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A general |$N$| -dimensional non-monotone delayed diffusive Lotka–Volterra model is considered in our paper. First, we obtain the global stability of the model subject to Neumann boundary condition by using a small delay result for delayed systems. Second, the limits at |$+\infty $| of bounded travelling wave solutions are confirmed by virtue of such global stability. Therefore, the existence of co-existence state travelling wave solutions is established. Finally, an example is given to illustrate the biological significance of the assumptions in the current paper. [ABSTRACT FROM AUTHOR]

This paper considers the adaptive two-bit-triggered containment control problem for nonlinear multi-agent systems in the presence of input saturation. Since input saturation occurs frequently in practical systems, which can affect the stability of the multi-agent systems under consideration, an auxiliary design system is introduced to address this issue. Meanwhile, considering limited transmission resources in practical systems, this paper mainly focuses on the triggering condition and the control signal transmission bits, presenting a two-bit-triggered control approach to optimize the utilization of transmission resources. Furthermore, a command filter is introduced into the design process to solve the problem of complexity explosion. The proposed method ensures that all signals of the closed-loop system are bounded and the output signals of all followers converge to a convex hull spanned by the outputs of the leaders. Finally, two simulation examples are provided to verify the validity of the presented control scheme. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel discrete-time consensus algorithm based on the new min–max criterion for the discrete-time second-order linear agents. To boost the convergence speed, the proposed algorithm allocates three different operating modes to the network agents. Unlike most of the existing consensus algorithms in which the links of the communication graph have specific weights and these weights are required to have positive lower bounds to achieve asymptotic convergence, the communication graph in this paper has unspecific link weights. Accordingly, because of data transmission errors and faults, the weights of the communication links can even go from a positive to a negative value. Thus, the proposed algorithm can bring the agents to consensus under more general conditions. To demonstrate the efficacy of the proposed algorithm, numerical simulations are performed, and their results are compared with those of the minimum consensus algorithm, which shows a significantly faster convergence speed. [ABSTRACT FROM AUTHOR]

This paper investigates the bipartite tracking control problem for a family of networked multi-agent systems with periodic disturbances as well as input saturation. A low-computation two-bit-triggered adaptive control strategy is proposed to achieve precise trajectory tracking and maintain the boundedness of the closed-loop signals. Compared with the existing results, first, this paper considers the problems for the coexistence of cooperation and competition in multi-agent systems, which represents a more common situation; secondly, the explosion of complexity issue is avoided without introducing any auxiliary filters, making our result more applicable and less complex; thirdly, a function approximator incorporating Fourier series expansion and a radial basis function neural network is utilized to model time-varying periodic disturbance functions and lastly, unlike traditional event-triggered control, the issue of controlling signal transmission bits is further explored to conserve system transmission resources. The result from a comparative simulation illustrates the advantages of the proposed method. [ABSTRACT FROM AUTHOR]

This paper addresses the exponential stability of nonlinear delay differential equations with Markovian switching. Drawing upon the comparison principle, we introduce the explicit criteria for achieving the exponential stability in mean square (sense). These criteria are formulated in terms of the equation coefficients and the generator of the Markovian switching process. As a result, these criteria can be verified without needing to construct the Lyapunov functions, a departure from the conventional approach found in the Razumikhin-type theorems. The paper includes an illustrative example and also demonstrates an application to the switched neural networks. [ABSTRACT FROM AUTHOR]

We focus in this paper on determining whether or not a periodic stochastic feedback control based on Lévy noise can stabilize or destabilize a given non-linear hybrid system. Using the Lyapunov functions and the periodic functions, we establish some sufficient conditions on the stability and instability for non-linear hybrid systems with Lévy noise. Moreover, we use some numerical examples and simulations to illustrate that an unstable (or stable) non-linear hybrid system can be stabilized (or destabilized) via periodic stochastic feedback control based on Lévy noise. [ABSTRACT FROM AUTHOR]

