addressed by utilising the parameter-dependent multiple piecewise Lyapunov function method. First, for the switched LPV systems, a finite-time bumpless transfer performance is proposed, which only demands that bumpless transfer inequation holds in the activated interval in place of entire intervals. Second, a switching law depending on external parameters, system state, dwell time is designed to guarantee switching frequency. Third, a time-varying switching controller is designed, under which a solvable condition of the FTBTC issue is presented. It allows the FTBTC issue of each subsystem to be unsolvable. Finally, an aero-engine model is established to confirm the availability of the proposed scheme.

Robust exponential stabilization and L2‐gain analysis for saturated switched nonlinear systems subject to actuator failure under asynchronous switching

AbstractFor the nonlinear continuous‐time switched system with input saturation under asynchronous switching action, the problem of actuator failure is investigated in the presence of external disturbances. Firstly, a sufficient condition for the robust exponential stabilization of system is obtained by using the minimum dwell‐time method combining the piecewise Lyapunov function method. Secondly, a sufficient condition for the tolerance disturbances of the system is obtained by using the similar approach. Thirdly, the weighted ‐gain is analysed. Then, we maximize the estimation of the domain of attraction for the closed‐loop system by taking the shape of a set into consideration. Furthermore, the fault‐tolerant state feedback controllers are designed, which aim at enlarging the estimation of domain of attraction for the closed‐loop system and obtaining the maximum value of tolerance disturbance and the minimum upper bound on the weighted ‐gain. Last but not least, we give a numerical example to verify the effectiveness of the proposed approach and compare the state responses curve under the action of the fault‐tolerant and the standard controller.

Adaptive Tracking Control of Hybrid Switching Markovian Systems with Its Applications

This paper focuses on the model reference adaptive tracking control problem of uncertain hybrid switching Markovian systems. The stochastic multiple piecewise Lyapunov function method is set up for designing a hybrid switching signal and a piecewise dynamic switching adaptive controller. The hybrid switching signal is presented to improve the adaptive tracking capability by providing plenty of adjusting time during the stochastic switching stage. A piecewise dynamic parameter projection adaptive control technique is developed, which provides more freedom in designing a model reference adaptive law. A set of piecewise dynamic switching adaptive controllers are designed such that all the signals of the tracking error system remain within a bounded region under the proposed hybrid switching signal, and the tracking error converges to a neighborhood of zero where the radius of the neighborhood can be made arbitrarily small by choosing the regulation parameters appropriately. Finally, the developed adaptive tracking control theory of uncertain hybrid switching Markovian systems is illustrated by using a numerical example and an application example of an electro-hydraulic model.

Exponential input‐to‐state stabilization of semilinear systems via intermittent control

AbstractThis paper is concerned with the exponential input‐to‐state stabilization of semilinear systems via aperiodically intermittent control and aperiodically intermittent sampled‐data control, respectively. The aperiodically intermittent control is characterized from the average sense. By designing an auxiliary timer to make a compromise between control activation intervals and control rest intervals and employing the piecewise Lyapunov function method, novel sufficient criteria are obtained to guarantee the exponential input‐to‐state stability of considered systems. As for the aperiodically intermittent sampled‐data control, the sampling instants can also be aperiodic. Especially, if the sampling instants are periodic, we employ a mixed piecewise Lyapunov functional method to obtain a relatively less conservative condition to guarantee the exponential input‐to‐state stability. Finally, a numerical example is presented to illustrate the effectiveness of the theoretical results.

Resilient control for T-S fuzzy systems with multiple transmission channels under asynchronous denial-of-Service attacks

This paper investigates the resilient control problem of the T-S fuzzy system with multiple transmission channels under asynchronous denial-of-service (DoS) attacks. A part of the transmission channels are chosen as ones corresponding to the premise variables of the T-S fuzzy system. The considered asynchronous DoS attacks occur on the sensor-to-controller transmission channels, which may DoS attacks cause the system state to be unstable. The stability of the T-S fuzzy system under random DoS attack mode is considered, including the influence of the premise variables attacked. A class of parallel distributed compensation controllers are proposed, which adopts the strategy of discarding the attacked channels information. By using a piecewise Lyapunov function method and a class of linear matrix inequalities, the system stability sufficient conditions related to the duration and frequency of DoS attacks on the transmission channels are presented. Compared with the existing method, the more general relationship between premise variables and transmission channels are considered in this paper. Finally, a numerical example is used to illustrate the effectiveness of the proposed scheme.

