Feedback control design using model predictive control formulation and Carleman approximation method

• Published in: AIChE journal Vol. 65; no. 9
• Main Authors: Hashemian, Negar, Armaou, Antonios
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 01.09.2019; American Institute of Chemical Engineers
• Subjects: Approximation; Approximation method; Carleman approximation; Chemical reactors; Computer simulation; Cost analysis; Dynamical systems; Feedback; Feedback control; input‐to‐state stability; Mathematical analysis; model predictive control; Nonlinear control; Nonlinear dynamics; Nonlinear systems; Optimization; Organic chemistry; Predictive control; process control; Sensitivity analysis
• ISSN: 0001-1541; 1547-5905
• DOI: 10.1002/aic.16666

Model predictive control (MPC) for nonlinear systems involves a nonlinear dynamic optimization (NDO) step, which is required to be solved repeatedly. This step is computationally demanding, specially in dealing with constrained and/or nonlinear large‐scale systems. This paper presents a method for accelerating the NDO in state‐feedback regulation problems. Exploiting Carleman approximation, this method represents the nonlinear dynamics in a bilinear form and discretizes the resulting system in the time domain. The gradient and Hessian of the cost function with respect to the feedback gains are also analytically derived. The Carleman approximation of the nonlinear system may introduce errors in the prediction and sensitivity analysis. The manuscript derives a criterion under which the input‐to‐state stability of the new design is guaranteed. The proposed MPC is implemented in a chemical reactor example. Simulation results show that replacing conventional MPC schemes by the presented method reduces the computation time by an order of magnitude.