In this paper, for the first time, a linear Lyapunov–Razumikhin function is introduced to find an |$\alpha$| -exponential state estimate for positive systems with time delays. A new set of conditions for the existence of exponential state boundedness of positive systems with bounded time-varying delays is established. Two procedures are then proposed to find the factor vector of |$\alpha$| -exponential state estimate, in which some techniques of optimization are applied to find the smallest possible factor vector. Numerical experiments are presented to demonstrate the effectiveness of the linear Lyapunov–Razumikhin function as well as of the optimization techniques. [ABSTRACT FROM AUTHOR]

In this paper, we propose an efficient analytical approach based on fractional calculus and singularity value theory to designing the finite-time |$H_\infty $| controller for linear singular fractional differential equations with time-varying delay. By introducing new fractional-order |$H_\infty $| norm, the state feedback controller is designed to guarantee that the closed-loop system is singular, impulse-free and finite-time stable with prescribed |$H_\infty $| performance. New sufficient conditions for designing the |$H_\infty $| finite-time controller are presented. The results of this paper improve the corresponding ones of integer-order singular systems with time-varying delay. Finally, a numerical example demonstrates the validity and effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, approximations of the set of trajectories and integral funnel of the control system described by non-linear ordinary differential equation with integral constraint on the control functions are considered. The set of admissible control functions is replaced by a set, consisting of a finite number of piecewise-constant control functions. It is shown that the set of trajectories generated by a finite number of piecewise-constant control functions is an internal approximation of the set of trajectories. Further, each trajectory generated by a piecewise-constant control function is substituted by appropriate Euler's broken line and it is proved that the set consisting of a finite number of Euler's broken lines is an approximation of the set of trajectories of given control system. An approximation of the system's integral funnel by a set consisting of a finite number of points is obtained. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of stability and consensus of non-linear multi-agent system by utilizing the sampled-data control. The innovative part of this paper is that the nonlinearity of this class of nonlinear systems is considered to satisfy a quasi one-sided Lipschitz condition. Communication among agents are assumed to be a switching directed graph. The principle target of this paper is to design a sampled data controller such that for all permissible uncertainties, the resulting closed-loop system is stable in the sense of mean square. For this reason, through the development of an appropriate Lyapunov–Krasovskii functional with dual integral terms and usage of Kronecker product properties alongside the matrix inequality techniques, a new set of stability and consensus conditions for the prescribed system is obtained in the form of a linear matrix inequality, which can be easily solved by the well-known effective numerical programming. Finally numerical examples are given to show the validity of the proposed hypothetical results. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with adaptive stabilization for a wave equation subject to boundary control matched harmonic disturbance. We use the adaptive and Lyapunov approach to estimate unknown disturbance and construct an adaptive boundary feedback controller. By the semigroup theory and Lasalle's invariance theorem, the well-posedness and asymptotic stability of the closed-loop system is proved, respectively. At the same time, it is shown that the parameter estimates involved in the constructed controller converge to their own real values as time goes to infinity. Some numerical simulations are offered at the end of the paper to illustrate the effectiveness of theoretical results. [ABSTRACT FROM AUTHOR]

This paper deals with the global finite-time synchronization of a class of third-order chaotic systems with some intersecting nonlinearities, which cover many famous chaotic systems. First, a simple, continuous and dimension-reducible control by the name of the variable-substitution and feedback control is designed to construct a master–slave finite-time synchronization scheme. Then, a global finite-time synchronization criterion for the synchronization scheme is proven and the synchronization time is analytically estimated. Subsequently, the criterion and optimization technique are applied to the well-known brushless direct current motor (BLDCM) system and the classic Lorenz system, respectively, further obtaining some new optimized synchronization criteria in the form of algebra. Two numerical examples for the BLDCM system and a numerical example for the Lorenz system are simulated and analyzed to verify the effectiveness of the theoretical results obtained in this paper. [ABSTRACT FROM AUTHOR]

We propose a method of solving the controllability problem using almost linearizable control systems. Developing an idea of triangular systems, proposed by the first author of this paper in 1973, we introduce a wider class of almost triangular systems for which it is possible to find explicitly a control steering the system from one given point to another given point. We give conditions of almost linearizability for nonlinear single-input systems of the class |$C^{1}$| and discuss a method of solving the controllability problem for such systems. [ABSTRACT FROM AUTHOR]

