Distributed finite‐time optimisation algorithm for second‐order multi‐agent systems subject to mismatched disturbances

Abstract

In this study, the distributed finite-time optimisation problem is investigated for second-order multi-agent systems subject to mismatched disturbances. The whole control design is conducted within a feedforward–feedback composite control framework, which consists of two main sessions. In the first session, based on homogeneous systems theory, a finite-time optimisation control algorithm is presented for a nominal second-order single system with a quadratic cost function. In the second session, via the result in the first session and by combining finite-time disturbance observer, homogeneous systems theory, integral sliding-mode control, and distributed finite-time estimator techniques together, a distributed finite-time optimisation control algorithm is proposed for second-order multi-agent systems with mismatched disturbances and quadratic local cost functions. Under the proposed control algorithm, the outputs of all the agents reach finite-time consensus on the minimiser of the global cost function. Simulations demonstrate the effectiveness and superiority of the proposed distributed finite-time optimisation control algorithm.