Incremental Quadratic Constraints Research Articles

Stubborn State and Disturbance Observer Co‐Design for Nonlinear Descriptor Systems With δQC$$ \delta \mathrm{QC} $$ via a Dynamic Event‐Triggered Mechanism

ABSTRACTThis article studies the state and disturbance simultaneous estimation problem for a class of nonlinear descriptor systems with using a dynamic event‐triggered mechanism. refers to incremental quadratic constraints, which can provide a unified description of many types of common nonlinear functions. To reduce the negative impact of measurement outliers on the identification estimation, a stubborn state and disturbance observer co‐design scheme is proposed for the first time by embedding dynamic saturation output estimation errors. Meanwhile, a dynamic event‐triggered mechanism is introduced to avoid the need for continuously available output information, which can reduce the pressure on communication resources. By constructing a Lyapunov function, existence conditions of the stubborn state and disturbance observer are obtained in the form of a convex optimization problem so that the error estimation maintains an acceptable estimation performance. Finally, simulation examples illustrate the universality and stubbornness of the proposed observer.

Observer-based output feedback control for switched T–S fuzzy systems with local nonlinear segments by using past output measurements

This paper researches the observer-based exponential stabilization problem for switched Takagi–Sugeno (T–S) fuzzy systems with unmeasurable premise variables and local nonlinearities. The local nonlinear parts that satisfy the incremental quadratic constraint exist in the systems and observers, which have the merit of being able to contain many common nonlinearities in a unified framework. Because the premise variables are not measurable, the performance of the observers in estimation is critical. Different from existing observer-based control strategies, the strategy of this paper not only depends on the current outputs of the systems but also relates to the past outputs of the systems which can provide a way to improve performance. In order to tackle the difficulties caused by introducing the past outputs and design a set of non-fragile fuzzy controllers to stabilize the systems, a new augmented state vector is constructed. Then, the conditions for designing the observer-based controller are derived by using auxiliary scalars, projection Lemma and S-procedure. Finally, the effectiveness of the control strategy obtained in this paper is proved by two examples.

The Event-Triggered Resilient Control of Discrete-Time Nonlinear Semi-Markov Jump Systems Based on Incremental Quadratic Constraints

This paper explores resilient control problems for discrete-time nonlinear semi-Markov jump systems characterized by incremental quadratic constraints. Considering the system’s uncertainties and external environmental factors, mode-dependent resilient controllers are developed to ensure the system’s mean-square stability. A proposed event-triggering mechanism is suggested to alleviate the communication burden within the system. Additionally, the system’s nonlinearity is characterized by using incremental quadratic constraints to derive a less conservative feasible solution. Sufficient conditions for the system’s mean-square stability are established by employing the Lyapunov stability theory. Finally, a numerical simulation example is given to prove the conclusion’s validity.

Group consensus of nonlinear semi-Markov multi-agent systems by a quantity limited controller

This paper solves the group consensus problem of incremental quadratic constraints nonlinear multi-agent systems with semi-Markov switching parameters via a quantity limited controller. The quantity limited controller is designed according to the stationary probability distribution of the system modes, and the number of controllers can be selected from 1 to the number of system modes. Therefore, the controller can be applied in cases where there is a mismatch between the number of system modes and the number of controllers. Next, the more general incremental quadratic constraint is used to handle the nonlinear terms. Finally, in the simulation section, the method of adding topology links is used to implement external equitable partitions of arbitrary topologies, and the validity of the proposed method is verified by a spring damping system.

Adaptive observer design for systems with incremental quadratic constraints and nonlinear outputs – application to chaos synchronization

Adaptive observer design for systems with incremental quadratic constraints and nonlinear outputs – application to chaos synchronization

Consensus control of nonlinear multi‐agent systems with semi‐Markov switching topology and incremental quadratic constraints

AbstractThe consensus problem of nonlinear multi‐agent systems with incremental quadratic constraints and semi‐Markov switching topology is discussed in this article. In order to simulate the delay of the communication network in the actual system, the nonlinear function, which contains the delay term is considered in this article. The control protocol is designed based on the dynamics of the adjacent agent states and the desired agent states. Through the use of the characteristics of the Kronecker product, the distributed system is converted to a centralized system. It is worth mentioning that for saving computational resources, the slack variable method is used to deal with the time‐varying transition rate, and the sufficient condition is expressed by the standard linear matrix inequality. Finally, the effectiveness of the control protocol is demonstrated by numerical simulations.

