Discrete-time Inverse Optimal Control for Consensus of Multi-Agent Systems via a Novel Meta-Heuristic Algorithm

This paper illustrates a novel perspective for inverse optimal control of the multi-agent systems (MAS) via a linear quadratic regulator (LQR) based on Jaya algorithm (JA), teaching-learning algorithm (TLBO) aSnd a novel meta-heuristic algorithm which is called advanced teaching-learning (ATLBO). In this regard, first the consensus protocol is designed and then the cost function is optimized via meta-heuristic algorithms for finding the consensus controller. The Laplacian matrix is a key tool in this paper, and this research sheds light on the fact that the Laplacian matrix is inverse optimal for the related cost function. Moreover, this paper shows that the LQR approach based on these three meta-heuristic algorithms leads all agents to reach the optimal consensus. The novel meta-heuristic algorithm (ATLBO) optimizes the cost function faster than the other mentioned algorithms therefore it decreases the runtime for the problem. Also, the combination of inverse optimal control approach and meta-heuristic algorithms is suggested for solving the consensus problem considering the least cost. Finally, simulation results illustrate the usefulness of the novel algorithm and method.