In this paper, we study consensus robustness and performance problems for continuous-time multi-agent systems. We consider first-order unstable agents interconnected by an undirected graph, coordinated by a delayed output feedback protocol. Our objectives are twofold. First, we seek to determine the largest range of delay permissible so that the agents may achieve robustly consensus despite variation of the delay length, herein referred to as the delay consensus margin. Second, we attempt to determine consensus error performance quantified under an H 2 norm criterion, which measures the disruptive effect of random nodal noises on consensus. For both problems, we obtain analytical solutions. The explicit expressions provide conceptual insights and exhibit how the agents' unstable pole, nonminimum phase zero, as well as the network topology may limit fundamentally the consensus robustness and performance.

The paper starts from the challenge of the critical cases in difference operator stability for neutral functional differential equations (NFDE). Such cases occur in the NFDE associated to 1 D hyperbolic partial differential equations (PDE) dynamics in Mechanical and Hydraulic Engineering. For some of such applications it resulted that the aforementioned critical (non-asymptotic) stability is connected to the character and level of the energy losses. It is shown that suitable choice of the losses to be taken into account can remove the critical stability properties and give the difference operator the asymptotic stability thus ensuring asymptotic stability for the system’s dynamics and also other asymptotic properties.

This paper addresses the boundary control problem of the transport equation. Namely, we propose a control method, which is merely a delayed output feedback relying on a partial pole placement idea, that consists in assigning an appropriate exponential decay rate to the closed-loop system's solution. The proposed control structure appearing in the transport boundary, which has proven its effectiveness in controlling finite dimensional systems, consists of an autoregressive relation linking the transport equation's input and output. The obtained result provides an analytical lower bound for the solution's exponential decay.

We review some known bounds for eigenvalues of matrices and use similar techniques to derive bounds for nonlinear eigen problems and the eigenvalues for LTI systems with delays as a special case. There are two classes of results. The first are based on Hermitian decompositions, the second on Gershgorin's theorem. The bounds are easily computable. We reflect on implications for stability theory, which may be contrasted with bounds that have been obtained via Riccati stability based on Lyapunov-Krasovskii theory.

This paper proposes a hybrid observer for state estimation over a network. The network provides delayed measurements of the output of the plant at time instants that are not necessarily periodic and are accompanied by timestamps provided by a clock that synchronizes with the clock of the observer in finite time. The proposed observer, along with the plant and communication network, are modeled by a hybrid dynamical system that has two timers, a logic variable, and two memory states to capture the mechanisms involved in the events associated with sampling and arrival of information, as well as the logic in the estimation algorithm. The hybrid model also includes a generic clock synchronization scheme to cope with a mismatch between the clocks at the plant and the observer. Convergence properties of the estimation error of the system are shown analytically and supported by numerical examples.

In this paper, we provide a systematic and constructive way to build a Lyapunov-Krasovskii functional for time-delay systems whose stability can be established through the Razumikhin or the Halanay approaches. The constructed Lyapunov-Krasovskii functional turns out to be coercive, meaning sandwiched between functions of the state history norm, and to dissipate in terms of the whole history norm. We present these results in the framework of input-to-state stability (ISS) in order to further account for the influence of input disturbances. A special emphasis is also given on exponential stability and exponential ISS. We illustrate our findings though the study of a coupled ODE-PDE model of a chemical reactor, and show that, unlike most results in that area, our approach happens to ensure ISS in terms of the supremum norm of the state.

This paper handles the identification of nonlinear systems through linear time-varying (LTV) approximation. The mathematical form of the nonlinear system is unknown and regenerated through an experiment followed by LTV and linear parameter-varying (LPV) estimation and integration. By employing a well-designed experiment the linearized model of the nonlinear system around a time-varying trajectory is obtained. The result is an LTV approximation of the nonlinear system around that trajectory. Having estimated the LTV model, an LPV model is identified. It is shown that the parameter-varying (PV) coefficients of this LPV model are partial derivatives of the nonlinear system evaluated at the trajectory. In this paper, we will show that there exists a relation between the LPV coefficients. This structural relation in the LPV model ensures the integrability of PV coefficients for nonlinear reconstruction. Indeed, the vector of the LPV coefficients is the gradient of the nonlinear system evaluated at the trajectory. Then, the nonlinear system is reconstructed through symbolic integration of the coefficients. The proposed method is a data-driven scheme that can reconstruct an estimate of the nonlinear system and its mathematical form using input-output measurements. Finally, the use of the proposed method is illustrated via a simulation example.

