Input-to-state Stability Research Articles

Predictive cloud control for nonlinear multiagent systems based on extended state observer and quantizers

AbstractIn this article, predictive cloud control is investigated for nonlinear networked multiagent system (NMAS) with quantizers via extended state observer (ESO). Considering the network‐induced delays in NMAS, the cloud control scheme is designed. Then, arbitrary region quantizers are used to decrease the quantity of data packets. Moreover, the ESO that can estimate the state and uncertainty of nonlinear NMAS is used to obtain the prediction of data packets. Input‐to‐state stability (ISS) can guarantee the validity of ESO. Sufficient conditions that can achieve stability and consistency for NMAS are given by the zoom strategy. The significance of the scheme is verified by simulation results.

Event-Triggered Impulsive Control for Input-to-State Stabilization of Nonlinear Time-Delay Systems.

This article investigates the event-triggered impulsive control (ETIC) problem for a class of nonlinear time-delay systems subject to exogenous disturbances. An original event-triggered mechanism (ETM) which utilizes the information of system state and external input is constructed based on Lyapunov function approach. To achieve the input-to-state stability (ISS) of the considered system, some sufficient conditions are presented, in which the underlying relationship among ETM, exogenous input, and impulse action is established. Furthermore, the possible Zeno behavior induced by the proposed ETM is excluded simultaneously. As an application, the design criterion of ETM and impulse gain is put forward for a class of impulsive control systems with delay according to the feasibility of some linear matrix inequalities (LMIs). Finally, two examples with numerical simulations are provided to confirm the effectiveness of the developed theoretical results, where the synchronization issue of delayed Chua's circuit is considered.

Non-smooth finite-time adaptive stabilisation of cascade switched systems with asymmetric output constraints

In this article, the problem of non-smooth finite-time (FT) adaptive state feedback stabilisation is investigated for asymmetric output-constrained cascade switched nonlinear systems (AOCCSNSs) with mixed powers, parametric uncertainties and zero dynamics. To better address the uncertain parameters and the asymmetric output constraints, a new type of common Lyapunov function (CLF) including a quadratic squared term of the estimated error and a tangent-type barrier Lyapunov function ( T t -BLF) is constructed. Then, with some mild assumptions, such as input-to-state stability (ISS) property of zero dynamics, upper boundedness of subsystems' nonlinear terms and some well-known small signal conditions, state feedback controllers (SFCs) constructed by adding a power integrator (AAPI) technique and the update law to estimate the unknown parameter are proposed to guarantee resultant closed-loop switched systems FT stable. The proposed method for switched systems is presented in a unified manner, capable of addressing FT stabilisation by effectively handling situations with or without output constraints. This is achieved through the construction of T t -BLF, which degenerates into a quadratic form when the output constraint disappears or approaches infinity. At last, the method is verified by a switched RLC circuit system (RLC-CS) and a numerical simulation.

Data-driven ensemble optimal compensation control for partially known delayed and persistently disturbed nonlinear systems

In almost all industrial processes, the development of an accurate mathematical model that comprehensively characterizes the regulated system poses a substantial obstacle. Diverse factors, such as unidentified system components and time-varying external disturbances, contribute to this phenomenon. This can result in a disparity between the model and the plant and thereby compromising the performance of the designed controller. In this study, a novel data-driven ensemble optimal compensation control framework is proposed for partially known nonlinear systems with state delays and structural disturbances. Initially, the estimated system model is leveraged to construct a robust fuzzy model predictive controller (RFMPC) based on the Lyapunov–Krasovskii functional (LKF), ensuring the input-to-state stability (ISS) of the plant. Then, a reinforcement learning (RL)-based compensator is assembled to gradually minimize the model-plant mismatch across the entire state space. To streamline the training process of the compensator and facilitate its stability, a dynamic network update scheme is devised, incorporating a moving average gradient calculation method and a learning rate tuning strategy. Furthermore, comparative discussions with some prevalent methods are demonstrated. With the established control framework, the performance of the RFMPC can be securely enhanced, and convergence is ensured within a narrow proximity to equilibrium, despite time-varying perturbation dynamics. By integrating this approach with deep learning (DL) methods, the efficacy of numerous industrial processes could be significantly improved. A numerical simulation and a discretized continuous-time stirring tank reactor (CSTR) example validate the effectiveness and benefits of the proposed control strategy.