Retracted: State estimation of Takagi‐Sugeno fuzzy system in networked control system with stochastic time delays under unknown attacks

AbstractThis article concerns the event‐triggered fuzzy filter design for Takagi‐Sugeno (T‐S) fuzzy systems subject to deception attacks under the stochastic multiple time‐varying delays. A sequence of random variables, which are mutually independent but obey the Bernoulli distribution, is introduced to account for the randomly occurring communication delays. In order to efficiently utilize limited network communication bandwidth resources, the event‐triggering scheme is adopted. A fuzzy filter with the attacked input signal is presented. Moreover, due to communication delays caused by event‐triggering schemes and transmission, the filter adopts non‐synchronous premise variables with the system. Then, by utilizing a model transformation technique, the fuzzy systems are developed. Furthermore, using the piecewise Lyapunov functional method technique, the resulting criterion provides sufficient conditions to ensure that fuzzy systems under deception attacks are stochastically stable with an H∞ performance. Accordingly, the conditions for the co‐design of the fuzzy filter and event‐triggering schemes are given. Finally, numerical simulation with the industrial process provided to verify the proposed event‐triggered design.

Asynchronous Decentralized Event-Triggered Control for Switched Large-Scale Systems Subject to Data Congestions and Disorders

In this article, the asynchronous sampling based decentralized event-triggered H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control for switched large-scale systems with disturbance and network communication delay is studied. For each sub large-scale system, distributed sensors are adopted to sample at different rates on multiple channels and transmit measurements asynchronously. Specifically, an asynchronous sampling based decentralized event-triggering scheme (AS-DETS) is first developed. Then, data buffers are utilized to organize multiple released data from different channels to update controllers. With the AS-DETS and data buffers, the resulting closed-loop switched large-scale system is derived. In particular, for the problem of data congestions and disorders caused by asynchronous sampling and large transmission delay, a packet loss method is proposed to ensure the performance of the developed system. Moreover, by using piecewise Lyapunov functional and average dwell time method, sufficient conditions are constructed to guarantee the global exponential stability with an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance of the closed-loop system. In view of the stagger between the event-triggered instants and the switching instants, their coupling effect on the system analysis is explained. Subsequently, sufficient conditions for solving state feedback gains and event-triggering parameters in terms of linear matrix inequalities are presented. Finally, numerical simulations are given to verify the effectiveness of the proposed method.

Event-Triggered $H_\infty$ Filtering for Networked Switched Systems With Packet Disorders

This paper deals with event-triggered H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering problem for switched continuous-time systems with quantization. A multiple periodic sampling-based event-triggering strategy is adopted to select those “necessary” sampled signals to be transmitted. As a result, the amount of communication and the frequency of signal updates can be reduced significantly. Regarding the nonideal communication network, we consider network-induced delays and packet disorders, which are common during packet transmission through networks. In order to cope with packet disorders, an active packet loss approach is introduced. As such, a new time-delay system model is established, by which the filtering error system is modeled as a switched system with an interval time-varying delay. Then, by employing piecewise Lyapunov functional method and average dwell time technique, some criteria are derived to ensure that the filtering error system can achieve a prescribed level of H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance. Moreover, the relationship between switching instants and the data updating instants in filter is discussed in detail, and the filter gains and event-triggering parameters can be jointly designed in terms of solutions to some linear matrix inequalities. Finally, numerical simulation is provided to verify the effectiveness of the proposed method.

Sampled-Data Resilient Control for Hybrid Nonlinear Stochastic Systems Under Periodic DoS Attacks

This paper concerns the sampled-data resilient control for hybrid nonlinear stochastic systems under periodic denial of service (P-DoS) attacks. First of all, considering that the system is attacked by P-DoS and using the zero-order holder (ZOH) technique to further analyze the impact of such attacks on the control input. Secondly, via using the time-delay transform method, the attacked sampled-data resilient control system is modeled as a switched stochastic nonlinear time-delay closed-loop system. Thirdly, by using the piecewise Lyapunov functional method, the sufficient conditions to guarantee the mean square exponential stability of the attacked system are given. Then, according to these sufficient conditions, the controller parameters are solved when specific Lyapunov functional and controller design are given. Finally, an example is given to illustrate the efficiency of our results.

Event‐based switching control for networked switched systems under nonperiodic DoS jamming attacks

This study addresses the event-based control of networked switched systems subject to cyber attacks. A novel mode-based event-triggered mechanism is proposed, which is capable of characterising non-periodic denial-of-service (DoS) attacks. A switching control law is employed in each subsystem to weaken the negative effects caused by DoS attacks. The time sequences of system switchings, event triggerings and intermittent DoS attack behaviours are fully investigated, which yields a resultant closed control system. Then, by using piecewise Lyapunov functional methods, sufficient conditions are formulated to guarantee the concerned system exponentially stable. Meanwhile, the co-design methods for switching controllers and event-triggering parameters can be developed. Finally, a numerical simulation example and a practical example of a second-order oscillating circuit are presented to verify the proposed methods.

