Optimal Linearization–Based Computationally Proficient Predictive Control of MIMO Nonlinear System Using Least Square Support Vector Machine

In this work, the concept of optimal linearization is explored to develop computationally proficient model predictive control (MPC) algorithms for multi-input multi-output (MIMO) nonlinear processes. The algorithms use Laguerre filters and pruned least square support vector machine (LSSVM)–based Wiener model for predictions. Taylor's series–based model linearization is predominantly used to improve the computational efficiency of nonlinear MPCs. This approach gives good control performance at many times. However, certain processes exhibit significant nonlinearity and experience large set point variations. In such cases, the closed-loop control accuracy obtained through above (Taylor's series based) approach is very poor and demands an alternative solution. In this paper, instead of Taylor series–based linearization, an optimization-based solution is derived to determine linearizing coefficients' matrix. Based on the optimally linearized model, a classical MPC and explicit MPC algorithms are proposed. The proposed algorithms are tested for the multivariable control of polymerization reactor. The optimal linearization–based proposed explicit algorithm is found to be 6.25 times computationally faster than the nonlinear MPC. When compared with Taylor series linearization–based MPC, the proposed algorithm provides 3 times (for monomer concentration) and 15 times (for reactor temperature) better control accuracy.