Finite L2-gain Research Articles

Asynchronous encoder-based event-triggered control of nonlinear networked control system under DoS attacks

This paper discusses the stability of a nonlinear networked control system with limited channels under denial-of-service (DoS) attacks. The transmitted signals in both plant-to-controller and controller-to-plant channels are asynchronous, and each channel is under the threat of DoS attacks. To overcome the negative effects raised by imperfect channels and DoS attacks, the relationship among encoder structure, DoS attacks and triggering characteristics is thoroughly analyzed and the asynchronous encoder-based event-triggered control mechanisms are novelly proposed. Moreover, both encoding and decoding schemes are designed to ensure the transmission efficiency. Furthermore, the QSR-dissipativity, finite-gain L2 stability and input-feedforward output-feedback passivity of the nonlinear system are analyzed. Finally, experiments are conducted to illustrate the validity and superiority of the proposed scheme.

Dynamic output feedback control of uncertain nonlinear systems based on co-design adaptive event-triggered scheme

This paper presents a framework to design a robust dynamic output feedback (DOF) controller for a class of nonlinear systems, based on the adaptive event-triggered control (AETC) method. The considered system contains parametric uncertainty and to design the event-triggered mechanism (ETM) Finite-gain L2 stability criteria are used. In this paper, a robust adaptive event-triggered mechanism (AETM) is first designed using a pre-designed controller. Then, in a co-design approach, the AETM and the DOF controller are designed together to increase the closed-loop performance. Indeed, the matrices of the DOF controller and the sufficient conditions for the AETM are obtained simultaneously. These conditions are represented as linear matrix inequalities (LMIs) and lead to a significant increase in the update interval. Moreover, the proposed design method guarantees the stability of the closed-loop system in the presence of the proposed triggering event. Finally, to illustrate the performance of the controller three examples are simulated.

Hybrid dynamic event-triggered leader-following consensus for multi-agent systems with external disturbances

Herein, we address the leader-following consensus for multi-agent systems with a directed graph while considering external disturbances. To optimize resource utilization, we propose a hybrid dynamic event-triggered mechanism (HDETM) that minimizes the inter-agent communication and reduces the frequency of controller updates. Furthermore, regularization techniques are employed to ensure that the considered system maintains a Zeno-free behavior even in the presence of an external disturbance by guaranteeing a strictly positive inter-event time. Additionally, we propose a hybrid system framework incorporating auxiliary variables to depict both flow and jump dynamics. A Lyapunov consensus analysis is performed within this framework to verify finite-gain L2 stability. Finally, we validate the efficacy of the HDETM design method through numerical simulations.

Observer-based adaptive event-triggered control method for input-saturated systems

This paper presents an adaptive event-triggered control method for linear systems subject to input saturation. At the first, using convex hull properties, an observer-based controller is designed and then a generalized event-triggering mechanism is regarded. In order to extend more time interval between any two successive events, an adaptive event-triggered control method is also proposed. The proposed control methodology is based on finite-gain L2 stability. It is noteworthy that the proposed methods are designed in a co-design framework where the observer-based controller design with the event-triggering mechanisms are performed at the same time. Moreover, the presented adaptive approach offers more degrees of freedom as well as preserves the performance criteria high. Besides, Zeno avoidance analysis is studied by introducing a lower bound on inter-event times. Finally, the efficiency of the proposed methods is shown through a case-study numerical example.

Finite-time Boundedness of Polytopic Uncertain Systems with Guaranteed Cost Output Feedback Control

A problem of designing robust guaranteed cost reduced-order output feedback controllers for finite-time boundedness of linear time-varying uncertain systems is considered in this paper. Assuming the system parameters to lie in a polytopic set, differential linear matrix inequality (DLMI) conditions for the design of reduced-order dynamic controllers to handle worst-case exogenous disturbances are derived. The designed controller guarantees the cost on considered disturbance attenuation performance on the system to be below an upper bound, while simultaneously satisfying the conditions for finite-time boundedness and finite L2 gain. Numerical simulations are carried out to demonstrate the applicability of the proposed method in bounding the system trajectories to a predefined set.

