Nature-inspired and teaching-learning-based methods for improving convergence speed in multi-agent systems

Nature-inspired and teaching-learning-based methods for improving convergence speed in multi-agent systems

Ramin Fotouhi, Mahdi Pourgholi


This paper suggests a novel method for inverse optimal control of the multi-agent systems (MAS) via a linear quadratic regulator (LQR) based on meta-heuristic algorithms. In this regard, first, the consensus protocol is designed and then the cost function is optimized via Jaya algorithm (JA), teaching-learning algorithm (TLBO), a novel meta-heuristic algorithm called advanced teaching-learning (ATLBO) and water cycle algorithm (WCA). ATLBO consists of two phases with two random values in both phases which affect the convergence rate. The optimal value of the controller’s parameter is obtained via these algorithms. Simulation outputs show the usefulness of nature-inspired and learning-based methods to calculate the cost with a better convergence rate. This research consists of an inverse optimal control approach and meta-heuristic algorithms for solving the consensus problem with the least cost.


Control systems, optimal control, multi-agent systems, algorithms, distributed systems


  • [1] Y. Cao and W. Ren, "LQR-based optimal linear consensus algorithms," American Control Conference, pp. 5204-5209, 2009
  • [2] Y. Cao and W. Ren, "Optimal Linear-Consensus Algorithms: An LQR Perspective," in IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 40, no. 3, pp. 819-830, June 2010.
  • [3] B. Mu and Y. Shi, "Distributed LQR Consensus Control for Heterogeneous Multiagent Systems: Theory and Experiments," in IEEE/ASME Transactions on Mechatronics, vol. 23, no. 1, pp. 434443, 2018.
  • [4] Y. Li, H. Yang, Y. Yang, Y. Liu, and Y. Sun, “LQR-Based Optimal Leader-Following Consensus of Heterogeneous Multi-agent Systems,” Lecture Notes in Electrical Engineering Proceedings of 2019 Chinese Intelligent Systems Conference, pp. 122–130, 2019.
  • [5] R. Fotouhi and M. Pourgholi, "Discrete-time Inverse Optimal Control for Consensus of Multi-Agent Systems via a Novel Meta-Heuristic Algorithm," 2021 7th International Conference on Control, Instrumentation and Automation (ICCIA), pp. 1-5, 2021.
  • [6] R. Fotouhi and M. Pourgholi, "Water Cycle Algorithm-Based Control for Optimal Consensus Problem," 2021 26th International Computer Conference, Computer Society of Iran (CSICC), pp. 1-5, 2021.
  • [7] F. Chen and J. Chen, "Minimum-Energy Distributed Consensus Control of Multiagent Systems: A Network Approximation Approach," in IEEE Transactions on Automatic Control, vol. 65, no. 3, pp. 1144-1159, 2020.
  • [8] W. Ren and R. W. Beard, “Consensus seeking in multi-agent systems under dynamically changing interaction topologies,” IEEE Transactions on Automatic Control, vol. 50, no. 5, pp. 655–661, 2005.
  • [9] R. Olfati-Saber, J. A. Fax, and R. M. Murray, “Consensus and Cooperation in Networked Multi-Agent Systems,” Proceedings of the IEEE, vol. 98, no. 7, pp. 1354–1355, 2010.
  • [10] R. V. Rao, “Jaya: A simple and new optimization algorithm for solving constrained and unconstrained optimization problems,” International Journal of Industrial Engineering Computations, pp. 19–34, 2016.
  • [11] R.V. Rao, V. J. Savsani, and D. P. Vakharia, “Teaching-Learning- based optimization: A novel method for constrained mechanical design optimization problems,” Computer-Aided Design, vol. 43, no. 3, pp. 303-315, 2011.
  • [12] H. Eskandar, A. Sadollah, A. Bahreininejad, and M. Hamdi. "Water cycle algorithm–A novel metaheuristic optimization method for solving constrained engineering optimization problems." Computers & Structures, Vol. 110, pp. 151-166, 2012.