This paper presents two novel mixed-uncertainty state estimators for discrete-time descriptor linear systems, namely linear time-varying mixed-uncertainty filter (LTVMF) and linear time-invariant mixed-uncertainty filter (LTIMF). The former estimator is based on the minimum-variance approach, from which quadratic and explicit formulations are derived and addressed to LTI and LTV systems. Both formulations incorporate the knowledge of state linear constraints, such as equality (in the descriptor form) and inequality, to mitigate precision and accuracy issues related to initialization and evolution of the state estimates. The explicit version is developed to reduce the computational burden of quadratic solvers, which is based on a particularity of the state inequality constraints. The LTIMF algorithm is based on the mixed H 2 / H ∞ criterion motivated by performing low-cost computations. This speed benefit is originated from a reachability analysis involving constant design matrices. Both LTVMF and LTIMF algorithms solve state-estimation problems in which the uncertainties are combined to yield the so-called mixed-uncertainty vector, which is composed by set-bounded uncertainties, characterized by constrained zonotopes, and stochastic uncertainties, characterized by Gaussian random vectors. As mixed-uncertainty vectors imply biobjective optimization problems, we innovatively present multiobjective arguments to justify the choice of the solution on the Pareto-optimal front. According to these arguments, LTVMF is introduced with a cost normalization, which enables the combination of beyond minimum-variance approaches. Likewise, the mixed H 2 / H ∞ criterion of LTIMF is introduced with slack variables to improve the quality of the state estimates. In order to discuss the advantages and drawbacks, the state estimators are tested in two numerical examples.

This paper aims to develop a robust decomposed system control (RDSC) strategy under input constraints for an electro-mechanical linear actuator (EMLA) with model uncertainty and external disturbances. At first, a state-space model of a complex multi-stage gearbox EMLA system, driven by a permanent magnet synchronous motor (PMSM), is developed, and the non-ideal characteristics of the ball screw are presented through the model. This results in a six-order nonlinear strict-feedback form (NSFF) system that is decomposed into three subsystems. As the paper’s main result, a novel RDSC strategy with uniform exponential stability for controlling subsystem states is presented. This developed controller avoids the “explosion of complexity” problem associated with backstepping by treating the time derivative of the virtual control input as an uncertain system term. The proposed method, while assuming load disturbances and input constraints with arbitrary bounds, offers a straightforward control approach for a broader range of applications. The controller’s performance is evaluated through the simulation of two distinct duty cycles, each representing different levels of demand on the actuator facing load disturbances near the rated motor performance.

In the emergency rescue and disposal of social public emergencies, supply transportation effectively provides a strong supply foundation and realistic conditions. The trajectory tracking control of emergency supplies transportation robot is the key technology to ensure the timeliness of transportation. In this paper, the emergency supplies transportation robot is taken as the research object, based on Koopman operator theory, combined with radial basis function (RBF) neural network disturbance observer and adaptive prediction horizon event-triggered model predictive control (APET-MPC) algorithm to investigate the purely data-driven trajectory tracking control problem of emergency supplies transportation robot when the model parameters and models are unknown. Firstly, the Koopman operator is used to establish a high-dimensional linear model of the robot. Secondly, the RBF neural network disturbance observer is designed to estimate the disturbance during the robot operation and compensate it to the controller. Thirdly, APET-MPC is used to optimize the trajectory tracking control of the emergency supplies transportation robot to reduce computational complexity. Finally, the performance of the proposed trajectory tracking controller is verified by Carsim/ Simulink joint simulation. The simulation results show that the model established by Koopman operator theory can achieve the high accuracy approximation of the robot. Compared with the MPC trajectory tracking controller, the APET-MPC trajectory tracking controller based on RBF neural network disturbance observer (RBF-APET-MPC) improves the tracking accuracy of the robot and reduces the total triggering times of the system by more than 50%.

