Article - Control Transactions of the Institute of Measurement and Control 1–14 Ó The Author(s) 2020 Article reuse guidelines: sagepub.com/journals-permissions DOI: 10.1177/0142331220966308 journals.sagepub.com/home/tim Constrained cuckoo search algorithm and Takagi-Sugeno fuzzy models for predictive control Adel Taeib 1 , Hichem Salhi 2 and Abdelkader Chaari 1 Abstract In this paper, a new predictive control scheme formulated by using the Takagi-Sugeno fuzzy modeling method and a new constrained cuckoo search algorithm. The cuckoo search algorithm is used to determine the predictive controls by minimizing a constrained criterion. The Takagi-Sugeno fuzzy modelling approach is applied to forecast the states of the process. At the optimization stage, the proposed cuckoo search provides the control action taking into account constraints. The performances of the developed method are tested during its application in the three-tank process. Therefore, the experimental results demonstrate that the combination of the philosophy of the fuzzy model and cuckoo search is very good in the controlling of non- linear processes. In addition, the closed-loop performance of the developed method is compared to approach based with the particle swarm optimisa- tion algorithm and those obtained with fuzzy model predictive controller. Keywords Model predictive control, adaptive Takagi-Sugeno fuzzy model, cuckoo search algorithm, three tank system Introduction Model predictive control (MPC) has been an active field of research during the last eight decades thanks to its ability to deal with control challenges such as hard nonlinearity, large delay time and constrained variables (Clarke et al., 1987; Licheng et al., 2010; Miladi et al., 2019). The MPC strategy is based on the use of an explicit model to predict the process future behaviour over a finite horizon and then to compute a sequence of future control actions by minimizing a given cost function (Arahal et al., 2019; Thamallah et al., 2019). This optimization determines the best values to be applied in the consequent sample times. However, only the first input is applied and the problem is reoptimized for each sample step. Linear MPC techniques, which use a linear model for the pro- cess, have been successfully used in many industrial applica- tions (Espinosa et al., 2005; Licheng et al., 2010). However, the majority of the industry processes are nonlinear where some of these plants show a high degree of nonlinearity. For these nonlinear system, MPC algorithm does not give satis- factory dynamic performance. However, thanks to its ability ability to give an accurate approximation of the complex non- linear systems, the fuzzy models of the Takagi-Sugeno (TS) type proved to be suitable for the use in nonlinear MPC. So, an adaptive fuzzy logic systems (AFLS) is employed to deter- mine the parameters of the AFLS as well as the controller structure (Angelov and Filev, 2004; Belarbi and Megri, 2007). In this strategy, the AFLS is used as the prediction model of the nonlinear process and the system performance is greatly dependent upon the online optimization. To solve the prob- lems found during the control of these nonlinear systems, several methods have been used to be effective in control of a class of nonlinear process (Lee et al., 2012, Ma et al., 2010). However, most of these works provide local optimal, require the adaptive fuzzy MPC cost function differential, and they are still a complex procedure for calculating the inverse hes- sian matrix at each sampling step which is difficult to achieve in real time. Another reason, a major problem in nonlinear programming when the function optimized is highly non-con- vex, which will in general have several local minima (Niknam et al., 2011). Previous studies have been conducted to design and optimize a predictive controller. TS fuzzy predictive con- trol is a common method used to develop nonlinear models or express the dynamic nature of systems with strong con- straints and nonlinearity. Real-time fuzzy controllers can be generated based on input-output data of systems (Guo et al., 2020; Nunez et al., 2009; Song et al., 2007; Taylor, 2015). It is therefore a combination of TS fuzzy model and generalized predictive control has been proposed to improve nonlinear controls. This problem treated as constrained optimization 1 National High School of Engineers of Tunis, Laboratory of Industrial Systems and Renewable Energies Engineering, University of Tunis, Tunisia 2 Faculty of Sciences of Tunis, Laboratory Analysis, Design and Control of Systems, University of Tunis El Manar, Tunisia Corresponding author: Adel Taeib, National High School of Engineers of Tunis, Laboratory of Industrial Systems and Renewable Energies Engineering, University of Tunis, 13 Avenue Taha Hussein, Tunis, 1008, Tunisia. Email: adel2taib@gmail.com