Stability analysis of nonlinear systems with delayed impulses: a generalised average dwell-time scheme

This paper studies the input-to-state stability (ISS) and uniform stability for impulsive nonlinear systems with delayed impulses, where delays are flexible between two consecutive impulsive instants. Illustrating effects caused by delays, concepts of generalised average impulsive delay and generalised reverse average impulsive delay are introduced, and more applicable in practice. Moreover, sufficient conditions for stability properties are formulated with destabilising and stabilising impulses through a general candidate ISS-Lyapunov function and the generalised conditions. It is shown that the double effects of delays in impulses (i.e. stabilising an initial unstable system, or contrarily, destabilising an initial stable system) coincide with the existing results using the exponential candidate ISS-Lyapunov function. Finally, two examples are provided to demonstrate our developed techniques.

Hybrid‐triggered predictive control of cyber‐physical‐systems under cyber‐attacks

AbstractIn this article, the hybrid‐triggered predictive control of cyber‐physical systems (CPSs) under cyber‐attacks is researched. Firstly, considering the unpredictable state of the CPSs, an observer‐based model is constructed, and the predictor is put forward to predict state. Secondly, a hybrid‐triggered scheme is adopted to avoid unnecessary‐data transmission by introducing a hybrid switch mode. Thirdly, the deception attacks and DoS attacks are existed in sensor‐to‐observer (S‐O) and observer‐to‐controller (O‐C), separately. Two types of attack modeling are established based on their characteristics. With the proposed control method, some sufficient conditions are obtained to ensure the input‐to‐state stability (ISS) of CPSs. Finally, the results of simulation examples are received to testify the advantage of developed control strategy.

Multi‐event‐triggered adaptive dynamic programming for non‐zero‐sum game of unknown nonlinear system

AbstractIn this article, a multi‐event‐triggered (MET) near‐optimal tracking control algorithm is developed for a discrete‐time (DT) nonlinear non‐zero‐sum game (NZSG). Firstly, the iterative dual heuristic dynamic programming (DHP) approach is utilized to obtain the optimal tracking control set. Subsequently, distinct independent triggering conditions are formulated for control inputs to improve the utilization efficiency of resources and ensure that the independence between them and the closed‐loop system has an excellent control performance. Meanwhile, input‐to‐state stability (ISS) is proven for the MET tracking plant. Additionally, neural networks (NNs) are designed in the iterative DHP algorithm to construct the model module, the critic module and the action modules, with aims to identify the unknown system, approximate costate function and estimate optimal tracking control strategy set, respectively. Finally, two numerical experimental simulations are conducted to verify the effectiveness of the proposed scheme.

A control scheme for interval type‐2 T‐S fuzzy systems at constrained bit rates: A coding and decoding scheme

SummaryThis study focuses on a class of interval type‐2 T‐S fuzzy systems under bit rate constraint(BRC), which can adapt to complex systems more flexibly than the traditional interval type‐1 T‐S fuzzy model. In order to guarantee the security of data transmission, and considering that the channel is affected by the bit rate during transmission, this study introduces a codec scheme in the interval type‐2 T‐S fuzzy system and applies it to the channel from the sensor to the controller. With the support of the codec scheme, this study explores the sufficient conditions to satisfy the data recoverability, and based on the satisfaction of these conditions, the system is proposed to satisfy the sufficient conditions for input‐to‐state stability (ISS) and the controller gain. Through the in‐depth analysis in this paper, this study proposes a control scheme that can fit complex systems more accurately and also confirms the importance of considering bit rate constraints in communication systems. Finally, the paper is validated by simulation with two specific examples, which fully demonstrate the superiority and effectiveness of the proposed control scheme.

