ORIGINAL ARTICLE Generalized BELBIC Ehsan Lotfi 1 • Abbas Ali Rezaee 2 Received: 23 November 2016 / Accepted: 5 January 2018 Ó The Natural Computing Applications Forum 2018 Abstract Brain emotional learning-based intelligent controller (BELBIC) is a developed class of model-free learning controllers (MFC), which has been inspired from the MFC mechanism of human brain. BELBIC suffers from a major drawback that is related to the learning module. The learning module of BELBIC is not universal approximator and cannot be used for model-based applications. In this paper, a generalized BELBIC (G-BELBIC) is proposed which is inspired from a model- based learning controller (MBC) of brain. In contrast to BELBIC, proposed G-BELBIC applies a nonlinear learning module with universal approximation (UA) property and can be applicable in various MBC engineering applications. The UA proof and stability analysis of G-BELBIC are presented, and the novel controller is tested on single-link robot arm and continuous stirred tank reactor as case studies. Comparative results indicate the superiority of the approach in terms of higher control accuracy and robustness property. Keywords BEL  BELBIC  Emotional controller  Bio-inspired controller  Model-based control  Robust controller 1 Introduction Brain emotional learning-based intelligent controller (BELBIC) [1, 2] is a developed class of bio-inspired model-free learning controllers (MFC) which has been successfully incorporated in PID controller [3], aerospace launch vehicle controller [4], omnidirectional robot [5], load–frequency control [6, 7] and many other engineering applications [8–13]. The learning module of BELBIC has been named brain emotional learning (BEL). BEL is an attempt to formulate the working mechanism of limbic system [1], and BELBIC is motivated by the MFC mech- anism of human’s brain. In human’s brain, there are two main approaches to learning control. The first is MFC, and the second is related to model-based learning controller (MBC) [14, 15]. The orbitofrontal cortex and amygdala region of the brain are involved in both MFC and MBC approaches [14–16], while cerebellum and some regions of neocortex are nec- essary only for MBC [14, 15]. The learning module of BELBIC (i.e., BEL) consists of amygdala, OFC and some other regions, and does not include the cerebellum and neocortex. As a result, BELBIC is a MFC model and cannot be applied for many MBC applications. In this paper, we aim to generalize BELBIC through the MBC approach and examine the resulting model in model predictive control application domains. In other words, the main novelty of the paper is to develop a generalized version of BELBIC that can be applied in many model- based applications and can increase their tracking control accuracy. Here, we examine our generalized BELBIC (G- BELBIC) on robot arm and stirred tank reactor problems and as a contribution of this paper, their tracking error decreases here. Additionally, as illustrated in this paper, the proposed G-BELBIC is a robust controller that can be applicable in a noisy environment. The organization of the paper is as follows: BELBIC is presented in Sect. 2. The G-BELBIC, its universal approximation (UA) property and stability analysis are proposed in Sect. 3. The Simulink implementation of proposed G-BELBIC is detailed in Sect. 4. Experimental & Ehsan Lotfi elotfi@bitools.ir; esilotf@gmail.com Abbas Ali Rezaee A_rezaee@pnu.ac.ir 1 Department of Computer Engineering, Torbat-e Jam Branch, Islamic Azad University, Torbat-e Jam, Iran 2 Department of Computer Engineering and Information Technology, Payam-e Noor University, P.O. BOX 19395-3697, Tehran, Iran 123 Neural Computing and Applications https://doi.org/10.1007/s00521-018-3352-1