In this paper, we mainly study a class of conformable impulsive delay differential equations (CIDDEs). We first define a conformable impulsive delayed matrix function, and construct an explicit solution for linear CIDDEs by virtue of variation of constants method. Subsequently, based on impulsive delayed Grammian matrix, we study the relative controllability for the addressed linear equations. Moreover, with the help of Krasnoselskii's fixed point theorem, relative controllability for the considered semilinear equations is proposed. Finally, two examples with numerical simulations are given to illustrate the main results. [ABSTRACT FROM AUTHOR]

The paper explores an optimal control problem concerning transport processes in a porous medium. The transport phenomena is governed by diffusion-reaction equations, which is basically a semi-linear parabolic system. An |$L^{2}$| -cost (energy) functional is introduced, and control (distributed) is applied in the porous part of the medium. The primary objective is to characterize a given control to be an optimal control and analyse the relationship between optimal control and the adjoint state. The analysis commences with the microscopic description of the controlled system followed by upscaling the system via periodic homogenization. [ABSTRACT FROM AUTHOR]

This paper deals with a hierarchical control problem for the heat equation with dynamic boundary conditions. The main goal consists of letting the state near from a prescribed target in a fixed observation region. The secondary objective is the null controllability. In other words, we reverse the roles of the leader and the follower addressed in the recent article. For this purpose, we combine some appropriate Carleman estimates and the Stackelberg strategy. We also extend our study for hierarchical-biobjective problems by applying the Stackelberg–Pareto strategy. [ABSTRACT FROM AUTHOR]

The main contribution of this paper is the development of |$H_{\infty }$| state and unknown input (UI) observers for noisy linear parameter-varying (LPV) systems. The observers are constructed in order to be unbiased (in particular the state estimation error is decoupled from the UI) and with a minimum |$L_{2}$| transfer between the perturbations (that are assumed to be with finite energy) and the estimation errors. Contrary to equivalent observers developed in the literature, the present one relaxes a widely used rank condition on the system matrices for decoupling the UI. In order to do so, high-order derivation is needed, which is done using a high-order sliding modes differentiator. A method is given to design observer gains for LPV systems under polytopic form. Finally, three examples illustrate some aspects of the theoretical contributions, and compare this work to the existing ones. [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]

The stability problem of Multiple n Inputs and Multiple n Outputs (MIMOn) cascade non-linear systems with random parameters is considered in this paper using the probability of stability estimation method. MIMOn cascade non-linear systems, particularly when the number of inputs and outputs exceeds three (n  > 3), exhibit a unique property: the appearance of spatial hyperchaos that can lead to system instability. To achieve desired spatial dynamics and prevent the occurrence of spatial hyperchaos, it is necessary to select the appropriate parameter values for these systems. Moreover, the optimal parameter values enable the attainment of the highest probability of stability for stochastic MIMOn systems. The research presents the results of stability analysis using tools such as bifurcation diagram, Lyapunov diagram and spatial phase portraits, generated through MATLAB M-files, with a specific focus on a stochastic MIMO5 system (five inputs and five outputs). [ABSTRACT FROM AUTHOR]

The paper addresses the problem of evaluating the Implicit McMillan degree |$\delta{m}$| of |$W^{-1}(s)$|⁠ , where |$W^{-1}(s)$| denotes the transfer function of a passive |$RLC$| electrical network.1 The Implicit McMillan degree |$\delta{m}$| specifies the minimum number of dynamic elements needed to completely characterize the passive |$RLC$| network, i.e. an electrical network that contains only passive elements (capacitors, inductors and resistors) and associates it with the rank properties of the passive element matrices. A fact that in the circuit literature is intuitively accepted but not rigorously proved is that this degree must be equal to the minimum number of independent dynamical elements in the network Livada (2017, Implicit network descriptions of RLC networks and the problem of re engineering. Ph.D. Thesis, City, University of London) and Leventides et al. (2014, McMillan degree of impedance, admittance functions of RLC networks. In 21st International Symposium on Mathematical Theory of Networks and Systems. The Netherlands: Groningen). In this paper, we investigate this finding, showing that the maximum possible Implicit McMillan degree |$\delta{m}$| of such networks is given by |$rankL+rankC$| and that this value is reached when certain necessary and sufficient conditions are satisfied. 1 [ABSTRACT FROM AUTHOR]