Building coercive Lyapunov–Krasovskii functionals based on Razumikhin and Halanay approaches

AbstractIn this article, we provide a systematic and constructive way to build a Lyapunov–Krasovskii functional for time‐delay systems whose stability can be established through the Razumikhin or the Halanay approaches. The constructed Lyapunov–Krasovskii functional turns out to be coercive, meaning sandwiched between functions of the state history norm, and to dissipate in terms of the whole history norm. We present these results in the framework of input‐to‐state stability (ISS) in order to further account for the influence of input disturbances. A special emphasis is also given on exponential stability and exponential ISS. We illustrate our findings though the study of a coupled ODE‐PDE model of a chemical reactor, and show that, unlike most results in that area, our approach happens to ensure ISS in terms of the supremum norm of the state.

Global inverse optimality for a class of recurrent neural networks with multiple proportional delays

This paper formulates two novel theoretical designs of input-to-state stabilizing control for a class of recurrent neural networks with multiple proportional delays. The analysis tool developed in this paper is based on Lyapunov function and inverse optimality method, which does not require solving Hamilton-Jacobi-Bellman equations. Two inverse optimal feedback laws are constructed via the dimensions of state and input, which ensure the input-state stability for the considered system. When the dimensions of state and input are different, we establish a scalar function and give one of the control laws by Sontag's formula. Furthermore, the designs of inverse optimal control reach both global inverse optimality and global asymptotic stability of the system for some meaningful cost functional. Four numerical examples are provided to show the effectiveness of the inverse optimal control.

Stabilization under unknown control directions and disturbed measurements via a time‐delay approach to extremum seeking

AbstractWe study stabilization of linear uncertain systems under unknown control directions using a bounded extremum seeking controller in the presence of a small time‐varying measurement delay. We assume that the measurements are subject to discontinuous disturbances. The main novelty is that these disturbances possess not only the constant part as in the existing results, but also small discontinuous part that may appear due to quantization. We consider two types of measurements: the state measurements and the state quadratic norm ones. In the latter case the constant part of the disturbances may be arbitrary large. By using the recently proposed time‐delay approach to Lie‐brackets‐based averaging, we transform the closed‐loop system to a time‐delay (neutral type) one with no terms depending on the disturbance derivative, which has a form of perturbed Lie brackets system. The input‐to‐state stability (ISS) of the time‐delay system guarantees the same for the original one. We further transform the neutral system to an ordinary differential equation (ODE) with delayed perturbations and employ variation of constants formula leading to explicit conditions in terms of simple inequalities with less conservative results in the most of numerical examples. Two numerical examples are provided to illustrate the efficiency of the method.

An event‐triggered subspace predictive control method for partially unknown linear parameter‐varying systems

AbstractThis article develops a novel event‐triggered subspace predictive control (ET‐SPC) method for discrete‐time linear parameter‐varying (LPV) systems with partially unknown system parameters. An event‐triggered law is developed to alleviate the heavy load of data transmission and computation in the conventional subspace predictive control methods for the LPV systems. The design of the event‐triggered law relies on the input‐to‐state stability (ISS) theory and applies the robust stability condition based on linear matrix inequalities (LMIs), which guarantees the stability of the proposed method. Consequently, the input component can be directly transmitted to the system without receding horizon optimization when the event‐triggered law evaluates that the system satisfies the stability condition. The simulation results illustrate its satisfactory performance, which indicates its potential application involving a considerable amount of data transmission and computation such as the network control systems (NCSs).

