Input-to-state Stability Research Articles

Resilient Event‐Triggered Control for Switched Systems With Reconstructed Switching Signals Under DoS Attacks

ABSTRACTIn this article, the resilient event‐triggered control issue for switched linear systems with the bounded disturbance is explored under the aperiodic denial‐of‐service (DoS) attacks. Unlike the discussions on asynchronous behavior caused by network transmission/DoS attacks, configure a copy of predictor at controller module to avert the negative impacts of asynchronous switching. Subsequently, by establishing a resilient event‐triggered strategy (RETS) to eliminate invalid sampling during DoS attacks intervals, the waste of network resources is reduced. Besides, a sufficient condition is derived to ensure the input‐to‐state stability (ISS) for the close‐loop switched systems under DoS attacks. The results indicate that the switched systems can resist a certain degree of DoS attacks under the average dwell time (ADT) constrained by DoS attacks frequency and duration. In addition, Zeno behavior is eliminated by calculating the lower bound of the triggering intervals. Finally, the availability of theoretical approach is verified through a numerical simulation.

Assessing Stability in Discrete-Time Systems Impacted by Interference and State Delays: An Approach Using ISS

In this study, we introduce a criterion for addressing the input to state stability (ISS) problem inherent in nonlinear discrete systems featuring state delay, saturation overflow (SO), and external interference (EI). This paper proposes three novel theorems by employing the Lyapunov function to assure the stability of the targeted discrete time systems (DTS) under complex conditions such as state delay, SO, EI and the first theorem utilizes system information more effectively by considering EI, state delay and SO, the second theorem focuses on asymptotic stability (AS) analysis of the system when EIs are zero, the third theorem proposes the system is AS when state delays are zero. These theorems impose fewer constrains additionally these conditions are demonstrated to be more relaxed and computationally less intensive to existing criteria. The advantage of the suggested technique is proven through three numerical examples and comparison research.

Active disturbance rejection control for systems with uncertainties and noise using super twisting differentiator-based event-triggered ESO

This paper focuses on the noise suppression issue of high-gain extended state observer (ESO) for systems with uncertainty and unknown measurement noise in the active disturbance rejection control (ADRC) paradigm. A special combination of super twisting differentiator (STD) and event-triggered ESO is devised with a designed event-triggered mechanism. Specially, the proposed STD-ETESO incorporates a finite-time switching strategy, which improves the poor transient performance of the STD acting as a pre-filter to prepare relatively smooth signals for the ESO. The locally asymptotic boundedness of the estimation error can be guaranteed by the Input-state-stability (ISS) and existing research for the STD. The effectiveness of the proposed method is validated by a general example and a practical motion control system. Different integral criteria is introduced to evaluate the overall tracking accuracy and energy usage for comparison with existing different ESOs, which reveals the superiority of the proposed STD-ETESO in noise attenuation and disturbance rejection.

Improving extensions for the global uniform asymptotic stability of continuous-time nonlinear systems

This paper considers the classical problems of global asymptotic stability (GAS) of nonlinear autonomous (time-invariant) systems and global uniform asymptotic stability (GUAS) of nonlinear non-autonomous (time-varying) systems. By imposing new conditions on the Lyapunov function and its derivative, the state convergence to the origin from any initial condition with bounded norm in the classical setting is extended to the initial conditions with unbounded norms in the present work. The proposed new notions of stability are called extended global asymptotic stability (EGAS) and extended global uniform asymptotic stability (EGUAS) in this paper. The proposed Lyapunov-based criteria yield the global asymptotic stability of the origin and fixed-time/predefined-time attractiveness of any selected neighbourhood of the origin. The result is that the dynamical behaviour of the state trajectories from the convergence time point of view is improved considerably. The relationship between the smoothness and input-to-state stability (ISS) properties is also studied from a quantitative point of view. Under some new sufficient conditions, it is shown that dynamical systems with smaller Lipschitz constants represent smaller ultimate bounds, and as a result, are more robust. The desirable dynamical behaviour and robustness property of the proposed stability notion makes it comparable with the finite/fixed/predefined/prescribed (exact) stable systems that are naturally non-Lipschitz at the origin. Numerical results illustrate the effectiveness of the proposed theoretical results.