Dual-terminal decentralized event-triggered control for switched systems with cyber attacks and quantization

This article concerns dual-terminal event-triggered communication and decentralized control of switched systems that are the target of cyber attacks. Due to different properties of physical system, this system uses decentralized communication channels to transmit feedback data. In order to make efficient use of communication resources in each channel, the information sent by the sub-system needs to meet the given event-triggering conditions before it can be released. Moreover, the quantization is employed in both sides of the controller to further improve the data transmission efficiency. Then, considering that the triggered and quantified data are affected by dual-terminal cyber attacks, the event-triggered closed-loop switched (CLS) systems under attacks are derived. Furthermore, by utilizing average dwell time (ADT) technique and piecewise Lyapunov function (LF) method, sufficient conditions are given to ensure that the event-triggered CLS systems subject to dual-terminal cyber attacks are globally exponentially stable (GES). Accordingly, the design conditions for the gains of event-triggered dynamic output feedback (DOF) controllers and the parameters of decentralized event-triggering mechanisms (DETMs) are presented. Finally, simulations for verifying the system stability with and without cyber attacks are given.

Decentralised event-triggered control for uncertain switched T–S fuzzy systems with asynchronous adaptive sampling communication

This paper investigates decentralised event-triggered control for uncertain switched Takagi-Sugeno (T-S) fuzzy systems subject to asynchronous adaptive sampling communication and exogenous disturbance. A set of adaptive sampling based on distributed sensors rather than a centralised sensor is applied to measure and sample the system's local signals. Moreover, it can enable local sensors to sample and transmit measured data asynchronously. In order to reasonably distribute network resources, decentralised event-triggering mechanisms (DETMs) are utilised. Furthermore, a data buffer is used to rearrange the released data from different channels to guarantee timely data utilisation. Then, under the proposed DETMs based on adaptive sampling and data buffer, a time-delay closed-loop uncertain switched T-S fuzzy system is developed by applying a modelling method. Subsequently, by utilising the average dwell time and piecewise Lyapunov functional method, sufficient conditions are obtained to ensure that the state of closed-loop uncertain switched T-S fuzzy system is exponentially stable with an performance level. For the coupling between switching instants and event-triggered instants in the system, their impact on the system is discussed in detail. Accordingly, the conditions for the co-design of state feedback controllers gains and event-triggering parameters are presented. Finally, simulations verify the proposed design approach.

Asynchronous Resilient Output Consensus of Switched Heterogeneous Linear Multivehicle Systems With Communication Delay

The resilient output consensus problem for a network of switched heterogeneous linear vehicle systems with asynchronous switching, controller gain variation, unknown disturbance, and communication delay is investigated. Based on the topology decoupling technique, the investigated problem is transformed into two subproblems: one is a robust asynchronous static output feedback (SOF) control problem and the other is an asynchronous SOF problem. Based on the piecewise Lyapunov functional method and the average dwell time switching scheme, some new sufficient conditions are proposed for the solutions to those subproblems. Moreover, some novel linear-matrix-inequality-based conditions are developed to calculate the SOF controller gains. A network of six vehicles is finally presented to show the effectiveness of the proposed resilient consensus controller.

Event-triggered [formula omitted] control for network-based switched linear systems with transmission delay

This paper investigates the event-triggered L∞ control for network-based switched linear systems with transmission delay. Necessary samplings of the feedback signal are determined by the improved periodic sampling based event-triggering schemes with extra design parameters, which can further reduce redundant signal transmissions and updates. Moreover, under the state feedback control, a time-delay closed-loop switched system is developed. Particularly, in the developing process an active packet loss technique is given to fully deal with the relationship between the network transmission delay and sampling period. Then by utilizing the piecewise Lyapunov functional method and average dwell time technique, sufficient conditions in terms of linear matrix inequalities (LMIs) are constructed to render the time-delay closed-loop switched system globally uniformly ultimately bounded (GUUB) and having an L∞ performance. In addition, since the event-triggered instants and switching instants both exist in the system and may stagger with each other, their coupling effect on the stability analysis is clarified. Subsequently, the conditions for finding the parameters of state feedback gains and improved event-triggering schemes are presented. An example is provided to show the effectiveness of the proposed method.

Intermittent control strategy for synchronization of fractional-order neural networks via piecewise Lyapunov function method

In this paper, the synchronization problem of fractional-order neural networks (FNNs) with chaotic dynamics is investigated via the intermittent control strategy. Two types of intermittent control methods, the aperiodic one and the periodic one, are applied to achieve the synchronization of the considered systems. Based on the dynamic characteristics of the intermittent control systems, the piecewise Lyapunov function method is employed to derive the synchronization criteria with less conservatism. The results under the aperiodically intermittent control show more generality than the ones via the periodically intermittent control. For each of the aperiodic and periodic cases, a simple controller design process is presented to show how to design the corresponding intermittent controller. Finally, two numerical examples are provided to demonstrate the effectiveness of the obtained theoretical results.