This paper addresses the topic of output feedback stabilization of general one-dimensional reaction–diffusion partial differential equations (PDEs) in the presence of a saturation in the measurement. The boundary control and the second boundary condition take the form of Dirichlet/Neumann/Robin boundary conditions. The measurement is selected as a boundary Dirichlet trace. The boundary measurement, as available for feedback control, is assumed to be subject to a saturation. In this context, we achieve the local exponential stabilization of the reaction–diffusion PDE while estimating a subset of the domain of attraction of the origin. [ABSTRACT FROM AUTHOR]

The paper considers the problem of model orientation, i.e. the classification of the external signals into inputs and outputs. The problem is considered in the behavioural context where the external model is an autoregressive system. Orientation of a system automatically induces equivalent first order models in state–space or descriptor form via a realization procedure. A new realization procedure is proposed where the realization is implemented in two steps, first an intermediate ARMA realization is obtained. Then, this realization is transformed into the final descriptor system via an appropriate reduction procedure corresponding to the input/output partition of the external variables. Studying the dependency of the resulting system properties and invariants on the different selections of input and output variables and the structure of the initial external behaviour is considered in the paper. [ABSTRACT FROM AUTHOR]

Our paper deals with the stabilization of a class of time-dependent linear autonomous complex systems with a switched structure. The initially given switched dynamic system is assumed to be controlled by a specific state feedback strategy associated with the linear quadratic regulator (LQR) type control. The proposed control design guarantees stabilization of the closed-loop system for all of the possible location transitions. In the solution procedure of the Algebraic Riccati Equation related to the LQR control strategy, only the knowledge of the algebraic structure related to the switched system are needed. We prove that the proposed optimal LQR type state feedback control design stabilizes the closed-loop switched system for every possible active location. The theoretical approach proposed in this paper is finally applied to a model of the Single Wing Quadrotor Aircraft , when changing from its Quadrotor Flight Envelope to its Airplane Flight Envelope. [ABSTRACT FROM AUTHOR]

The design of dynamic observers for nonlinear Lipschitz systems has considered great attention in past decades. Instead of applying the standard strictly explicit designs or LMI-based heuristic solutions, in this paper, an efficient systematic method is deployed by considering the existence of some arbitrary bounds on the nonlinear Lipschitz terms. The method enables to relax the observer design from the conventional restrictions and it is easily solved analytically without needing the solution of LMIs. As proven in the paper by a detailed and rigorous analysis, its main advantage is that it guarantees global asymptotic stability and ensures the observer response with desired decay characteristics satisfying simultaneously the Lyapunov equation. [ABSTRACT FROM AUTHOR]

The explosive growth of network data traffic puts new demands on traffic scheduling. In this paper, the scheduling algorithm based on the software-defined network (SDN) architecture is studied. Firstly, the SDN architecture was introduced, then an SDN-based adaptive multi-path load balancing algorithm was proposed and finally the algorithm was simulated on the Mininet simulation platform to compare the performance of the proposed algorithm and traditional equal-cost multi-path routing algorithm by using Ryu as the controller. It was found that the proposed algorithm had greater throughput, higher bandwidth utilization and shorter transmission time in allocation scheduling of network data traffic, which could effectively reduce network congestion and ensure the reliability of the network. This study verifies the effectiveness of the proposed method in allocation scheduling of network data traffic and provides some theoretical bases for the further application of the SDN architecture-based allocation scheduling algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we consider parameter estimation and velocity signal extraction from a disturbed boundary velocity signal for an unstable wave equation. Firstly, an adaptive observer is designed based on the boundary displacement and the corrupted boundary velocity. Then the design of the feedback law adopts the backstepping method of infinite dimensional system. Finally, as time approaches infinity, the estimated parameters converge to the unknown parameters, the initial value disturbance can be obtained, and the velocity signal can be asymptotically recovered. Meanwhile, the asymptotic stability of the closed-loop system can be proved by |$C_{0}$| -semigroup theory and Lyapunov method. Numerical simulation shows that the proposed scheme is reasonable. [ABSTRACT FROM AUTHOR]