Input-to-state stabilization of discrete-time delayed fuzzy systems via aperiodically intermittent control

This paper studies input-to-state stabilization of delayed discrete-time Takagi–Sugeno (T–S) fuzzy systems via aperiodically intermittent control. We first consider aperiodically intermittent time-triggered control, where we present sufficient conditions via the mathematical induction under the hypotheses of the quasiperiodicity condition. Based on the derived sufficient conditions, we apply a Lyapunov–Krasovskii (L–K) method together with the descriptor method to derive the explicit linear matrix inequalities (LMIs) that ensure the exponential stability and input-to-state stability (ISS), and show the existence of the aperiodically intermittent time-triggered controller that leads to efficient results with much less numerical complexity. We next consider aperiodically intermittent dynamic event-triggered control with an additional parameter that is larger than one. This strategy allows that the introduced dynamical variable does not remain constant but increases during the control rest interval. As a result, the proposed dynamic event-triggered strategy leads to a smaller number of sent signals than that for the case of the additional parameter which equals to one. Finally, numerical examples including a practical inverted pendulum on a cart are presented to verify the validity of the proposed method.

Input-to-State Stability of Switched Network Control Systems Under Unknown Deception Attacks.

This article focuses on the stability issue of switched network control systems (SNCSs) under deception attacks described by a Bernoulli process with unknown probability distribution. The false information in deception attacks is unknown but bounded and may be state dependent or state independent. By means of the input-to-state stability (ISS) tool and the convex combination method, an improved lemma is first developed for SNCSs, which facilitates the derivations of our results. After that, some attack-independent sufficient conditions for the ISS of SNCSs are obtained for mode-dependent average dwell time switching and stochastic switching, respectively. Different from existing results, the concerned switching contributes to the stability of SNCSs, which benefits the ISS performance of SNCSs even though the unknown deception attacks cause all subsystems to be non-ISS. The proposed results provide an effective solution with strong robustness to deal with unknown deception attacks or denial-of-service attacks.

Improved delay-dependent stability analysis of digital filters with generalized overflow arithmetic

This paper introduces a new set of conditions that establish Input-to-State Stability (ISS) for digital filters with external disturbance input and time-varying delays, all within the context of generalized overflow arithmetic. A unique augmented Lyapunov function and a novel summation inequality are applied to formulate a new criterion for ISS. This criterion assesses the ISS of digital filters in the presence of external disturbance, enabling the identification of asymptotic stability even in the absence of such disturbance. The criteria are developed using linear matrix inequalities (LMIs). The efficacy of the results is demonstrated through three numerical examples, highlighting that the proposed criteria are less conservative than some recent results.

On robustification of digital event-based controllers for control-affine nonlinear systems

In this paper, the robust digital stabilization problem of nonlinear systems is investigated. In particular, a methodology for the design of robust quantized sampled-data stabilizers updated via an event-triggered mechanism is provided for time-varying control-affine nonlinear systems affected by actuation disturbances and measurement noises. The notion of time-varying steepest descent feedback (TSDF), continuous or not, and the Input-to-State Stability (ISS) redesign methodology are used for the development of the proposed robust event-based digital controller. Under the assumption that the actuation disturbances and measurement noises are bounded with a-priori known bounds and that the amplitude of the measurement noises satisfies a certain condition related to the new added robustification term, the following result is proved: there exist a suitably fast sampling and an accurate quantization of the input/output channels such that the digital implementation of robustified TSDF controllers, updated through a proposed event-triggered mechanism, ensures semi-global practical stability of the related closed-loop system regardless of the above uncertainties. In the methodology here proposed, time-varying sampling periods and the non-uniform quantization of the input/output channels are allowed. Moreover, the theory here developed includes the analysis of the intersampling system behaviour. Possible discontinuities in the function describing the TSDF at hand are also managed. The provided results are validated through a numerical example.

