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Modeling collective motion in multi-agent systems has gained significant attention. Of particular interest are sufficient conditions for flocking dynamics. We present a generalization of the multi-agent model from Olfati-Saber, R (IEEE Trans Autom Control 51:401–420, 2006) with nonlinear navigational feedback forces. Unlike the original model, ours is not generally dissipative and lacks an obvious Lyapunov function. We address this by proposing a method to prove the existence of an attractor without relying on LaSalle's principle. Other contributions are as follows. We prove that, under mild conditions, agents' velocities approach the center of mass velocity exponentially, with the distance between the center of mass and the virtual leader being bounded. In the dissipative case, we show existence of a broad class of nonlinear control forces for which the attractor does not contain periodic trajectories, which cannot be ruled out by LaSalle's principle. Finally, we conduct a computational investigation of the problem of reducing propulsion energy consumption by selecting appropriate navigational feedback forces. [ABSTRACT FROM AUTHOR]

This research addresses the critical issue of dissipativity in Markovian jump stochastic competitive neural networks, particularly focusing on the complex challenges posed by mixed time delays and parameter uncertainties. The primary objective of this study is to derive adequate conditions for dissipativity by constructing suitable Lyapunov–Krasovskii functionals (LKFs) that incorporates triple integral terms, thereby providing a rigorous mathematical framework for analysis. To achieve this, a generalized delay-dependent reciprocal convex inequality is employed, which enables us to effectively calculate the derivative of the LKFs and derive a linear matrix polynomial. Our findings extend the conventional dissipativity criteria to include passivity, which is articulated in terms of linear matrix inequalities (LMIs). This enhancement significantly simplifies the computational process and allows for practical implementation using standard numerical software. Further, Numerical examples demonstrate that the proposed strategy outperforms existing findings. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of strongly dissipative dynamical systems. In particular, we construct a stronger version of the dissipation inequality that implies system dissipativity and generalises the notion of strict dissipativity but unlike strict dissipativity, which for a closed dynamical system implies asymptotic stability, the closed dynamical system possesses the property that system trajectories converge to a Lyapunov stable equilibrium state in finite time. The results are then used to derive Kalman-Yakubovich-Popov conditions for characterising necessary and sufficient conditions for strong dissipativity in terms of the system functions of the dynamical system using continuously differentiable storage functions and quadratic supply rates. Furthermore, using strong dissipativity concepts we present serval stability results for nonlinear feedback systems that guarantee finite time stability. For specific supply rates, these results provide generalisations of the feedback passivity and nonexpansivity theorems that additionally guarantee finite time stability. [ABSTRACT FROM AUTHOR]

Model-based control methods play an important role in control theory. Such controllers are designed via system identification; however, this approach is not applicable to cases where it is difficult to execute system identification owing to the large amount of data or experimental construction. To address these problems, data-driven control methods, in which controllers are designed by directly using target input–output data, have attracted attention for their effectiveness. Thus a framework has been proposed to reevaluate the aforementioned approaches and consider them in terms of data informativity. Herein, we use this framework to address the design problem of data-driven control for dissipativity. Using an algebraic approach, we derive necessary and sufficient conditions that data must satisfy to render a system dissipative via feedback control.

In this article, our objective is to explore a Cahn–Hilliard system with a proliferation term, particularly relevant in biological contexts, with Neumann boundary conditions. We commence our investigation by establishing the boundedness of the average values of the local cell density u and the temperature H. This observation suggests that the solution (u , H) either persists globally in time or experiences finite-time blow-up. Subsequently, we prove the convergence of u to 1 and H to 0 as time approaches infinity. Finally, we bolster our theoretical findings with numerical simulations. [ABSTRACT FROM AUTHOR]

