Finite‐time consensus of Euler‐Lagrange agents without velocity measurements via energy shaping

Abstract

Summary Motivated by the energy‐shaping framework and the properties of homogeneous systems, this paper deals with the problem of achieving consensus of multiple Euler‐Lagrange (EL) systems using the energy shaping plus damping injection principles of passivity‐based control. We propose a method to derive a novel family of decentralized controllers that is capable of solving the leaderless and the leader‐follower consensus problems in finite‐time in networks of fully actuated EL systems without employing velocity measurements. As in the energy‐shaping methodology, the controller is another EL system and the plant‐controller interconnection is the gradient of a suitable defined potential function. The potential energy and dissipation functions, of the controller, are provided with some homogeneous properties in order to achieve finite‐time convergence. This paper provides several simulations that corroborate the performance of different controllers.

Consensus-Based Formation Control of Multiple Nonholonomic Vehicles Under Input Constraints

“…Convergence: Assume, for the time being, that α i ≡ 0 for all i ∈ N . Then, a simple inspection of (19) shows that Ẅ ∈ L ∞ and, invoking Barbalǎt's Lemma, we conclude that Ẇ → 0, which implies in turn that lim t→∞ ω i (t) = 0. The same conclusion is drawn for ωi , after differentiating on both sides of ( 16) and observing that ωi is uniformly bounded.…”

“…An efficient recourse is to use saturated controllers to ensure that the inputs satisfy pre-imposed bounds [17]. Similar techniques have been also used for multiagent systems [18], [19], but more scarcely for networked nonholonomic vehicles. This is done, e.g., in [1], but only partial consensus is addressed.…”

Adaptive extreme learning machine‐based event‐triggered control for perturbed Euler–Lagrange systems

“…While the control function 𝜏 1 (t) in ( 17) is designed to eliminate the effects of perturbations caused by disturbances, estimate errors from the ELM network, and measurement errors from the event-triggered mechanism within a finite-time. It should be pointed out that the control gain parameter 𝜂 in ( 17) is selected together with the parameter 𝜆 based on the condition in (27) to make 𝜁 as large as possible for obtaining more relaxed triggering condition from (22). Besides, the adaptive weightings 𝛾 1 and 𝛾 2 in ( 19)-( 20) can affect the compensation ability of the controller.…”

“…To list a few, the finite‐time consensus and coordination behaviors of multiple Euler–Lagrange systems were studied in References 24‐26 by designing distributed control protocols in the cases of external disturbances, cooperation‐competition networks, and communication delays, respectively. Decentralized energy‐shaping control methodologies were developed in Reference 27 to obtain finite‐time consensus convergence of the networked Euler–Lagrange systems. Fault‐tolerant finite‐time control problem of Euler–Lagrange systems was addressed in References 28 and 29 to deal with modeling uncertainties, disturbances, and actuator faults by using adaptive control technique.…”

Cooperative fencing control of multiple second‐order vehicles for a moving target with and without velocity measurements

“…Recently, the authors in Reference 37 designed an equal-distance control method for a group of second-order nonlinear surface vessels to encircle multiple moving targets, where a decentralized estimator was introduced to estimate the center position and velocity of the target set. Also, these years have witnessed some effort on the consensus control [38][39][40][41] for second-order vehicles without velocity measurements.…”