Event-Triggered Control of Switched Nonlinear Time-Delay Systems With Asynchronous Switching.

This article investigates the event-triggered switching control (ETSC) of switched nonlinear time-delay systems (SNTDSs) with asynchronous switching. First, we study the input-to-state stability (ISS) and integral ISS (iISS) for SNTDSs with asynchronous switching, where switching instants are generated based on the designed event-triggered mechanism. Among existing works on the ETSC, systems behavior at event-triggered instants is neglected. In fact, whenever an event is triggered, the systems mode will jump suddenly such that a switch is imposed to the systems, leading to the change of subsystems. Moreover, asynchronous switching behavior may occur between the actual subsystem and its corresponding controller. These facts bring great challenges for the event-triggered mechanism design and ISS analysis. To tackle these problems, a new Lyapunov-based event-triggered mechanism with adjustable parameters is designed to establish the relationship between systems switches and event triggers, and exclude the Zeno phenomenon. The analysis of the asynchronous switching behavior can be implemented and some ISS and iISS criteria of SNTDSs are derived utilizing the merging switching technique. Finally, two numerical examples, including a practical stirred tank reactor system, are presented to show the validity of the proposed methods.

Semiglobal Exponential Stability for Dual-Quaternion-Based Rigid-Body Tracking Control

Semi-Global Exponential Stability (SGES) is proven for the combined attitude and position rigid-body motion tracking problem, presenting a significant upgrade compared to previously proposed controllers which can only guarantee asymptotic stability. Dual quaternions are used to jointly represent the rotational and translational tracking error dynamics of the rigid body. A novel nonlinear feedback tracking controller is proposed, and a Lyapunov-based analysis is provided to prove SGES of the closed-loop dynamics. The analysis does not place any restrictions on the reference trajectory or the feedback gains. This stronger SGES result aids in further analyzing the robustness of the rigid-body system by establishing input-to-state stability (ISS) in the presence of time-varying additive and bounded external disturbances. Motivated by the fact that, in many aerospace applications, stringent adherence to safety constraints such as approach path and input constraints is critical for overall mission success, a framework for safe control of spacecraft is presented that combines the proposed feedback controller with control barrier functions. Numerical simulations are provided to verify the SGES and ISS results and also showcase the efficacy of the proposed nonlinear feedback controller in several nontrivial scenarios, including trajectory tracking, transposition and docking, flip maneuvers, collision avoidance, and rendezvous.

Cascade/feedback interconnections of prescribed-time input-to-state stable systems

Achieving control objectives (e.g., stabilization or convergence of tracking error to zero, input-to-state stabilization) in “prescribed time” has attracted significant research interest in recent years. In this paper, we consider cascade and feedback interconnections of prescribed-time input-to-state stable (ISS) systems and study conditions under which the overall states of such interconnected systems also converge to the origin in the prescribed time interval. We show that these conditions are intrinsically related to properties of the time-varying “blow-up” functions that are central to prescribed-time control designs. We also generalize the results to interconnections of an arbitrary number of systems. As an illustrative example, we consider an interconnection of two uncertain systems that are prescribed-time stabilized using two different control design methods and show that the two separate controllers can be put together to achieve prescribed-time stability of the interconnected system.

