European Journal of Control最新文献

This paper introduces an algorithm for estimating the invariant set of closed-loop controlled dynamical systems identified using single-hidden layer Rectified linear units (ReLU) neural networks or piecewise affine ($\mathrm{PWA}$) functions, particularly addressing the challenge of providing safety guarantees for single-hidden layer ReLU networks commonly used in safety–critical applications. The invariant set of $\mathrm{PWA}$ dynamical system is estimated using single-hidden layer ReLU networks or its equivalent $\mathrm{PWA}$ function. This method entails formulating the barrier function as a $\mathrm{PWA}$ function and converting the search process into a linear optimization problem using vertices. We incorporate a domain refinement strategy to increase flexibility in case the optimization does not find a valid barrier function. Moreover, the objective of the optimization is to find a less conservative invariant set based on the current partition. Our experimental results demonstrate the effectiveness and efficiency of our approach, demonstrating its potential for ensuring the safety of $\mathrm{PWA}$ dynamical systems.

In this study, an equivalent-input-disturbance (EID) method with a dynamic state observer and a state decomposition technique (SDT) are used to explore the disturbance rejection of a class of linear switched singular systems. The EID approach defines an EID signal, is defined for the control input channel and has the same impact on the system as exogenous disturbances. Additionally, it employs an observer to estimate the EID and achieves good disturbance-rejection performance. However, in the EID method, the coefficient matrix of the observer needs to be consistent with the coefficient matrix of the original system, which limits the application of the method. So, a dynamic state observer is designed to reconstruct the system state and estimate the disturbance in this study. Based on the state feedback control strategy, a disturbance-rejection control law containing disturbance information is designed and a closed-loop control system structure is established. Subsequently, the state equation of the closed-loop system is reorganized and decomposed into an algebraic equation and a differential equation using the SDT. Then, a Lyapunov function with few decision variables is designed to obtain an admissible criterion for the closed-loop system and the controller gains under arbitrary switching signals. Finally, the effectiveness of the presented method is verified via numerical simulations.

This study focuses on the event-triggered finite-time extended dissipative control for the switched linear neutral systems with time-varying delays and frequent asynchronism. In comparison to previous event-triggered control, which restrict the minimum dwell time, we allow frequent switching to occur within an inter-event interval based on average dwell time (ADT) approach. Firstly, given the challenge of acquiring all information about the state, a dynamic output feedback controller (DOFC) is adopted to stabilize the switched neutral system. Secondly, the subjects of finite-time boundedness and extended dissipative performance for the resulting closed-loop system are analyzed by means of controller-mode-dependent Lyapunov functional. Furthermore, a lemma is applied to establish the sufficient criteria for co-designing the DOFC and mode-dependent event-triggered mechanism (ETM). Additionally, it is demonstrated that the Zeno phenomenon cannot occur since there exists a positive minimum threshold on the inter-event intervals. Finally, two examples are given to illustrate the efficacy of the obtained methods.

This paper presents a framework to design a robust dynamic output feedback (DOF) controller for a class of nonlinear systems, based on the adaptive event-triggered control (AETC) method. The considered system contains parametric uncertainty and to design the event-triggered mechanism (ETM) Finite-gain $L_2$ stability criteria are used. In this paper, a robust adaptive event-triggered mechanism (AETM) is first designed using a pre-designed controller. Then, in a co-design approach, the AETM and the DOF controller are designed together to increase the closed-loop performance. Indeed, the matrices of the DOF controller and the sufficient conditions for the AETM are obtained simultaneously. These conditions are represented as linear matrix inequalities (LMIs) and lead to a significant increase in the update interval. Moreover, the proposed design method guarantees the stability of the closed-loop system in the presence of the proposed triggering event. Finally, to illustrate the performance of the controller three examples are simulated.

A robust adaptive control law is designed for the class of nonlinear systems with uncertain time-varying parametric dynamics and input delays. The Constitution of control law design is based on filtered tracking errors, previous values of control input and estimate of uncertain parameters which is updated by the update law. An arbitrary large input delay compensation is guaranteed by deriving sufficient control gain conditions using Lyapunov–Krasovskii based stability analysis. The efficacy of the design is verified by Simulation results of two-link robot manipulator dynamical system.

Accurate state estimation plays a critical role in various applications, such as tracking, regulation, and fault detection in robotic and mechanical systems. Typically, the Kalman–Bucy filter is used as a linear state observer for this purpose. However, real-world robots often exhibit complex behavior, characterized by a combination of dynamics, making it essential to employ hybrid filters. In this context, the Switching Kalman filter stands out as a well-established solution. In this article we aim to generalize the Brownian-Markov Stochastic Model, a hybrid dynamic model for differential-drive wheeled mobile robots, to the case of a mobile robot whose center of mass is not aligned to the wheels axle middle point, and to design a geometric hybrid state estimator by exploiting the Lie groups theory. The Brownian-Markov Stochastic Model features two modes: “grip” and “slip”. These modes correspond to ideal grip and lateral slippage, with transitions governed by a state-dependent Markov chain. To validate the proposed switching filter, we conduct MATLAB® simulations of the robot’s motion in a scenario prone to lateral grip loss, comparing the state estimates produced by the switching geometric filter with those obtained using the switching Kalman filter.

We propose necessary and sufficient conditions for the synchronization of $N$ identical single-input–single-output (SISO) systems, connected through a directed graph without imposing any assumption on the graph interconnection. We consider both the continuous-time and the discrete-time case, and we provide conditions that are equivalent to the uniform global exponential stability, with guaranteed convergence rate, of the closed and unbounded attractor that corresponds to the synchronization set.

In this paper, we present a reaction–diffusion population model developed for a polluted environment, and investigate the impact of different control measures on population-toxicant dynamics. Toxicant concentrations is taken as the reference to determine whether to implement control measures, and sliding mode dynamics are studied. The dynamical behaviors of each subsystem are discussed, and results show that model solutions ultimately approach either two endemic equilibria or the sliding equilibrium on a surface of discontinuity. Furthermore, we formulate the near-optimal control problem by minimizing the control cost while reducing the toxicant concentration. The sufficient and necessary conditions for the near-optimality are established using Ekeland’s variational principle and Hamiltonian function. The theoretical results are illustrated by numerical simulations.

A stochastic linear-quadratic (LQ for short) problem with anticipative (i.e., not adapted) partial observations is studied. With the help of enlargement of filtration, we turn the anticipative signal observation system into a higher-dimensional adapted one, and obtain a linear filtering equation of the latter by the martingale representation theorem and a related equivalent control problem. By introducing a Riccati equation and an ordinary differential equation, we provide a unique optimal feedback control for another equivalent optimal control problem with the controlled state being the linear filtering equation. Finally, the optimal cost function for the original anticipative LQ problem is obtained, which is represented by the filtering of the extended adaptive system and some modified coefficients. Our result covers that of the classical stochastic LQ problem with adapted partial observations. As an application, the optimal control of an interception problem with anticipative radar tracking is explicitly given.

In this paper, a dynamic event-triggered mechanism (DETM) is designed for uncertain strict-feedback nonlinear systems with an infinite number of actuator faults. An adaptive fault-tolerant control strategy is put forward to accommodate actuator faults. A dynamic variable is introduced into the event-triggered schedule to achieve dynamically regulated threshold parameters and the DETM is recursively established depending on the backstepping technique. The designed control law ensures that all signals of the system are uniformly bounded, and the tracking error converges to a compact set while avoiding Zeno behavior. An expository simulation example reveals the advantages of the presented method.