Finite-time adaptive optimal consensus control for multi-agent systems subject to time-varying output constraints

• Published in: Applied mathematics and computation Vol. 427; p. 127176
• Main Authors: Xu, Jiahong, Wang, Lijie, Liu, Yang, Sun, Jize, Pan, Yingnan
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.08.2022
• Subjects: Adaptive optimal control; Finite-time control; Time-varying constraints; Finite-time control; Adaptive optimal control; Time-varying constraints
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2022.127176

•By designing proper barrier functions, the output of every follower is successfully constrained in the desired time-varying set. Compared with most existing constraint control strategies, the dynamic output constraint problem considered in this paper is a more general case. Here, the constraint boundary functions can be asymmetric, or have the same symbol, or even one of the boundary functions is equal to zero. Therefore, the proposed control strategy is more in line with the practical engineering requirements.•Compared with the existed optimal control algorithms with infinite-time convergence, the proposed control protocol can not only achieve the goal of optimization under worst-case perturbations, but also guarantee the stability of MASs in the finite time, which effectively accelerates the convergence rate.•In order to reduce the complexity of the network weights updating algorithm, a new positive function is constructed in the RL algorithm proposed in this paper to simplify the design of adaptive learning rules. Meanwhile, the persistent excitation condition that is difficult to verify online is no longer needed. In this paper, a finite-time optimal consensus control strategy is presented for unknown multi-agent systems (MASs) with the time-varying asymmetric output constraint. Different from existing results, the output constraint problem investigated here eliminates the requirements that constraint boundary functions must be strictly non-zero and have different signs, which is successfully handled by introducing special barrier functions. Moreover, to deal with disturbances well, a reinforcement learning (RL) with the critic-actor-disturbance structure is introduced. Meanwhile, the weights of neural networks are adjusted online by applying the gradient descent method to positive functions newly constructed, which not only significantly simplifies the algorithm but also eliminates the persistent excitation condition. For obtaining a fast convergence rate, the finite-time control technique is embedded into the RL algorithm, and an effective finite-time optimal control scheme is proposed to achieve the consistency of multi-agent system in a finite time. Finally, the effectiveness of the proposed protocol is demonstrated by two simulation examples.