Imitation learning enables synthesis of controllers for systems with complex objectives and uncertain plant models. However, ensuring an imitation learned controller is stable requires copious amounts of data and/or a known plant model. In this paper, we explore an input–output (IO) stability approach to imitation learning, which achieves stability with sparse data sets while only requiring coarse knowledge of the energy characteristics of the plant. A constrained optimization problem is developed, in which the controller learns to mimic expert data while maintaining stabilizing energy characteristics induced by the plant. While the learning objective is nonconvex, iterative convex overbounding (ICO) and projected gradient descent (PGD) are explored as methods to learn the controller. In numerical examples, it is shown that with little knowledge of the plant model and a small data set, the dissipativity constrained learned controller achieves closed loop stability and successfully mimics the behavior of the expert controller, while other methods often fail to maintain stability and achieve good performance. [ABSTRACT FROM AUTHOR]

We look at a stochastic time‐varying optimization problem and we formulate online algorithms to find and track its optimizers in expectation. The algorithms are derived from the intuition that standard prediction and correction steps can be seen as a nonlinear dynamical system and a measurement equation, respectively, yielding the notion of nonlinear filter design. The optimization algorithms are then based on an extended Kalman filter in the unconstrained case, and on a bilinear matrix inequality condition in the constrained case. Some special cases and variations are discussed, notably the case of parametric filters, yielding certificates based on LPV analysis and, if one wishes, matrix sum‐of‐squares relaxations. Supporting numerical results are presented from real data sets in ride‐hailing scenarios. The results are encouraging, especially when predictions are accurate, a case which is often encountered in practice when historical data is abundant. [ABSTRACT FROM AUTHOR]

In this paper, the non-fragile distributed fault detection (FD) problem is discussed for delayed Markov jump systems over sensor networks under the weighted try-once-discard protocol, where the randomly switching nonlinearities and the randomly occurring faults are considered. Specifically, a non-fragile distributed FD filter is constructed, and the compact residual dynamic system is obtained in terms of augmentation technique. Subsequently, by applying the Lyapunov stability theory and Wirtinger inequality, sufficient conditions are derived to ensure that the nominal system corresponding to residual dynamic system is stochastically stable and stochastically strictly (Q 1 , Q 2 , Q 3) - γ dissipative. On this basis, the explicit expressions of FD filter matrices are obtained by means of the linear matrix inequality method. At last, a simulation is provided to demonstrate the effectiveness of the proposed distributed FD scheme. [ABSTRACT FROM AUTHOR]

This paper investigates the long-time behavior of fractional-order complex memristive neural networks in order to analyze the synchronization of both anatomical and functional brain networks, for predicting therapy response, and ensuring safe diagnostic and treatments of neurological disorder (such as epilepsy, Alzheimer's disease, or Parkinson's disease). A new mathematical brain connectivity model, taking into account the memory characteristics of neurons and their past history, the heterogeneity of brain tissue, and the local anisotropy of cell diffusion, is proposed. This developed model, which depends on topology, interactions, and local dynamics, is a set of coupled nonlinear Caputo fractional reaction–diffusion equations, in the shape of a fractional-order ODE coupled with a set of time fractional-order PDEs, interacting via an asymmetric complex network. In order to introduce into the model the connection structure between neurons (or brain regions), the graph theory, in which the discrete Laplacian matrix of the communication graph plays a fundamental role, is considered. The existence of an absorbing set in state spaces for system is discussed, and then the dissipative dynamics result, with absorbing sets, is proved. Finally, some Mittag–Leffler synchronization results are established for this complex memristive neural network under certain threshold values of coupling forces, memristive weight coefficients, and diffusion coefficients. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the asymptotic behavior of a modified chemostat model. We first demonstrate the existence of equilibria. Then, we present a mathematical analysis for the model, the invariance, the positivity, the persistence of the solutions, and the asymptotic global stability of the interior equilibrium. Some numerical simulations are carried out to illustrate the main results. [ABSTRACT FROM AUTHOR]