This paper is addressed to the study of the null controllability for integer order integro-differential equations. Unlike the known results for partial differential equations, we need to consider the equation involving a |$\beta -$| power of the Laplace operator |$(-\varDelta)^\beta $| and an integral term. The key point is to construct a suitable state space of the controlled system at the final time. We first discuss a class of hyperbolic integro-differential equation. We prove that the controlled system is null controllable by an Ingham-type estimate. Also, the controllability time is given. On the other hand, by reduction to absurdity, we deduce that the null controllability property fails for a class of parabolic integro-differential equation with |$\beta \in \mathbb{N}^+$|⁠. [ABSTRACT FROM AUTHOR]

In this paper, a class of non-linear systems in normal form is considered, which is composed of internal and external dynamics. An adaptive finite time sliding mode observer is first designed so that the system states, unmatched uncertain parameters and matched uncertainties can all be observed in finite time. Then, the systematic backstepping design procedure is employed to develop a novel output feedback backstepping control (OFBC). The proposed OFBC method can stabilize the considered non-linear systems despite the presence of non-linear internal dynamics and unmatched uncertainties. A Lyapunov method is used to ensure that the closed-loop system is asymptotically stable. Two MATLAB simulation examples are used to demonstrate the method. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the null approximate impulse controllability of the heat equation with an inverse square potential subject to dynamic boundary conditions in the ball |$B(0, R_{0})$| of radius |$R_{0}=\left (\frac{4}{3}\right)^{\frac{3}{2}}$|⁠. To that purpose, we use the Carleman commutator approach to show a logarithmic convexity estimate traducing an observability inequality at one instant of time. [ABSTRACT FROM AUTHOR]

This paper concerns the stabilization problem for an underactuated robot called the Pendubot. Relying on a computational algorithm which is based on various results of the 'polynomial matrix approach', we propose an output-feedback-based internally stabilizing controller to stabilize the Pendubot at the unstable vertical upright position. The algorithm utilizes results for the solution of polynomial matrix Diophantine equations required for the computation and parameterization of proper 'denominator assigning' and internally stabilizing controllers for linear time invariant multivariable systems and reduces the problem to that of the solution of a set of numerical linear equations. The controller presented uses only the measured output which consists of the angles of the two links and does not require knowledge of the angular velocities which are usually not directly measurable. Comparative simulations are carried out to verify the good performance of the proposed controller. Finally, experimental results are provided to demonstrate the validity and feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we mainly studied the topological equivalence of linear time-varying (LTV) control system |$\dot{x}\left (t\right)=A(t)x(t)+B(t)u(t)$| defined on an interval |$I \subset \mathbb{R}^{+}$|⁠. After giving a new definition of the topological equivalence, we investigated the local equivalence of LTV control systems under two new hypotheses. These hypotheses were made by the local behavior of Krylov indices (which turned out to be controllability indices for the linear time-invariant (LTI) control systems). It was found out that Krylov indices play an important role in the classification problem of LTV control systems. Compared with our former work on the topological equivalence of LTI control systems, new methods and techniques were taken to deal with new difficulties occurred for LTV control systems. [ABSTRACT FROM AUTHOR]