Well-posedness and stability for a nonlinear Euler-Bernoulli beam equation

<abstract><p>We study the well-posedness and stability for a nonlinear Euler-Bernoulli beam equation modeling railway track deflections in the framework of input-to-state stability (ISS) theory. More specifically, in the presence of both distributed in-domain and boundary disturbances, we prove first the existence and uniqueness of a classical solution by using the technique of lifting and the semigroup method, and then establish the $ L^r $-integral input-to-state stability estimate for the solution whenever $ r\in [2, +\infty] $ by constructing a suitable Lyapunov functional with the aid of Sobolev-like inequalities, which are used to deal with the boundary terms. We provide an extensive extension of relevant work presented in the existing literature.</p></abstract>

Dynamic Short Circuit Ratio for Stability Assessment of Grid Connected VSC-HVDC Systems Considering the Impact of Time-Varying Phase Shift

As more renewable resources are integrated into the receiving-end AC grid through VSC-HVDC, the grid connected VSC-HVDC system is facing a critical dynamic stability issue involving multiple-frequency oscillatory behaviors, which mainly stems from the low-system-strength and the time-varying phase shift. This paper proposes a general stability analysis method to measure the dynamic stability of grid connected VSC-HVDC system from the point of view of input to state stability (ISS). A nonlinear time-varying discrete-time state space model (NTDS <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> M) of the grid connected VSC-HVDC system is built considering the impact of the time-varying phase shift. Then, the NTDS <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> M is decomposed into several interconnected subsystems. The general asymptotic gain matrix (GAGM), whose elements are derived from the proposed dissipative-form sum-type inequalities (DSIs), is constructed to quantify the interactions between multiple subsystems. Finally, a general dynamic stability analysis index, called dynamic short circuit ratio (DSCR), is proposed to effectively explain the critical dynamic instability point of the grid connected VSC-HVDC system, based on the spectral radius property of the GAGM. Moreover, the real-time simulations and multiple comparative studies are implemented in this paper to verify the effectiveness of the proposed NTDS <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> M and stability analysis method by using RT-LAB platform.

Asynchronous Event-Triggered Distributed Predictive Control for Multiagent Systems With Parameterized Synchronization Constraints

This paper proposes an asynchronous event-triggered distributed predictive control method for the cooperation of multi-agent systems with parameterized synchronization constraints. A novel event-triggering condition related to the parameterized information received from neighboring agents is derived for each agent based on the input-to-state stability (ISS) condition. In such a framework, the distributed optimization problem is solved and the parameterized information is exchanged between neighboring agents, only when the triggering condition is satisfied. In addition, the dual mode control is adopted in this work and no information will be exchanged between the agent and its neighbors when the agent enters the invariant set, reducing the computation and communication load. Moreover, the recursive feasibility of the proposed algorithm is proved, and a sufficient condition is developed to ensure the stability of the closed-loop system. Finally, numerical simulation is given to verify the effectiveness of the proposed method.

On the robustification of digital event-based stabilizers for nonlinear time-delay systems

In this paper, the robust stabilization problem by means of quantized sampled-data event-based (QSE) controllers is investigated for nonlinear systems affected by state delays and unknown disturbances. In particular, a methodology for the design of robust QSE stabilizers is provided for control-affine nonlinear systems affected by unknown actuation disturbances and unknown measurement errors. Firstly, the notion of Steepest Descent Feedback (SDF), continuous or not, is suitably revised in order to deal with the robustification of event-based controllers. Then, Input-to-State Stability (ISS) redesign methodologies are used to provide the robustification term which is added to the SDF at hand in order to arbitrarily attenuate the effects of unknown external disturbances affecting the considered control scheme. A spline approximation approach is used in order to cope with the problem of the possible non-availability in the buffer of suitable past values of the system state required for the correct application of the proposed robust QSE controller. It is proved that there exist a suitably fast sampling and an accurate quantization of the input/output channels such that: the robust QSE implementation of SDFs, continuous or not, ensures the semi-global practical stability of the related closed-loop system, regardless of the above disturbances, provided that the observation errors affects marginally the new added control term. The stabilization in the sample-and-hold sense theory is used as a tool to prove the results. The provided results include the case of non-uniform quantization of the input/output channels and the case of aperiodic sampling. Applications are presented in order to validate the results.