Based on dissipativity theory, the consensus via iterative learning control (ILC) is investigated for P-one-sided Lipschitz (P-OSL) nonlinear multi-agent systems (MASs). This paper only considers the P-OSL condition without using the quadratically inner-bounded constraint. Firstly, the ILC protocol is designed for such nonlinear MASs. Then, the convergence conditions of the consensus algorithm under a connected communication graph are presented from the viewpoint of dissipativity. It is shown that, on a fixed finite-time interval, the proposed algorithm can achieve perfect consensus tracking. Finally, two examples are constructed to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Partially stable systems involve dynamical systems whose motion lie in a subspace of the state space resulting in system stability with respect to part of the system's states. In this paper, we develop partial stability theorems for nonlinear continuous-time and discrete-time dissipative feedback systems. Specifically, by invoking additional structural constraints on the forward loop and feedback loop system storage functions, we develop feedback interconnection partial stability results for dissipative nonlinear dynamical systems. Our results provide extensions of the positivity and small gain theorems for guaranteeing partial stability of feedback interconnected systems. [ABSTRACT FROM AUTHOR]

Without altering the inertial system into the two first-order differential systems, this paper primarily works over the global exponential dissipativity (GED) of memristive inertial competitive neural networks (MICNNs) with mixed delays. For this purpose, a novel differential inequality is primarily established around the discussed system. Then, by applying the founded inequality and constructing some novel Lyapunov functionals, the GED criteria in the algebraic form and the linear matrix inequality (LMI) form are given, respectively. Furthermore, the estimation of the global exponential attractive set (GEAS) is furnished. Finally, a specific illustrative example is analyzed to check the correctness and feasibility of the obtained findings. [ABSTRACT FROM AUTHOR]

In this paper, the framework of dissipativity-based iterative learning control for singular systems (SSs) is established for the first time. Firstly, under the P-type learning algorithm, it has been demonstrated that the dissipative SSs can achieve the accurate tracking for the desired trajectory in a finite time interval. Secondly, a sufficient condition for the SSs to satisfy dissipativity is given by using the linear matrix inequality (LMI) method, and the solvability criterion of the LMI is further presented. Moreover, the relationship between dissipativity and positive realness is revealed. Finally, two examples are given to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper we extend dynamic programming techniques to the study of discrete-time infinite horizon optimal control problems on compact control invariant sets with state-independent best asymptotic average cost. To this end we analyse the interplay of dissipativity and optimal control, and propose novel recursive approaches for the solution of so called shifted Bellman Equations. [ABSTRACT FROM AUTHOR]

Model predictive control is a popular choice for systems that must satisfy prescribed constraints on states and control inputs. Although much progress has been made in distributed model predictive control, existing algorithms tend to be computationally expensive. This limits their use in systems with fast dynamics. In this paper, we propose a new distributed model predictive control algorithm that we term as instant distributed model predictive control (iDMPC). The proposed algorithm employs a realisation of the primal-dual algorithm in the controller dynamics for fast computation. We show that the closed-loop system trajectories with the proposed iDMPC algorithm converge asymptotically to a desired reference. To ensure the satisfaction of the state constraints during the transient, we also include an explicit reference governor in the feedback loop. [ABSTRACT FROM AUTHOR]

This article explores the dissipative control of two‐dimensional (2‐D) discrete‐time switched Fornasini–Marchesini local state‐space systems under dwell‐time switching. It introduces a new point‐dependent convex storage function to establish the criteria for the asymptotic stability and strict (Q,S,R)$$ \left(Q,S,R\right) $$‐β$$ \beta $$‐dissipativity of the 2‐D switched Fornasini–Marchesini local state‐space model based on LMIs. From these established findings, special cases of dissipative control such as strict passivity and H∞$$ {H}_{\infty } $$ performance can be derived. The article also presents the design of a state feedback point‐dependent convex controller using the proposed storage function approach, along with a sufficient condition for the dissipativity of the closed‐loop system. Finally, several examples are presented to corroborate the effectiveness and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

