International audience

Control and state estimation procedures need to be robust against imprecisely known parameters, uncertainty in initial conditions, and external disturbances. Interval methods and other set-based techniques form the basis for the implementation of powerful approaches that can be used to identify parameters of dynamic system models in the presence of the aforementioned types of uncertainty. Moreover, they are applicable to a verified feasibility and stability analysis of controllers and state estimators. In addition to these approaches which are typically used offline for analysis of system models designed with classical floating point procedures, interval and set-based methods have also been developed in recent years, which allow to directly solve the associated design tasks and to implement reliable techniques that are applicable online, i.e., during system operation. The latter approaches include set-based model predictive control, online parameter adaptation techniques for nonlinear variable-structure and backstepping controllers, interval observers, and fault diagnosis techniques. This paper provides an overview of the methodological background and reviews numerous practical applications for which interval and other set-valued approaches have been employed successfully.

This article presents a solution to the problem of achieving optimal prescribed-time stability and stabilization for nonlinear dynamical systems. In contrast to existing prescribed-time control methods, this article initiates by establishing sufficient conditions for prescribed-time stability through the use of continuous Lyapunov candidate functions. Building upon these conditions, we introduce an optimal prescribed-time stabilization method that incorporates specific differential inequalities. This method complies with the Hamilton-Jacobi-Bellman steady-state equation, ensuring both optimality and prescribed-time stability. Furthermore, we derive a set of optimal prescribed-time stabilizing control laws for a class of affine nonlinear dynamical systems. Finally, we demonstrate the effectiveness of the proposed approach through simulations and experiments involving the reference level tracking of a coupled tank system, thus ensuring that the tracking performance aligns with practical user specificationsNote to Practitioners—This article was instigated by the challenge of devising optimal feedback control strategies for a specific class of nonlinear dynamical systems at predetermined time instances. In recent years, there has been a growing interest in prescribed time stability and stabilization approaches, driven by their potential applications across diverse fields, including control engineering, robotics, and aerospace engineering. These methods facilitate the regulation of nonlinear dynamical systems to reach a desired steady state within a predefined finite time, offering a valuable solution for situations demanding rapid stabilization. In this article, we introduce a novel optimal prescribed-time stabilization method that relies on specific differential inequalities. This method not only adheres to the Hamilton-Jacobi-Bellman steady-state equation but also guarantees both optimality and prescribed-time stability. Furthermore, we derive a family of optimal prescribed-time stabilizing control laws tailored to a particular class of affine nonlinear dynamical systems. To validate the effectiveness of our proposed stabilization approach, we conduct experiments focusing on tracking the desired water level within a coupled tank system. Ultimately, the presented prescribed-time optimal feedback control strategy marks a significant stride forward in the advancement of optimal and efficient control methods for nonlinear dynamical systems, offering solutions that hold immense promise in practical applications.

This paper addresses the secure bipartite consensus control problem for multi-agent systems under denial-of-service (DoS) attacks. A class of aperiodic time-sequence-based DoS attacks is considered, and its impact on both undirected and directed network topologies is analyzed. The stability analysis is conducted using a Lyapunov function approach combined with an iterative method. To reduce energy consumption and prevent Zeno behavior, a hybrid dynamic event-triggered mechanism is introduced. This mechanism incorporates an improved dynamic event-triggering condition, which determines when each agent updates its control signal and transmits its currently triggered state to neighboring agents. The proposed approach integrates this mechanism with the developed distributed control protocol and to ensure bipartite consensus even in the presence of DoS attacks. The effectiveness of the method is demonstrated through two simulation examples.

International audience

The main goal of this article is to design interval observers for continuous nonlinear switched systems. The nonlinear modes are described by the multimodel approach of Takagi-Sugeno (T-S) fuzzy systems where premise variables depending on the state vector that is unmeasurable. In this article, we propose T-S interval observers that consider the unmeasurable premise variables as bounded uncertainties under common assumptions that additive disturbances as well as measurement noises are unknown but bounded. The stability and the nonnegativity conditions are given in terms of linear matrix inequality to ensure simultaneously the convergence and the nonnegativity of error dynamics. Furthermore, in the absence of measurement noises, optimal gains attenuating the effect of additive disturbances are computed using H∞approach to improve the accuracy of the present interval observers. Theoretical results are finally applied to a numerical example to highlight the performance of the proposed method.