Nonlinear Model Predictive Control with L₁ Cost-Function Using Neural Networks for Multivariable Processes

This work presents a computationally efficient Model Predictive Control (MPC) algorithm for nonlinear Multiple Input Multiple Output (MIMO) processes in which the sum of absolute values of predicted control errors (the L-1 norm) is minimized rather than the typically used sum of squared errors (the L-2 norm). An approximator of the absolute value function combined with an advanced online trajectory linearization scheme is used to obtain a computationally uncomplicated algorithm that requires solving online quadratic optimization tasks. For a nonlinear MIMO neutralization process, we show that the described algorithm gives control quality comparable to that possible in MPC with nonlinear optimization. We examine the effectiveness of polynomial and neural approximation of the absolute value function. Moreover, we show that the described algorithm gives better control quality than the classical approach to MPC with the L-2 cost-function.