This paper focuses on the asymptotic behavior of nonautonomous neural networks with delays. We establish criteria for analyzing the asymptotic behavior of nonautonomous recurrent neural networks with delays by means of constructing some new generalized Halanay inequalities. We do not require to constructi any complicated Lyapunov function and our results improve some existing works. Lastly, we provide some illustrative examples to demonstrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we discuss how to synthesize stabilizing model predictive control (MPC) algorithms based on convexly parameterized integral quadratic constraints (IQCs), with the aid of general multipliers. Specifically, we consider Lur'e systems subject to sector‐bounded and slope‐restricted nonlinearities. As the main novelty, we introduce point‐wise IQCs with storage in order to accordingly generate the MPC terminal ingredients, thus enabling closed‐loop stability, strict dissipativity with regard to the nonlinear feedback, and recursive feasibility of the optimization. Specifically, we consider formulations involving both static and dynamic multipliers, and provide corresponding algorithms for the synthesis procedures. The major benefit of the proposed approach resides in the flexibility of the IQC framework, which is capable to deal with many classes of uncertainties and nonlinearities. Moreover, for the considered class of nonlinearities, our method yields larger regions of attraction of the synthesized predictive controllers (with reduced conservatism) if compared to the standard approach to deal with sector constraints from the literature. [ABSTRACT FROM AUTHOR]

In this paper, we evaluate the robustness qualities of Model Predictive Control (MPC) algorithms applied for Linear Parameter Varying (LPV) systems. Specifically, we analyze gain‐scheduled LPV MPC schemes, that is, those that use model predictions based on the LPV scheduling variables available at each sampling instant. Accordingly, we extend previous results on finite‐horizon robustness analysis of linear time‐variant (LTV) systems, employing Integral Quadratic Constraints (IQCs) to describe the input‐output behavior of prediction uncertainties. We provide two main novelties in our formulation: (i) we propose a parameter‐dependent Karush–Kuhn–Tucker (KKT) inequality to describe the existence and feasibility of the LPV MPC control inputs; and (ii) we model the uncertainties that arise due to the unavailability of the scheduling trajectory along the prediction horizon as a bounded interconnection in the form of a Linear Fractional Transformation (LFT). Accordingly, we use dissipativity arguments (p$$ p $$‐hard IQCs) in order to compute robust induced gains of the closed‐loop system (specifically, the ℒ2$$ {\mathcal{L}}_2 $$ and ℒ2$$ {\mathcal{L}}_2 $$‐to‐Euclidean metrics), taking into account the MPC prediction uncertainties. We also generate the set of reachable states from a given initial condition. A benchmark example is used to illustrate the proposed analysis procedure. [ABSTRACT FROM AUTHOR]

We study the long time behavior of solutions for time-fractional pseudo-parabolic equations involving time-varying delays and nonlinear pertubations, where the nonlinear term is allowed to have superlinear growth. Concerning the associated linear problem, we establish a variation-of-parameters formula of mild solutions and prove some regularity estimates of resolvent operators. In addition, thanks to local estimates on Hilbert scales, fixed point arguments and a new Halanay type inequality, we obtain some results on the global solvability, stability, dissipativity and the existence of decay solutions to our problem. [ABSTRACT FROM AUTHOR]

In this work, the global dissipativity and exponential dissipativity of quaternion‐valued memristor‐based neutral‐type neural networks (QVNTMNNs) with time‐varying delays are studied. It is worth noting that the QVNTMNN is explored as a single entity without decomposition. Considering the QVNTMNNs as a switching system and utilizing Lyapunov theorem as well as inequality techniques, several sufficient criteria depending on the state‐dependent switching parameters to guarantee global dissipativity and exponential dissipativity of QVNTMNNs with time‐varying delays are obtained in the form of quaternion‐valued linear matrix inequalities (QVLMIs) and corresponding complex‐valued liner matrix inequalities (CVLMIs). Moreover, the positive invariant set, global attractive set, and exponential attractive set of QVNTMNNs with time‐varying delays can also be derived. Finally, two numerical examples are given to substantiate the reliability and validity of our theoretical criteria presented in this work. [ABSTRACT FROM AUTHOR]

