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

Model Predictive Control (MPC) algorithms typically use the classical L${}_2$ cost function, which minimises squared differences of predicted control errors. Such an approach has good numerical properties, but the L${}_1$ norm that measures absolute values of the control errors gives better control quality. If a nonlinear model is used for prediction, the L${}_1$ 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 L${}_1$ norm even gives better performance than the classical L${}_2$ one in terms of the classical control performance indicator that measures squared control errors.