Data-driven offset-free multilinear model predictive control using constrained differential dynamic programming. (November 2021) - Park, ByungJun; Kim, Jong Woo; Lee, Jong Min
Abstract: Multilinear model predictive control (MLMPC) can regulate a nonlinear process with wide operating regions based on a set of linear models. Although online computational cost is reduced compare to nonlinear MPC (NMPC), it is difficult to obtain a reliable full nonlinear model or set of linear models in practice. In this paper, we propose a combination of MLMPC with differential dynamic programming (DDP), so that the system can be controlled offset-free in the absence of a full nonlinear model. DDP is a 'trajectory-centric' optimization technique that solves nonlinear optimal control problems. The trajectory can be optimized even if the full model for the system is unknown, because DDP uses only the gradients around the visited trajectory, which is easily obtained by input excitations. Moreover, the gradient information can provide linear models in the subsequent MLMPC step. In the proposed scheme, a novel model selection based on gap metric and weighting method are employed for MLMPC. We prove the offset tracking property of DDP assisted MLMPC. A continuous stirred tank reactor (CSTR) process is studied to demonstrate the effectiveness of the proposed algorithms. Simulation studies show that CDDP designed by the proposed algorithm improves the trajectory over iterations, and the resulting MLMPC achieves offset-free tracking property regardless of an initial point and a set-point in the operating region. Highlights: Data-driven DDP is proposed to find the optimal trajectory without models of nonlinear systems. LTV model is obtained from Data-driven DDP and exploited for the model of MLMPC. A novel clustering method based on gap metric is proposed to choose linear models for MLMPC. MLMPC with a novel prediction-based weighting method is proposed and its stability is discussed. The proposed MLMPC strategy achieves offset-free control over large operating ranges.