This paper investigates an average dwell time (ADT) based networked predictive control for discrete-time linear systems with data transmission time-varying delays. Since the data transmission time-varying delays and packet dropouts simultaneously exhibit in the sensor-to-controller and the controller-to-actuator channels, a predictor is proposed to approximate the current state with the delayed state measurement. Based on the estimation state, a synchronous switching controller is proposed, and its mode-dependent and mode-independent design methods are presented. The proposed methods not only guarantee the desired stability of the closed-loop systems but also tolerate some locally unstable subsystems. In addition, the decay rate of the closed-loop system can be pre-regulated. Moreover, given some prior activation probabilities of subsystems, the ADT can be further reduced, thus more frequent switching dynamics can be allowed. Numerical example is provided to show the effectiveness of the developed method. [ABSTRACT FROM AUTHOR]

In this paper, the problem of global decentralized output feedback control is addressed for a class of large-scale nonlinear systems with zero dynamics and unknown time-varying delay. System disturbance nonlinearities are subject to feedforward growth restrictions with unknown growth rate. In the spirit of dynamic scaling change technique, a novel pair of time-varying-gain observer and controller is proposed. Compared with the existing results, the controller proposed is capable of handling the difficulties caused by the zero-dynamics, the uncertainties and the unknown time-varying delay. With the help of the Razumikhin theorem, it is shown that the closed-loop states asymptotically converge to zero. Finally, the effectiveness of the proposed control scheme is illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

In this paper, the finite-time stabilization of stochastic coupled systems on networks (SCSNs) is studied. Different from previous research methods, the method used in this paper combines Lyapunov method with graph theory, and some novel sufficient conditions are obtained to ensure finite-time stability for SCSNs. Meanwhile, the convergence time is closely related to topological structure in networks. As a practical application in physics, we address a concrete finite-time stabilization problem of stochastic coupled oscillators through our main results. In addition, a numerical example is presented to illustrate the effectiveness and feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with a kind of first-order singular differential system with impulses. Based on the Schaefer fixed-point theorem, some new verifiable algebraic criteria are given to ensure the controllability of bounded solutions for the considered system. The results obtained in this paper not only achieve the controllability of the singular differential system with impulses for the first time, but also complement the previous researches on singular differential system with impulses. Consequently, the results established are essentially new. Finally, the effectiveness of the obtained results are illustrated via a numerical example. [ABSTRACT FROM AUTHOR]

This paper addressed the problem of asymptotic regional stabilization of a class of two-dimensional mixed Roesser models. Based on the analysis of the polynomial solution of the parameter dependent linear matrix inequality (LMI), the sufficient condition for the existence of the regional stabilization controller is obtained in terms of LMI. Moreover, the robust controller is also given to stabilize the systems with uncertainties in the coefficient matrices of the system. Finally, several numerical simulations are provided to illustrate the efficiency and feasibility of the proposed results in this paper. [ABSTRACT FROM AUTHOR]

In this paper, a framework for designing an event-based sliding mode controller is proposed to track a time-varying reference signal by a single-input, single-output non-linear system. In the proposed method, the control updates are fulfilled using the event-triggered method to decrease the number of control signal updates significantly. The system disturbance is tackled using an sliding mode control (SMC)-based tracker where the finite-time reachability to the sliding surface is guaranteed. Moreover, for the proposed event-based controller, a general triggering criteria is designed which is based on state variables, the reference signal and its derivatives. As a result, the control system is agile enough to track fast maneuvering reference trajectories. Another contribution of this paper is to reduce effectively the computational burden of the controller using the Lipschitz coefficients of non-linear terms. Applicability of the proposed approach is demonstrated via simulation of a control system in tracking acceleration and sinusoidal reference trajectories. [ABSTRACT FROM AUTHOR]

In this paper, we propose a class of simplified background neural networks model with two subnetworks on time scales. Some basic dynamic properties including positive invariance, boundedness, global attractivity and complete convergence of networks are analyzed. The main contributions in this paper are listed as follows: (1) the global attractive set of the model is verified and conditions for global attractivity are derived. (2) Complete convergence for the new networks are proved by constructing a novel energy function on time scales. Finally, three simulation examples are presented to illustrate the feasibility and effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, a class of time-delay fractional optimal control problems (TDFOCPs) is studied. Delays may appear in state or control (or both) functions. By an embedding process and using conformable fractional derivative as a new definition of fractional derivative and integral, the class of admissible pair (state, control) is replaced by a class of positive Radon measures. The optimization problem found in measure space is then approximated by a linear programming problem (LPP). The optimal measure which is representing optimal pair is approximated by the solution of a LPP. In this paper, we have shown that the embedding method (embedding the admissible set into a subset of measures), successfully can be applied to non-linear TDFOCPs. The usefulness of the used idea in this paper is that the method is not iterative, quite straightforward and can be applied to non-linear dynamical systems. [ABSTRACT FROM AUTHOR]