Robust state and sensor fault estimation for switched nonlinear systems based on asynchronous switched fuzzy observers

SummaryThis article aims to address state and sensor fault estimation issue for a class of continuous‐time nonlinear switched systems, modelled as Takagi‐Sugeno (T‐S) models with nonlinear consequent parts and subject to norm bounded disturbances. This modelling approach helps to prevent Unmeasured Premise Variables (UPVs) problem. The primary contribution of this study consists of proposing robust asynchronous switched observers to simultaneously estimate state and sensor faults under state‐dependent switching. Based on a candidate multiple Lyapunov function, the design of the proposed observer is formulated in terms of Linear Matrix Inequalities (LMIs) conditions. These conditions are dwell‐time‐independent and less conservative compared with similar previous studies, thanks to some usual relaxation techniques and the incremental quadratic constraints applied on unmeasured nonlinear consequent parts. Another contribution consists to perform the estimation of the attraction domain of the estimation error using an optimization procedure. In order to illustrate the effectiveness of the proposed design approach, two simulation examples are considered. The first one concerns the conservatism reduction brought by our proposal compared with previous studies, while the second one is dedicated to show through an illustrative example the performance of the proposed switched T‐S observers under mismatching switching laws.

State and adaptive disturbance observer co‐design for incrementally quadratic nonlinear descriptor systems with nonlinear outputs

AbstractThe problem of designing state and adaptive disturbance observers for a class of nonlinear descriptor systems with the disturbance generated by an unknown exogenous system is addressed in this paper. Especially, the nonlinear terms satisfy incremental quadratic constraints parameterized by a bunch of multiplier matrices, which can represent various classes of nonlinearities. For three different cases in the output equation, the state and adaptive disturbance observers are proposed. Some sufficient conditions formulated in terms of linear matrix inequalities and algebraic constraints are derived to guarantee that state and disturbance error systems, simultaneously, are asymptotically stable with performance level. The availability of proposed observers is validated by two practical examples.

Finite-time stability of switched stochastic systems with incremental quadratic constraints

Finite-time stability of switched stochastic systems with incremental quadratic constraints

Composite event‐triggered H∞ control for nonlinear switched singular systems with a mode‐dependent triggering strategy

SummaryThis paper considers the event‐triggered control problem of nonlinear switched singular systems (NSSSs) with incremental quadratic constraints (IQCs) via a mode‐dependent hybrid triggering strategy. First, impulsive control is introduced to reduce the effect of impulse caused by switching, and the closed‐loop system is modeled as an impulsive NSSS. Then, a novel mode‐dependent hybrid event‐triggering strategy (ETS) consisting of disturbance‐influenced ETS and Lyapunov‐function‐dependent ETS is constructed to avoid Zeno behavior and asynchronous phenomena. Based on this ETS and admissible edge‐dependent average dwell time (AED‐ADT) method, some new sufficient conditions in terms of linear matrix inequalities (LMIs) are derived to ensure that the closed‐loop system is regular, impulse‐free, has a unique solution, and is globally uniformly asymptotically stable (GUAS) with a weighted performance. Further, Zeno behavior is excluded by calculating the minimum lower bound of inter‐event time. Finally, a numerical example and a practical application are proposed to demonstrate the validity of the results.

Design of asynchronous switched Takagi–Sugeno model‐based H∞ filters with nonlinear consequent parts for switched nonlinear systems

