*Article* **Multi-Agent Reinforcement Learning Using Linear Fuzzy Model Applied to Cooperative Mobile Robots**

### **David Luviano-Cruz 1,\*, Francesco Garcia-Luna 1, Luis Pérez-Domínguez 1 and S. K. Gadi 2**


Received: 5 September 2018; Accepted: 30 September 2018; Published: 3 October 2018

**Abstract:** A multi-agent system (MAS) is suitable for addressing tasks in a variety of domains without any programmed behaviors, which makes it ideal for the problems associated with the mobile robots. Reinforcement learning (RL) is a successful approach used in the MASs to acquire new behaviors; most of these select exact Q-values in small discrete state space and action space. This article presents a joint Q-function linearly fuzzified for a MAS' continuous state space, which overcomes the dimensionality problem. Also, this article gives a proof for the convergence and existence of the solution proposed by the algorithm presented. This article also discusses the numerical simulations and experimental results that were carried out to validate the proposed algorithm.

**Keywords:** multi-agent system (MAS); reinforcement learning (RL); mobile robots; function approximation