Conditions for the existence, uniqueness and boundedness of global solutions, as well as ultimate boundedness of solutions, and conditions for the blow-up of solutions of nonregular semilinear differential-algebraic equations have been obtained. An example demonstrating the application of the obtained results has been considered. Isothermal models of gas networks have been proposed as applications. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to study generalizations of the Caginalp phase-field system based on a thermomechanical theory involving two temperatures and a nonlinear coupling. In particular, we prove well-posedness results. More precisely, the existence and uniqueness of solutions, the existence of the global attractor and the existence of an exponential attractor.

The problem of dissipative fuzzy control for singular Markovian jump systems is studied with generally uncertain transition rates. Firstly, a new Lyapunov-Krasovskii functional is established to develop the new bounded real lemma（BRL） which guarantee the system to be stochastically admissible with given dissipative performance α. Delay decomposition approach and new inequality to deal with functional are used, which can reduce the conservatism to a certain extent. Secondly, based on these ingredients, the explicit expression of the desired controller is obtained by solving a set of strict linear matrix inequalities（LMIs）. In the design process of the controller, the generally uncertain transition rates are divided into two cases, and then obtain the LMIs in two different cases. Finally, some numerical examples reflect the less conservatism and effectiveness of the method in this article. [ABSTRACT FROM AUTHOR]

We focus in this article on a Cahn-Hilliard-Oono-Navier-Stokes system, which is a model consisting of a Navier-Stokes equation governing the fluid velocity coupled to the Cahn-Hilliard-Oono equation. We start our study by establishing the a priori estimates, the existence and uniqueness of the solution, and then the existence of a continuous dissipative semigroup generated by the system. Moreover, we prove the existence of the exponential attractors and, thus, of finite-dimensional global attractors. Finally, we construct a robust family of exponential attractors as a nonnegative parameter $ \alpha $ goes to zero. [ABSTRACT FROM AUTHOR]

The problem of dissipativity analysis is discussed for Lur'e systems with two additive time‐varying delays (ATDs) in this paper. Based on the dynamic delay interval (DDI) method, some novel Lyapunov‐Krasovskii functionals (LKFs) are constructed, in which part of Lyapunov matrices are requested to be positive definite. Then strictly dissipativity criteria of Lur'e systems with ATDs are presented in terms of linear matrix inequalities (LMIs). As by‐products, the stability criteria of Lur'e systems with ATDs and the systems with ATDs are derived. Finally, several numerical examples are used to illustrate the effectiveness and superiority of these criteria. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to study generalizations of the Caginalp phase-field system based on a thermomechanical theory involving two temperatures and a nonlinear coupling. In particular, we prove well-posedness results. More precisely, the existence and uniqueness of solutions, the existence of the global attractor and the existence of an exponential attractor. [ABSTRACT FROM AUTHOR]

This paper introduces the event-triggered scheme to study the problems of dissipative control and dissipativity-based sliding mode control (SMC) for switched nonlinear systems. Firstly, based on a designed event-triggered scheme, a piecewise continuous state feedback controller is constructed; sufficient conditions for Q , S , R - α -dissipativity of the resulting system are derived by the approaches of a switched Lyapunov function and an average dwell time. Secondly, these two methods are extended to the study of H ∞ performance and passive performance; the corresponding sufficient conditions are provided. Thirdly, the dissipative control problem is solved by introducing an event-triggered scheme into SMC method. Sufficient conditions for dissipativity of the resulting system are derived, and an SMC law is designed to guarantee the reachability. At the end of this paper, the correctness of the proposed methods is proved by two numerical examples. [ABSTRACT FROM AUTHOR]

The objective of this research is to examine the global dissipativity and quasi-synchronization of fractional-order neural networks (FNNs). A global dissipativity criterion is established through the creation of an appropriate Lyapunov function, together with some fractional-order inequality techniques. Additionally, the issue of quasi-synchronization for drive-response FNNs is investigated using linear state feedback control. The study reveals the synchronization error converges to a bounded region by choosing an appropriate control parameter. Finally, the effectiveness of the obtained works are validated through three numerical examples. [ABSTRACT FROM AUTHOR]