SummaryThis paper investigates the design of asynchronous switched nonlinear filters for a class of continuous‐time nonlinear switched systems with mismatching switching laws and norm‐bounded disturbances. In this context, the switched nonlinear system is modelled as a switched Takagi–Sugeno (T‐S) model with nonlinear consequent parts, that is, where unmeasured nonlinear terms are kept in the nonlinear consequent parts in order to circumvent the occurrence of unmeasured premise variables, which is usually faced in conventional T‐S modeling without nonlinear consequent parts. In this framework, asynchronous switched T‐S filters with unmeasured nonlinear consequent parts are proposed to estimate unmeasured and/or disturbed system's outputs, even when the filter's switching law mismatches the switched nonlinear system's one, which can be in practice unknown or imprecisely measured. Based on a candidate multiple Lyapunov function, combined with a criterion, conditions are proposed in terms of Linear Matrix Inequalities for the design of the considered asynchronous switched T‐S filters with unmeasured nonlinear consequent parts. Compared with previous related works, these conditions have the advantage of being dwell‐time‐independent and less conservative, thanks to the incremental quadratic constraints employed to deal with the unmeasured nonlinear consequent parts. Furthermore, acknowledging that T‐S models are only representing nonlinear ones on subsets of their state space, an optimization procedure to estimate the filtering error's domain of attraction is developed. Two illustrative examples are considered to validate the proposed results. An academic one is presented to illustrate the improvements brought in terms of conservatism by the proposed switched T‐S filter design methodology with regards to previous related studies. Then, a case study illustrates the effectiveness of this proposal from a switched nonlinear mass‐spring system inspired from related literature.

Static Output Feedback Control for Nonlinear Time-Delay Semi-Markov Jump Systems Based on Incremental Quadratic Constraints

This paper is concerned with the problem of static output feedback control for a class of continuous-time nonlinear time-delay semi-Markov jump systems with incremental quadratic constraints. For a class of time-delay semi-Markov jump systems satisfying incremental quadratic constrained nonlinearity, an appropriate mode-dependent Lyapunov–Krasovskii functional is constructed. Based on the matrix transformation, projection theorem and convex set principle, the mode-dependent static output feedback control laws are designed. The feedback control law is given in the form of a linear matrix inequality, which is convenient for a numerical solution. Finally, two practical examples are given to illustrate the effectiveness and superiority of the proposed method.

Robust Synchronization of Fractional-Order Chaotic System Subject to Disturbances

This paper studies the synchronization problem for a class of chaotic systems subject to disturbances. The nonlinear functions contained in the master and slave systems are assumed to be incremental quadratic constraints. Under some assumptions, a feedback law is designed so that the error system behaves like the H∞ performance. Meanwhile, the detailed algorithm for computing the incremental multiplier matrix is also given. Finally, one numerical example and one practical example are simulated to show the effectiveness of the designed method.

On consensus control of nonlinear multiagent systems satisfying incremental quadratic constraints

In this paper, we investigate the problem of leaderless consensus control for the multiagent systems whose nonlinear dynamics satisfying incremental quadratic constraints. A distributed dynamic consensus protocol, decided by communication among neighboring agents, is presented to render nonlinear agent consensus with appropriate coupling weights. Next, an observer-based distributed protocol is considered to ensure consensus of nonlinear system without knowing full state information. Further, extensions to consensus strategies with nonlinear dynamics for the leader-following fashion are also addressed. By comparison to the traditional nonlinear consensus control methodologies, the proposed approach generalizes the Lipschitz nonlinearity as well as the combined nonlinearity of one-sided Lipschitz condition and quadratic inner-boundness condition towards a more generalized type of nonlinearity, which shows us a less conservative result in the Lyapunov proof. Finally, the numerical simulations for six agents are illustrated to show the feasibility and performance of the proposed control protocol with or without the presence of the observer.

Security switching control of cyber-physical system with incremental quadratic constraints under denial-of-service attack

This paper presents an observer-based security control scheme for a nonlinear cyber-physical system (CPS). Specially, the nonlinearity satisfies the incremental quadratic constraints ([Formula: see text]) which can represent many types of common nonlinearities. The problems are discussed under the assumption that both the feedback and forward channels may suffer from denial-of-service (DoS) attacks. The attack model is constructed in the form of time-delayed switching system with four subsystems corresponding to different attack situations. Then by using the attack model, an observer-based controller is constructed in the cyber layer to stabilize the CPS encountering DoS attacks. The closed-loop stability is analyzed based on H∞ index of switching systems in view of average dwell time (ADT) concept. Besides, the gain matrices of the controller and the observer are obtained by solving a series of matrix inequalities using an algorithm designed in this paper. Finally, the performance of security control scheme is presented by a simulation example.

