Computationally Efficient Nonlinear Model Predictive Control Using the L1 Cost-Function

Abstract

Model Predictive Control (MPC) algorithms typically use the classical L2 cost function, which minimises squared differences of predicted control errors. Such an approach has good numerical properties, but the L1 norm that measures absolute values of the control errors gives better control quality. If a nonlinear model is used for prediction, the L1 norm leads to a difficult, nonlinear, possibly non-differentiable cost function. A computationally efficient alternative is discussed in this work. The solution used consists of two concepts: (a) a neural approximator is used in place of the non-differentiable absolute value function; (b) an advanced trajectory linearisation is performed on-line. As a result, an easy-to-solve quadratic optimisation task is obtained in place of the nonlinear one. Advantages of the presented solution are discussed for a simulated neutralisation benchmark. It is shown that the obtained trajectories are very similar, practically the same, as those possible in the reference scheme with nonlinear optimisation. Furthermore, the L1 norm even gives better performance than the classical L2 one in terms of the classical control performance indicator that measures squared control errors.