Summary: A novel dissipativity characterization is proposed for linear time‐invariant circuits and systems whose dynamic behavior depends on one external parameter. The proposed formulation extends to the parameterized case standard Hamiltonian‐based algebraic dissipativity characterizations and is structured as an underdetermined multiparameter eigenvalue problem. Resulting from a polynomial parameterization, the proposed characterization leads to an effective set of algorithms that are able to determine the regions of local dissipativity and local activity in the frequency‐parameter plane, which in turn can be exploited by dissipativity enforcement algorithms to produce uniformly passive models. The reference application of proposed technique is behavioral modeling of complex circuits or systems, whose dynamic behavior can be compressed into a low‐order system through dedicated model order‐reduction processes. Various examples ranging from integrated components to microstrip filters and networks are used to illustrate the proposed characterization. [ABSTRACT FROM AUTHOR]

This paper focuses on the dissipativity and contractivity of a second-order numerical method for fractional Volterra functional differential equations (F-VFDEs). Firstly, an averaged L1 method for the initial value problem of F-VFDEs is presented based on the averaged L1 approximation for Caputo fractional derivative together with an appropriate piecewise interpolation operator for the functional term. Then the averaged L1 method is proved to be dissipative with an absorbing set and contractive with an algebraic decay rate. Finally, the numerical experiments further confirm the theoretical results. [ABSTRACT FROM AUTHOR]

This article addresses the robust dissipativity and passivity problems for a class of Markovian switching complex-valued neural networks with probabilistic time-varying delay and parameter uncertainties. The main objective of this article is to study the proposed problem from a new perspective, in which the relevant transition rate information is partially unknown and the considered delay is characterized by a series of random variables obeying bernoulli distribution. Moreover, the involved parameter uncertainties are considered to be mode-dependent and norm-bounded. Utilizing the generalized It$ \hat{o} $'s formula under the complex version, the stochastic analysis techniques and the robust analysis approach, the $ (M, N, W) $-dissipativity and passivity are ensured by means of complex matrix inequalities, which are mode-delay-dependent. Finally, two simulation examples are provided to verify the effectiveness of the proposed results.

We propose a general notion of dissipativity with dynamic supply rates for nonlinear systems. This extends classical dissipativity with static supply rates and dynamic supply rates of miscellaneous quadratic forms. The main results of this paper concern Lyapunov and asymptotic stability analysis for nonlinear feedback dissipative systems that are characterised by dissipation inequalities with respect to compatible dynamic supply rates but involving possibly different and independent auxiliary systems. Importantly, dissipativity conditions guaranteeing stability of the state of the feedback systems, without concerns on the stability of the state of the auxiliary systems, are provided. The key results also specialise to a simple coupling test for the interconnection of two nonlinear systems described by dynamic (Ψ , Π , Υ , Ω) -dissipativity, and are shown to recover several existing results in the literature, including small-gain, passivity indices, static (Q , S , R) -dissipativity, dissipativity with terminal costs, etc. Comparison with the input–output approach to feedback stability analysis based on integral quadratic constraints is also made. [ABSTRACT FROM AUTHOR]

We study an explicit two-level in time and symmetric in space finite-difference scheme for a linearized 2D and 3D gas dynamic system of equations with a kinetic-type regularization. For an initial-boundary value problem on any nonuniform rectangular mesh, sufficient Courant-type conditions for the L²-dissipativity are derived for the first time by the energy method. For the Cauchy problem on the uniform mesh, recent both necessary conditions and sufficient conditions for the L²-dissipativity in the spectral method are improved. A new form for the relaxation parameter is suggested which guarantees that the Courant-type number is uniformly bounded from above and below with respect to the mesh and the Mach number. [ABSTRACT FROM AUTHOR]