Passivity-based boundary control with the backstepping observer for the vibration suppression of the flexible beam

In engineering applications, flexible beam vibration control is an important issue. Although several researchers have discussed controlling beam vibration, there are few strategies for implementing it in actual applications. The passivity-based boundary control for suppressing flexible beam vibration was investigated in this paper. The controller was implemented using a moving base, and the beam model was an undamped shear beam. The control law was established using the storage function in the design technique. The finite-gain L2 - stability of the feedback control system was then proven. This method dealt directly with the PDE of the beam model with no model reduction. Because of the non-collocated measurement and actuation in many applications, the backstepping observer was required for state estimation. Since the controller was implemented at the end of the beam via a moving base, the beam domain remained intact. Therefore, the method is simple to apply in applications. With the use of the finite-difference approach, the PDEs were numerically solved. The controller's performance of the proposed control scheme was demonstrated using computer simulation.

Hierarchical Robust Adaptive Control for Wind Turbines With Actuator Fault

Abstract This article solves the problem of regulating the rotor speed tracking error for wind turbines in the full-load region by an effective robust adaptive control strategy. The developed controller compensates for the uncertainty in the control input effectiveness caused by a pitch actuator fault, unmeasurable wind disturbance, and nonlinearity in the model. Wind turbines have multilayer structures such that the high-level structure is nonlinearly coupled through an aggregation of the low-level control authorities. Hence, the control design is divided into two stages. First, an L2 controller is designed to attenuate the influence of wind disturbance fluctuations on the rotor speed. Then, in the low-level layer, a controller is designed using a proposed adaptation mechanism to compensate for actuator faults. The theoretical results show that the closed-loop equilibrium point of the regulated rotor speed tracking error dynamics in the high level is finite-gain L2 stable, and the closed-loop error dynamics in the low level is globally asymptotically stable. Simulation results show that the developed controller significantly reduces the root mean square of the rotor speed error compared to some well-known works, despite the largely fluctuating wind disturbance, and the time-varying uncertainty in the control input effectiveness.

Nonlinear Robust Control on Yaw Motion of a Variable-Speed Unmanned Aerial Helicopter under Multi-Source Disturbances

This paper studies the multi-source disturbances attenuation problem on the yaw motion of unmanned aerial helicopter with a variable-speed rotor. The yaw motion subsystem dominated by an electrically-driven tail rotor is firstly introduced, and its trajectory accuracy requires particularly close attention. To this end, we establish a fourth-order yaw error dynamic equation; subsequently, a nonlinear robust control scheme based on optimal H∞ principle is developed, consisting of laws of virtual functions, parameter estimation and a compensation signal. The novelty of this scheme lies in unifying the techniques to deal with the uncertain parameters, noise perturbations, actuator output fault and external airflow turbulence into a simple framework. Stability analysis guarantees that the yaw closed-loop system has the predefined performance of disturbance suppression in the sense of a finite L2-gain. Comparison results with the extended state observer based backstepping controller verify the effectiveness and superior performance of proposed scheme in an aircraft prototype.

Active Event-Triggered Control for Nonlinear Networked Control Systems With Communication Constraints.

In this paper, a novel reference input and hysteresis quantizer-based active event-triggered control (RIHQAETC) scheme is proposed for nonlinear networked control systems with quantizer, networked induced delay, and packet dropout. Different from the traditional methods, such a design method is constructed involving the structure of the hysteresis quantizer. In view of the network induced delay and the potential packet dropout, our RIHQAETC method is designed to actively compensate the negative effects caused by these two issues. The corresponding coder and decoder are also excogitated on account of the potential packet dropout based on the proposed triggering mechanism. Furthermore, the transmission of the important triggering information can be ensured as well as the finite-gain L2 stability performance. It is demonstrated by an example that our RIHQAETC method presents a more balanced updating frequency between the plant and the controller output sides and reduces the number of total triggering.

Robust stability analysis of incommensurate fractional-order systems with time-varying interval uncertainties

This paper focuses on the stability analysis of the incommensurate fractional-order systems describing by the pseudo-state-space form in the presence of interval uncertainties. By using the generalized small-gain theorem and the properties of M-matrices, a condition is achieved for robust finite-gain L2 stability of these systems. In addition, satisfying this condition ensures the asymptotic stability of uncertain fractional-order systems, based on the Caputo definition. Unlike the methods which are based on the eigenvalue argument checking, the proposed robust stability analysis method can be used for systems with irrational fractional orders and time-varying uncertainties. Compared with the Lyapunov based methods, the conservatism due to the lack of relation between stability condition and fractional-order of the system does not occur in the proposed method. An illustrative example is presented to confirm this method does not lead to conservatism generated by reformulation of the interval uncertainty, which is the basis of the commonly used methods in the literature. Finally, the suggested method is employed for robust stability checking of the Sallen–Key filter including fractional capacitors with irrational orders.