Input‐to‐state stability of impulsive stochastic systems with state‐dependent impulses and regime‐switching

AbstractThis article introduces a unified criterion for input‐to‐state stability (ISS), integral input‐to‐state stability (iISS) and ‐input‐to‐state stability (‐ISS) of impulsive stochastic system with switching. The criterion demonstrates that the premise of a switching‐impulse system to achieve three types of ISS is that a mutually constraining relationship between switching, impulse and continuous dynamics needs to be satisfied. Furthermore, using it we know that switching can stabilize a system containing stabilizing factors by affecting both continuous dynamics and impulses, that switching itself is one of the factors in system instability, and that impulses have a dual effect on the stability of the system. The coefficients of the upper bound of Lyapunov functional differential operators are time‐varying functions and the impulses contain stable and unstable impulses, including the case of constants, which advances and improves the existing results. Finally, an example and its simulation results are given to verify the validity of theoretical analysis.

Intermittent event‐triggered control for input‐to‐state stability of stochastic systems

AbstractIn this article, we investigate the input‐to‐state stability (ISS) of stochastic systems via intermittent event‐triggered control. The control update sequence during the control intervals is determined through an event‐triggered mechanism (ETM), where the periodic ETM and continuous ETM are considered separately. For the continuous ETM, a positive minimum inter‐execution time is ensured by adding waiting time, which avoids Zeno behavior. For the periodic ETM, with the help of Halanay‐like inequality, the maximum allowable bound of the sampling period is given. The number of control updates is further reduced by adding a dynamic term. In addition, sufficient conditions for ISS in stochastic systems are proposed by designing an auxiliary timer and applying the Lyapunov method. Finally, two numerical examples are presented to verify the validity of the results.

Hybrid control for non-overshooting step responses of linear systems

This paper focuses on the problem of applying hybrid control to overcome overshoot performance limitations of linear time-invariant (LTI) systems, and puts forward a systematic method for the joint design of a hybrid controller. By modeling the whole closed-loop system in the framework of a hybrid system, an input-to-state stable (ISS) criterion for the system is established, and on the basis of this, conditions for non-overshooting step responses are obtained. In the proposed hybrid controller, apart from its input and output information, state information of the LTI plant and a basic LTI controller is used to design flow and jump sets. The advantage is that when the trigger matrix of flow and jump sets is unknown, it can be designed conveniently. Based on the conditions, the hybrid controller synthesis is formulated in linear matrix inequalities and the algorithm of solving controller matrices and the triggering matrix is given. In addition, the design method of the hybrid controller with a certain triggering matrix is derived. The effectiveness and reliability of the obtained results are demonstrated through a numerical example.

Input-to-state stability of discrete-time impulsive switched delayed systems with delay-dependent impulse under two asynchronous cases

This paper studies a class of discrete-time impulsive switched delayed systems with delay-dependent impulses, aiming to solving the input-to-state stability (ISS) problem in the case of asynchronous switching signal between subsystem and controller and asynchrony of switching signals and impulsive signals. Among them, the delay effect is handled by a new Lyapunov-Krasovskii function divided into a delay-dependent part and a delay-independent part. In contrast to admissible edge-dependent average dwell time (AED-ADT) methods that address switching signals, we propose admissible edge-dependent average impulsive interval (AED-AII) to deal with delayed impulses, thereby establishing the relationship between these methods and the decay rate. Meanwhile, a stabilizing controller for discrete impulsive switched linear delayed systems is proposed and the minimum average dwell time and controller gain are obtained. Compared with the previous work, the parameters of Lyapunov functional relation depend on the directed edges; the operation of subsystem is divided into asynchronous time and synchronous time, which are less conservative; the combination of AED-ADT and AED-AII can be applied to a wider range of impulsive switched systems. Finally, two examples are given to show the effectiveness of the results.

Nonlinear sparse variational Bayesian learning based model predictive control with application to PEMFC temperature control

The accuracy of the underlying model predictions is crucial for the success of model predictive control (MPC) applications. If the model is unable to accurately analyze the dynamics of the controlled system, the performance and stability guarantees provided by MPC may not be achieved. Learning-based MPC can learn models from data, improving the applicability and reliability of MPC. This study develops a nonlinear sparse variational Bayesian learning based MPC (NSVB-MPC) for nonlinear systems, where the model is learned by the developed NSVB method. Variational inference is used by NSVB-MPC to assess the predictive accuracy and make the necessary corrections to quantify system uncertainty. The suggested approach ensures input-to-state stability (ISS) and the feasibility of recursive constraints in accordance with the concept of an invariant terminal region. Finally, a PEMFC temperature control model experiment confirms the effectiveness of the NSVB-MPC method.