This paper is devoted to the robust consensus tracking problem of second-order nonlinear multi-agent systems (MASs) with the interval uncertain topologies. For the second-order MASs including one leader agent and multiple follower agents, a control protocol is proposed by combining the iterative learning control scheme with the sliding mode control method. By analyzing the convergence of sliding mode variables, the consensus conditions including the unknown eigenvalues and the undetermined weight coefficient are obtained. In order to deal with the difficulties of weight coefficient design caused by the unknown eigenvalues of graphs, a min-max optimization problem is formulated based on the fastest convergence of the λ-norm of sliding mode variables, then the optimal weight coefficient is obtained by solving the min-max optimization problem. Moreover, for the undirected and directed interval uncertain graphs, two algorithms about the optimal weight coefficients are proposed, respectively. Finally, three numerical simulation examples are presented to demonstrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

The event-triggered formation control of first-order continuous multi-agent systems is studied based on complex Laplacian in this paper. Periodic event-triggered control is designed in which continuous communication between agents is not required. For each agent, two different triggering conditions are discussed. The first one relies on the inter-neighboring communication at each verification time, while the second one only need the broadcast states of neighbors at their triggering instants. According to the Lyapunov stability theory and algebraic graph theory, consensus conditions on the verification period and parameters in the triggering conditions are also provided. It is demonstrated that the maximum verification period under two triggering conditions are two times larger than the existing results. And a certain amount of communication between neighbors can be further reduced in the second one. Finally, the simulation examples prove the validity of the results proposed. [ABSTRACT FROM AUTHOR]

In this paper, by the transformation form of the discrete algebraic Riccati equation (DARE), we propose a new inverse-free iterative algorithm to obtain the positive definite solution of the DARE. Furthermore, the monotone convergence is proved and convergence rate analysis is presented for the derived algorithm. Compared with some existing algorithms, numerical examples demonstrate the feasibility and effectiveness of our algorithm. [ABSTRACT FROM AUTHOR]

It is observed that the reduced-order models (ROMs) by some existing limited Gramians-based techniques deviate significantly from the high-order model, resulting in a large approximation inaccuracy. Therefore, this paper introduces a novel solution for finite-frequency model reduction using new frequency-weighted Gramians by employing balanced truncation. This work provides a novel structure of fictitious input and output matrices, resulting in the proposed continuous-time system Gramians. The suggested strategy provides stable ROMs even when input and output weightings are incorporated into the system. Furthermore, the proposed approach is extended with the frequency-interval Gramians, ensuring stable ROMs. The proposed simulation outcomes are compared with other well-known frequency-weighted and frequency-interval Gramians-based techniques using numerical examples to demonstrate the efficacy of the suggested strategies. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the topic of model order reduction (MOR) for coupled systems. At first, an approximation via Laguerre polynomials expansions to controllability and observability gramians for such systems are presented, which provides a low-rank decomposition form whose factors are constructed from a recurrence formula instead of Lyapunov equations. Then, in combination of balanced truncation and dominant subspace projection method, a series of MOR algorithms are proposed that preserve the coupled structures. What's more, some main properties of reduced-order models, such as stability preservation, are well discussed. Finally, three numerical simulations are provided to illustrate the effectiveness of our algorithms. [ABSTRACT FROM AUTHOR]

This paper concerns some spectral properties of the scalar dynamical system defined by a linear delay-differential equation with two positive delays. More precisely, the existing links between the delays and the maximal multiplicity of the characteristic roots are explored, as well as the dominance of such roots compared with the spectrum localization. As a by-product of the analysis, the pole placement issue is revisited with more emphasis on the role of the delays as control parameters in defining a partial pole placement guaranteeing the closed-loop stability with an appropriate decay rate of the corresponding dynamical system. [ABSTRACT FROM AUTHOR]