On the Converse Passivity Theorems for LTI Systems

Converse passivity theorems are established for finite-dimensional (FD) linear time-invariant (LTI) systems. Consider an FD LTI system G1 interconnected in positive feedback with another FD LTI system G2. It is demonstrated that when the closed-loop system is (robustly) stable (in the sense of finite L2 gain) for arbitrary strictly passive G2, then -G1 must necessarily be passive. It is also demonstrated that when the closed-loop system is uniformly stable across the set of arbitrary passive G2, then -G1 must necessarily be strictly passive. The proofs are constructive; i.e., we show how to find a de-stabilizing FD LTI G2 when G1 violates the necessity condition of stability.

An integral sliding mode approach to distributed control of coupled networks with measurement Quantization

This paper is concerned with the distributed sliding mode control problem of complex networks under quantization mechanism. The complex networked control system is considered with inner coupling, uncertainties and quantized measurements among the agents. The quantizer, which is adopted as a logarithmic one, is designed to be on the sensor unit to implement the digital communication. In order to avoid the discontinuity of the sliding mode control law, namely, the sliding surface, an adaptive filter is utilized. Based on the filtered signal, an integral sliding-mode manifold is designed for each agent. A series of dynamic sliding mode control laws are synthesized to achieve the exponential reaching onto the sliding surface within a finite time for the whole networked system. The resulting sliding motion is analyzed using the Lyapunov functional approach, and a finite-gain L2 stability criterion is established. Finally, the effectiveness of the designed distributed sliding mode control scheme is illustrated with some simulation results.

A robust adaptive event-triggered control scheme for dynamic output-feedback systems

In this paper, a new output-based adaptive event-triggered control (AETC) method is introduced for a general class of nonlinear systems. A crucial aspect of the AETC method is to design an event-triggering mechanism (ETM) determining when the sampling operation should be done. The proposed ETM, which is derived from the finite-gain L2 stability condition, reduces the number of updating operations while the performance of the closed-loop system is maintained. Thanks to the Lipschitz property, the avoidance of Zeno behavior is also guaranteed by introducing a positive lower bound on the inter-event times. This lower bound is obtained by solving a set of proposed ordinary differential equations. In addition, the proposed method is developed into robust control of uncertain linear time invariant (LTI) systems through some matrix inequalities (such as linear matrix inequalities (LMIs)). Finally, several numerical simulations are presented to demonstrate the ability of the proposed method to achieve greater average inter-event times and to preserve the system performance rather than other references.

On the converse of the passivity and small-gain theorems for input–output maps

We prove the following converse of the passivity theorem. Consider a causal system given by a sum of a linear time-invariant and a passive linear time-varying input–output map. Then, in order to guarantee stability (in the sense of finite L2-gain) of the feedback interconnection of the system with an arbitrary nonlinear output strictly passive system, the given system must itself be output strictly passive. The proof is based on the S-procedure lossless theorem. We discuss the importance of this result for the control of systems interacting with an output strictly passive, but otherwise completely unknown, environment. Similarly, we prove the necessity of the small-gain condition for closed-loop stability of certain time-varying systems, extending the well-known necessity result in linear robust control.

Sampled-data distributed [formula omitted] control of a class of 1-D parabolic systems under spatially point measurements

This paper considers the sampled-data distributed H∞ control problem for 1-D semilinear transport reaction equations with external disturbances. It is assumed that a finite number of point spatial state measurements are available. A Razumikhin-type approach is developed for stability and L2-gain analysis of the closed-loop system. In contrast to Halanay׳s inequality based approach, the proposed Razumikhin-type approach not only provides a subtle decay estimate of the selected Lyapunov functional, but also guarantees the H∞ performance index to be negative if certain conditions are satisfied. By introducing a time-dependent Lyapunov functional combined with the use of Wirtinger׳s inequality, sufficient conditions for the internal exponential stability and finite L2-gain are derived in terms of linear matrix inequalities. The obtained conditions establish a quantitative relation among the upper bounds on the spatial sampling intervals and the time sampling intervals, and L2-gain. Two numerical examples are provided to illustrate the usefulness of the proposed theoretical results.