Input-to-state stability of stochastic complex networks based on aperiodically intermittent sampled control

This paper focuses on the problem of input-to-state stability (ISS) of stochastic complex networks (SCNs). In this paper, an aperiodically intermittent control strategy based on sampled control is designed. By means of graph theory and Lyapunov method, two stability criteria on ISS are derived in this paper. After giving the estimate between E∑i=1m|xi(t)−xi(δ(t))|2 and E∑i=1m|xi(t)|2, a stability criterion is proposed on ISS of the SCN under aperiodically intermittent sampled control (AISC). When AISC degenerates into sampled control, another stability criterion on ISS of SCN is acquired. Finally, a numerical example is utilized to illustrate the effectiveness and feasibility of the proposed results.

Event‐triggered control of Itô stochastic nonlinear delayed systems with state quantization

AbstractThe problem of event‐triggered control (ETC) of stochastic nonlinear delayed systems with state quantization is investigated. In order to reduce the communication burden and computational cost, an ETC mechanism and state quantization are introduced in the control scheme. Two configurations are considered to investigate their interaction: quantization before event‐trigger (QE) and quantization after event‐trigger (EQ), respectively. Based on this, a static event‐triggered mechanism (ETM) is designed while avoiding the Zeno phenomenon. The system allows known input‐to‐state stability (ISS) control law, followed by utilizing the Halanay inequality to achieve stabilization. In both configurations, the stabilization of the closed‐loop system is guaranteed. We show that communication times can be reduced by adjusting parameters and selecting the suitable configuration. Moreover, to further enhance resource conservation, we illustrate the feasibility of dynamic ETMs in this framework. Numerical simulation results validate the effectiveness of the proposed ETC schemes.

A Sampling Control Framework and Its Applications to Robust and Adaptive Control

In this paper, we propose a novel sampling control framework based on the emulation technique where the sampling error is regarded as an auxiliary input to the emulated system. Utilizing the supremum norm of sampling error, the design of periodic sampling and event-triggered control law renders the error dynamics bounded-input-bounded-state (BIBS), and when it is coupled with system dynamics, achieves global or semi-global stabilization. The proposed framework is then extended to tackle the stabilization problem for a system where the state of dynamic uncertainty is not available for feedback and the dynamics is subject to parameter uncertainties. The proposed framework is further extended to solve two classes of event-triggered adaptive control problems where the emulated closed-loop system does not admit an input-to-state stability (ISS) Lyapunov function. For the first class of systems with linear parameterized uncertainties, even-triggered global adaptive stabilization is achieved without the global Lipschitz condition on nonlinearities as often required in the literature. For the second class of systems with uncertainties whose bound is unknown, the event-triggered adaptive (dynamic) gain controller is designed for the first time. Finally, theoretical results are verified by three numerical examples.

Dynamic event-triggered output feedback control for networked Markovian jump systems under hybrid attacks

This paper investigates the dynamic event-triggered control problem for a networked Markovian jump system under hybrid attacks. In the concerned system, both the sensor-controller (S-C) network and the controller-actuator (C-A) network suffer from hybrid attacks, including denial-of-service (DoS) attacks and deception attacks. Two dynamic event-triggers at the controller and the sensor are designed to handle these dual-network hybrid attacks. Moreover, a unified framework is constructed to design an observer-based output feedback controller (OBOFC) which simultaneously considers hybrid attacks and dynamic event-triggering strategies (DETSs). Sufficient conditions to ensure the input-to-state stability (ISS) of the concerned system are derived. Furthermore, a set of linear matrix inequalities (LMIs) are proposed to obtain the desired observer-based feedback control gains and event-triggering parameters. A simulation example is given to further verify the effectiveness of the proposed control and event-triggered schemes.