Fast Nonlinear Model Predictive Control Using a Custom Cost-Function: Preliminary Results

Typically, in Model Predictive Control (MPC) algorithms, the squared sum of predicted control errors (the L2 norm) is minimised on-line. This work discusses an alternative approach in which a custom, user-defined cost-function is used; it may be defined analytically or in a graphical form. To obtain a computationally fast procedure, a differentiable neural approximation of the custom cost-function is used and the predicted trajectory of the controlled variable is linearised on-line. As a result, a quadratic optimisation MPC task is derived. Efficiency of the described approach is discussed for a simulated polymerisation reactor. In particular, it is shown that the discussed algorithm gives better results in terms of the custom cost-function than the classical L2 approach. Moreover, it is shown that the algorithm gives similar results to those possible in MPC with full nonlinear optimisation repeated at each sampling instant.