Characterization of multi-channel denial-of-service

The embedded closed-loop in integrated systems can be compromised when attackers execute a successful malicious attack. Hence, over the past decade, interest in enhancing the safety of Cyber-Physical Systems (CPSs) has risen. This article examines the resilient control problem for CPSs with numerous transmission channels under Denial-of-Service (DoS). To begin with, a partial observer technique is developed in response to the Multi-Channel DoS (MCDoS) condition. Secondly, the changing frequency of MCDoS is characterized while maintaining the Input-to-State Stability (ISS) of the closed-loop system. Next, an event-based control strategy is developed to address Full-Scale DoS (FSDoS). Finally, the optimal control parameters are designed to make the system resilient against maximum MCDoS changing frequency.

Small-disturbance input-to-state stability of perturbed gradient flows: Applications to LQR problem

This paper studies the effect of perturbations on the gradient flow of a general nonlinear programming problem, where the perturbation may arise from inaccurate gradient estimation in the setting of data-driven optimization. Under suitable conditions on the objective function, the perturbed gradient flow is shown to be small-disturbance input-to-state stable (ISS), which implies that, in the presence of a small-enough perturbation, the trajectories of the perturbed gradient flow must eventually enter a small neighborhood of the optimum. This work was motivated by the question of robustness of direct methods for the linear quadratic regulator problem, and specifically the analysis of the effect of perturbations caused by gradient estimation or round-off errors in policy optimization. We show small-disturbance ISS for three of the most common optimization algorithms: standard gradient flow, natural gradient flow, and Newton gradient flow.

Adaptive neural event‐triggered near‐optimal control for affined uncertain nonlinear discrete‐time system

AbstractA novel event‐triggered heuristic dynamic programming (HDP) algorithm is proposed for the near‐optimal control of uncertain discrete‐time nonlinear input‐affine systems. Based on input‐to‐state stability (ISS) analysis, a new event‐triggered mechanism (ETM) is designed. Under constant coefficients, a Lipschitz‐like assumption that forms the basis of the event‐triggering condition is considered to be conservative. To further reduce the conservativeness of the triggering condition and enlarge the average interevent time, an adaptive threshold parameter is utilized in the proposed ETM. In the HDP algorithm framework, model, critic, and action network are adopted to achieve state estimation, approximation to the optimal cost function, and solution to Hamilton–Jacobian–Bellman (HJB) equation. Under the proposed event‐triggered HDP algorithm, the closed system is proved to possess semiglobal uniform ultimate boundedness (SGUUB). Finally, by conducting simulation, it shows that on the premise of satisfying control performance, the event‐triggered strategy can realize reduction on the updating frequency of the controller.

Partial‐state feedback adaptive stabilization for a class of uncertain nonholonomic systems

SummaryIn this paper, we investigate the global adaptive stabilization problem via partial‐state feedback for a class of uncertain chained‐form nonholonomic systems with the dynamic uncertainty and nonlinear parameterization. The notions of Sontag's input‐to‐state stability (ISS) and ISS‐Lyapunov function, together with the changing supply rates technique are used to overcome the dynamic uncertainty. The nonlinear parameterization is well treated with the aid of the parameter separation technique. The discontinuous input‐to‐state scaling technique is employed in this procedure to derive the global stabilization controllers. Additionally, we develop a switching adaptive control strategy in order to get around the smooth stabilization burden associated with nonholonomic systems. The simulation results illustrate the efficacy of the presented algorithm.