In this paper, we study the output regulation problem (ORP) of non-linear systems with full-state constraints (FSC). First, in order to deal with the ORP of non-linear systems with FSC, a radical constraint function is proposed to avoid the drawbacks of the barrier Lyapunov functions (BLF) and the logarithmic constraint functions. Then, a control algorithm is proposed based on neural network control method without using the backstepping method, so that all signals of the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB), and the tracking error converge to a small neighbourhood of the origin, and all states of the system can be constrained. Finally, a simulation example illustrates its effectiveness. [ABSTRACT FROM AUTHOR]

For a linear time invariant system, the system stability is equivalent to the stability of the system matrix. Thus, finding the conditions for the matrix stability becomes a key to analysis and design of large-scale linear systems. This paper is aimed at studying the large-scale matrix stability problem by means of matrix partitioning. The sufficient conditions for the large-scale matrix stability are proposed. For matrices with normal block diagonal submatrices, a concise and practical expression for testing matrix stability is derived. Additionally, for block diagonally dominant matrices, a sufficient condition, which is used to determine whether the matrix is stable, is proposed. Finally, numerical examples are provided that not only validate theoretical results obtained in this paper, but also demonstrate the analysis and design of large-scale linear systems. [ABSTRACT FROM AUTHOR]

This paper investigates the quadratic optimal control problem for constrained Markov jump linear systems with incomplete mode transition probability matrix (MTPM). Considering original system mode is not accessible, observed mode is utilized for asynchronous controller design where mode observation conditional probability matrix (MOCPM), which characterizes the emission between original modes and observed modes is assumed to be partially known. An LMI optimization problem is formulated for such constrained hidden Markov jump linear systems with incomplete MTPM and MOCPM. Based on this, a feasible state-feedback controller can be designed with the application of free-connection weighting matrix method. The desired controller, dependent on observed mode, is an asynchronous one which can minimize the upper bound of quadratic cost and satisfy restrictions on system states and control variables. Furthermore, clustering observation where observed modes recast into several clusters, is explored for simplifying the computational complexity. Numerical examples are provided to illustrate the validity. [ABSTRACT FROM AUTHOR]

The frequency-weighted model order reduction techniques are used to find a lower-order approximation of the high-order system that exhibits high-fidelity within the frequency region emphasized by the frequency weights. In this paper, we investigate the frequency-weighted |$\mathcal{H}_2$| -pseudo-optimal model order reduction problem wherein a subset of the optimality conditions for the local optimum is attempted to be satisfied. We propose two iteration-free algorithms, for the single-sided frequency-weighted case of |$\mathcal{H}_2$| -model reduction, where a subset of the optimality conditions is ensured by the reduced system. In addition, the reduced systems retain the stability property of the original system. We also present an iterative algorithm for the double-sided frequency-weighted case, which constructs a reduced-order model that tends to satisfy a subset of the first-order optimality conditions for the local optimum. The proposed algorithm is computationally efficient as compared to the existing algorithms. We validate the theory developed in this paper on three numerical examples. [ABSTRACT FROM AUTHOR]

This paper considers the problem of representing a sufficiently smooth non-linear dynamical [system] as a structured potential-driven system. The proposed method is based on a decomposition of a differential one-form associated to a given vector field into its exact and anti-exact components, and into its co -exact and anti-coexact components. The decomposition method, based on the Hodge decomposition theorem, is rendered constructive by introducing a dual operator to the standard homotopy operator. The dual operator inverts locally the co-differential operator, and is used in the present paper to identify the symplectic structure of the dynamics. Applications of the proposed approach to gradient systems, Hamiltonian systems and generalized Hamiltonian systems are given to illustrate the proposed approach. Finally, integrability conditions for generalized Hamiltonian systems are established using the proposed decomposition. [ABSTRACT FROM AUTHOR]