Simultaneous state and unknown input set‐valued observers for quadratically constrained nonlinear dynamical systems

AbstractIn this article, we propose fixed‐order set‐valued (in the form of ‐norm hyperballs) observers for several classes of quadratically constrained nonlinear dynamical systems with unknown input signals that simultaneously/jointly find bounded hyperballs of states and unknown inputs that include the true states and inputs. Necessary and sufficient conditions in the form of linear matrix inequalities (LMIs) for the stability (in the sense of quadratic stability) of the proposed observers are derived for ()‐quadratically constrained (()‐QC) systems, which includes several classes of nonlinear systems: (I) Lipschitz continuous, (II) ()‐QC* and (III) linear parameter‐varying (LPV) systems. This new quadratic constraint property is at least as general as the incremental quadratic constraint property for nonlinear systems and is proven in the paper to embody a broad range of nonlinearities. In addition, we design the optimal observer among those that satisfy the quadratic stability conditions and show that the design results in uniformly bounded‐input bounded‐state (UBIBS) estimate radii/error dynamics and uniformly bounded sequences of the estimate radii. Furthermore, we provide closed‐form upper bound sequences for the estimate radii and sufficient conditions for their convergence to steady state. Finally, the effectiveness of the proposed set‐valued observers is demonstrated through illustrative examples, where we compare the performance of our observers with some existing observers.

Consensus based on output for nonlinear multi-agent systems with switching topologies

This article addresses the consensus problem based on static output feedback for a kind of leader-following multi-agent systems. Traditional nonlinear constraints, such as Lipschitz and one-sided Lipschitz, cannot describe most nonlinear functions. The incremental quadratic constraints and switching topologies are considered to extend the application range and practical significance of the existing consensus control protocol. By investigating the topology having a directed spanning tree and constructing a proper Lyapunov function, this article gives sufficient conditions for the consensus problem, including the dwell time by a threshold value. Then, a design method for the static output feedback gain matrix is deduced and an algorithm for achieving consensus is presented. Finally, two simulation examples are used to verify the validity as well as the superiority of the designed protocol. It is the first piece of work to study the consensus problem of multi-agent with incremental quadratic constraints under switching topologies.

Generalized Full Order Observer Subject to Incremental Quadratic Constraint (IQC) for a Class of Fractional Order Chaotic Systems

In this paper, we used Lyapunov theory and Linear Matrix Inequalities (LMI) to design a generalized observer by adding more complexity in the output of the dynamic systems. Our designed observer is based on the optimization problem, minimizing error between trajectories of master and slave systems subject to the incremental quadratic constraint. Moreover, an algorithm is given in our paper used to demonstrate a method for obtaining desired observer and gain matrixes, whereas these gain matrixes are obtained with the aid of LMI and incremental multiplier matrix (IMM). Finally, discussion of two examples are an integral part of our study for the explanation of achieved analytical results using MATLAB and SCILAB.

Adaptive quantized controller design for synchronization of uncertain fractional-order nonlinear systems satisfying incremental quadratic constraints

This paper proposes the adaptive quantized controller design for the synchronization of a class of fractional-order nonlinear systems satisfying incremental quadratic constraints governed by an incremental multiplier matrix. The incremental quadratic constraints can describe many commonly encountered nonlinearities in existing literature. The adaptive quantized controller are designed and formulated in terms of matrix inequalities to make the error system asymptotically stable. Meanwhile, the sufficient conditions can be obtained via solving linear matrix inequalities. Moreover, an algorithm is presented to illustrate the steps of designing adaptive quantized controllers. Finally, examples about fractional-order Lorenz chaotic system and fractional-order Bloch system are provided to illustrate the effectiveness of the designed controller.

A Convex Parameterization of Robust Recurrent Neural Networks

Recurrent neural networks (RNNs) are a class of nonlinear dynamical systems often used to model sequence-to-sequence maps. RNNs have excellent expressive power but lack the stability or robustness guarantees that are necessary for many applications. In this letter, we formulate convex sets of RNNs with stability and robustness guarantees. The guarantees are derived using incremental quadratic constraints and can ensure global exponential stability of all solutions, and bounds on incremental ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> gain (the Lipschitz constant of the learned sequence-to-sequence mapping). Using an implicit model structure, we construct a parametrization of RNNs that is jointly convex in the model parameters and stability certificate. We prove that this model structure includes all previously-proposed convex sets of stable RNNs as special cases, and also includes all stable linear dynamical systems. Numerical experiments illustrate the utility of the proposed model class in the context of non-linear system identification.