A class of robust consensus algorithms with predefined‐time convergence under switching topologies

Abstract

Summary This paper addresses the robust consensus problem under switching topologies. Contrary to existing methods, the proposed approach provides decentralized protocols that achieve consensus for networked multiagent systems in a predefined time. Namely, the protocol design provides a tuning parameter that allows setting the convergence time of the agents to a consensus state. An appropriate Lyapunov analysis exposes the capability of the current proposal to achieve predefined‐time consensus over switching topologies despite the presence of bounded perturbations. Finally, this paper presents a comparison showing that the suggested approach subsumes existing fixed‐time consensus algorithms, which allows to provide extra degrees of freedom to obtain predefined‐time consensus protocols with improved convergence characteristics, for instance, to reduce the slack between the true convergence time and the predefined upper bound. Numerical results are given to illustrate the effectiveness and advantages of the proposed method.

Enhancing the settling time estimation of a class of fixed‐time stable systems

“…As future work, we consider the case of consensus algorithms, online differentiators, observers, and controllers satisfying prescribed‐time and prescribed‐performance objectives. The extension to fixed‐time stability analysis of high‐order systems will also be considered in the future.…”

“…= 0. The function ∶ ℝ n → ℝ n is assumed to be nonlinear and continuous, and the origin is assumed to be an equilibrium point of system (6), so f(0; ) = 0. Let us first recall some useful definitions and lemma on finite-time, fixed-time, and predefined-time stability.…”

“…For the parameter vector of system (6) and an arbitrarily selected constant T c ∶= T c ( ) > 0, the origin of (6) is said to be predefined-time stable if it is fixed-time stable and the settling-time function T ∶ ℝ n → ℝ is such that…”

On the design of nonautonomous fixed‐time controllers with a predefined upper bound of the settling time

“…Recently, there has been a great deal of attention in the control community on the analysis of a class of systems, known as fixed‐time stable systems, because they exhibit finite‐time convergence with an upper bound of the settling time (UBST) that is independent of the initial conditions of the system 1-5 . This effort has produced many contributions on algorithms with the fixed‐time convergence property, such as multiagent coordination, 6-9 distributed resource allocation, 10 synchronization of complex networks, 11,12 stabilizing controllers, 1,13-16 state observers, 17 and online differentiation algorithms 18,19 …”

Finite-time and fixed-time input-to-state stability: Explicit and implicit approaches

“…In the case of finite-time stability, the system's trajectories converge exactly to zero in a finite amount of time [4]; in the case of fixed-time stability exact convergence to the origin occurs in a maximum amount of time that is independent of the system's initial state [8,9,10]. Nonasymptotic convergence rates are a major feature in Sliding Mode Control [11,12,13,14] and some further developments in non-asymptotic convergence include a bound on the convergence time that is not only fixed but also arbitrarily selected [15,16,17], a better control performance when initial conditions are far away from the origin by separating low and high growing terms [18,19] and finite-time stable controllers with an enhancement of the domain of attraction for state-constrained systems [20]. Although systems with nonasymptotic rates of convergence may exhibit numerical inconsistencies [21] or lose some of its properties under discretization algorithms [22], recent advances in consistent discretization provide algorithms that overcome these issues [23,24].…”