The robustness of a linear system in the view of parametric variations requires a stability analysis of a family of polynomials. If the parameters vary in a compact set A, then obtaining necessary and sufficient conditions to determine stability on the family F A is one of the most important tasks in the field of robust control. Two interesting classes of families arise when A is a diamond or a box of dimension n+1. These families will be denoted by F D n and F B n , respectively. In this paper a study is presented to contribute to the understanding of Hurwitz stability of families of polynomials F A . As a result of this study and the use of classical results found in the literature, it is shown the existence of an extremal polynomial f ( α ∗ , x ) whose stability determines the stability of the entire family F A . In this case f ( α ∗ , x ) comes from minimizing determinants and sometimes f ( α ∗ , x ) coincides with a Kharitonov’s polynomial. Thus another extremal property of Kharitonov’s polynomials has been found. To illustrate the versatility/generality of our approach, this is addressed to families such as F D n and F B n , when n≤5. Furthermore, the study is also used to obtain the maximum robustness of the parameters of a polynomial. To exemplify the proposed results, first, a family F D n is taken from the literature to compare and corroborate the effectiveness and the advantage of our perspective. Followed by two examples where the maximum robustness of the parameters of polynomials of degree 3 and 4 are obtained. Lastly, a family F B 5 is proposed whose extreme polynomial is not necessarily a Kharitonov’s polynomial.

In this paper, we consider the non-fragile containment control problem of nonlinear multi-agent systems (MASs) with exogenous disturbance where the communication links among agents under consideration is directed. Firstly, based on relative output measurements between the agent and its neighbors, a disturbance observer-based control protocol is proposed to solve the containment control problem of MASs with inherent nonlinear dynamics and exogenous disturbances. Secondly, because of the additional tuning of parameters in the real control systems, uncertainties in the designing of observer and controller gains always occur, and as a result, an output feedback controller with disturbance rejection is conceived and the containment control problem of nonlinear MASs with non-fragility is thoroughly investigated. Then, depending on matrix transformation and inequality technique, sufficient conditions of the designed controller gains exist, which is derived from the asymptotic stability analysis problem of some containment error dynamics of MASs. Finally, two simulation examples are exploited to illustrate the effectiveness of the proposed techniques.

This study proposes a fault estimation and tolerant anti-disturbance switching control (ADSC) approach for the switched systems subject to the system fault and multiple disturbances. The fault dose not required to have a model.The disturbances contain the modeled unmeasurable part and the unmodeled measurable part. First, a composite switching estimator is constructed to simultaneously estimate the unavailable system state, fault and modeled disturbance. Then, by means of the estimator, a switching controller is developed to tolerant the fault and complement the modeled disturbance. Further, under the dwell time relevant switching signals, criteria are established to ensure the fault estimation performance and robustness property for the switched systems. Finally, via implementing the presented fault estimation and tolerant ADSC scheme on a switched circuit system to regulate the charge and flux, the reasonability of the established result is verified.

In recent works, well-known three-dimensional localization methods studied in the aerospace field have been revisited for applications on multirotor aerial vehicles (MAVs). However, most of these classic methods employ stochastic estimators that are asymptotically stable, in a stochastic sense, and exhibit high sensitivity to disturbances and model uncertainties. The goal of this paper is to propose and evaluate a novel solution to the localization problem of MAVs, employing multivariable robust observers based on sliding-mode techniques. Aiming to improve on the existing methods usually based on the extended Kalman filter, this paper investigates sliding-mode techniques to reach finite-time stabilization of the estimation error and provide robustness to disturbances and uncertainties. The super-twisting algorithm (STA) is considered as a starting point for its recognized performance when used to design differentiators. In particular, a modification of the STA is proposed, replacing one of its terms with a certain time-varying function that allows the upper bound of the settling time of the resulting algorithm to be a direct adjustable parameter. The proposed algorithm’s behavior is numerically evaluated and is shown to yield the predicted properties even in the presence of bounded disturbances and uncertainties. Additionally, an attitude determination problem employing the proposed algorithm is presented as an application. The three-dimensional attitude and angular velocity of an MAV are accurately estimated under strict settling-time restrictions, using only the vector measurements provided by an accelerometer and a magnetometer.