H∞ filter design for nonlinear systems with quantised measurements in finite frequency domain

ABSTRACTThis paper deals with the problem of finite frequency (FF) H∞ full-order fuzzy filter design for nonlinear discrete-time systems with quantised measurements, described by Takagi–Sugeno models. The measured signals are assumed to be quantised with a logarithmic quantiser. Using a fuzzy-basis-dependent Lyapunov function, the finite frequency ℓ2 gain definition, the generalised S-procedure, and Finsler's lemma, a set of sufficient conditions are established in terms of matrix inequalities, ensuring that the filtering error system is stable and the H∞ attenuation level, from disturbance to the estimation error, is smaller than a given value over a prescribed finite frequency domain of the external disturbances. With the aid of Finsler's lemma, a large number of slack variables are introduced to the design conditions, which provides extra degrees of freedom in optimising the guaranteed H∞ performance. This directly leads to performance improvement and reduction of conservatism. Finally, we give a simulation example to demonstrate the efficiency of the proposed design method, and we show that a lower H∞ attenuation level can be obtained by our developed approach in comparison with another result in the literature.

Stability and stabilisation of reset control systems with uncertain output matrix

The stability analysis of reset control systems is challenging when reset time instants are uncertain, because such uncertainties may damage or even destabilise the system. This study considers reset control systems with uncertain output matrix, and presents sufficient conditions for the quadratic stability and finite gain ℒ2 stability of the closed-loop reset systems. Then, the results are extended to piecewise quadratic stability, which is much less conservative. The design of the reset controller is also discussed. All the results are given as linear matrix inequalities by using a lemma about multi-convex function. Several examples are given to show the effectiveness of the obtained results.

Reset observers for linear time-varying delay systems: Delay-dependent approach

Reset observer consists of linear observer and a reset element, when the input and output of the reset element have opposite signs, the state of the reset element is reset. This paper considers using reset observer to estimate states of linear time-varying delay systems. The delay-dependent approach is used for stability analysis, and global asymptotic stability and finite gain L2 stability are obtained. Moreover, less conservative piecewise Lyapunov stability conditions are developed based on partition of the state space. All the obtained results are given in the form of linear matrix inequalities (LMIs). Simulation example shows the effectiveness of the obtained results.

Stochastic stabilization and induced [formula omitted]-gain for discrete-time Markov jump Lur’e systems with control saturation

This paper addresses the problem of control synthesis for locally stabilizing and minimizing the finite ℓ2 gain for discrete-time Markov jump Lur’e systems with control saturation and exogenous ℓ2-type disturbance. We consider that the jump parameter defining the active mode for both the linear and the cone-bounded nonlinearity is governed by a finite state homogeneous Markov chain. The local stochastic stability is established by exploiting the invariant probability measure of the Markov chain to define the level set of the expected value of the stochastic Lur’e type Lyapunov function. Optimization problems for maximizing our estimate of the domain of stochastic stability and minimizing the induced ℓ2 gain with respect to exogenous disturbances are presented subject to LMI constraints. The paper is concluded with an academic example.

On relationships among passivity, positive realness, and dissipativity in linear systems

The notions of passivity and positive realness are fundamental concepts in classical control theory, but the use of the terms has varied. For LTI systems, these two concepts capture the same essential property of dynamical systems, that is, a system with this property does not generate its own energy but only stores and dissipates energy supplied by the environment. This paper summarizes the connection between these two concepts for continuous and discrete time LTI systems. Beyond that, relationships are provided between classes of strictly passive systems and classes of positive real systems. The more general framework of dissipativity is introduced to connect passivity and positive realness and also to survey other energy-based results. The frameworks of passivity indices and conic systems are discussed to connect to passivity and dissipativity. After surveying relevant existing results, some clarifying results are presented. These involve connections between classes of passive systems and finite-gain L2 stability as well as asymptotic stability. Additional results are given to clarify some of the more subtle conditions between classes of these systems and stability results. This paper surveys existing connections between classes of passive and positive real systems and provides results that clarify more subtle connections between these concepts.