Conditions for the Stability of Switched Systems Containing Unstable Subsystems

This brief studies the stability of switched systems in which all the subsystems may be unstable. In addition, some of the switching behaviors of the systems are destabilizing. By using the piecewise Lyapunov function method and taking a tradeoff between the increasing scale and the decreasing scale of the Lyapunov function at switching times, the maximum dwell time for admissible switching signals is obtained and the extended stability results for switched systems in a nonlinear setting are first derived. Then, based on the discretized Lyapunov function method, the switching stabilization problem for linear context is solved. By contrasting with the contributions available in the literature, we do not require that all the switching behaviors of the switching system under consideration are stabilizing. More specifically, even if all the subsystems governing the continuous dynamics are not stable and some of the switching behaviors are destabilizing, the stability of the switched system can still be retained. A numerical example is given to illustrate the validity of the proposed results.

Event-triggered quantized [formula omitted] control for networked control systems in the presence of denial-of-service jamming attacks

The problem of event-triggered quantized H∞ control of networked control systems (NCSs) under denial-of-service (DoS) jamming attacks is investigated in this paper. Firstly, a new resilient event-triggering transmission scheme is proposed to lighten the load of computing and communications while offsetting the DoS jamming attacks imposed by power-constrained Pulse-Width Modulated (PWM) jammers. Secondly, a new switched system model is established, which characterizes the effects of the event-triggering scheme, quantization and DoS jamming attacks within a unified framework. Thirdly, linear matrix inequality (LMI)-based sufficient conditions for ensuring the exponential stability of the resulting switched system under the DoS jamming attacks are derived by using the piecewise Lyapunov functional method. Moreover, if the obtained LMIs are feasible, the co-design of the event-triggering parameter and the feedback gain matrix can be obtained. Finally, a satellite yaw angle control system is given to verify the effectiveness and feasibility of the developed theoretical results.

Exponential H ∞ output tracking control for coupled switched systems with states of different dimensions

This paper is concerned with the output tracking control for complex switched systems with non-diffusively delayed coupling. The states' dimensions are different in the coupled switched systems and reference system. On the base of the average dwell time and piecewise Lyapunov functional methods, a delay-dependent exponential stability criterion is derived for the switched systems under the QUAD condition which is less conservative than the Lipschitz condition. The state feedback controller is employed in the design of output tracking, and the tracking performance is guaranteed by solving a linear matrix inequality. Finally, three numerical examples are provided to show the advantage and effectiveness of the proposed theoretical results.

Decentralized event-triggered H∞ control for switched systems with network communication delay

This paper is concerned with the decentralized event-triggered H∞ control for switched systems subject to network communication delay and exogenous disturbance. Depending on different physical properties, the system state is divided into multiple communication channels and decentralized sensors are employed to collect signals on these channels. Furthermore, decentralized event-triggering mechanisms (DETMs) with a switching structure are proposed to determine whether the sampled data needs to be transmitted. In particular, an improved data buffer is presented which can guarantee more timely utilization of the sampled data. Then, with the proposed DETMs and data buffer, a time-delay closed-loop switched system is developed. After that, sufficient conditions are presented to guarantee the H∞ performance of the closed-loop switched system by utilizing the average dwell time and piecewise Lyapunov functional method. Since the event-triggered instants and the switching instants may stagger with each other, the influence of their coupling on the H∞ performance analysis is systematically discussed. Subsequently, sufficient conditions for designing the event-triggered state feedback controller gains are provided. Finally, numerical simulations are given to verify the effectiveness of the proposed method.

$$H_\infty $$ H ∞ switching synchronization for multiple time-delay chaotic systems subject to controller failure and its application to aperiodically intermittent control

This paper is concerned with the \(H_\infty \) synchronization control problem for a class of chaotic systems with multiple delays in the presence of controller temporary failure. Based on the idea of switching, the synchronization error systems with controller temporary failure are modeled as a class of switched synchronization error systems. Then, a switching condition that incorporates the controller failure time is constructed by using piecewise Lyapunov functional and average dwell-time methods, such that the switched synchronization error systems are exponentially stable and satisfy a weighted \(H_\infty \) performance level. In the meantime, a switching state feedback \(H_\infty \) controller is derived by solving a set of linear matrix inequalities. More incisively, the obtained results can also be applied to the issue of aperiodically intermittent control. Finally, three simulation examples are employed to illustrate the effectiveness and potential of the proposed method.