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.

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This work is concerned with Model Predictive Control (MPC) algorithm for vehicle obstacle avoidance. The second objective of the algorithm is on-line minimization of fuel utilization. At first, the rudimentary nonlinear MPC optimization problem is formulated. Next, the constraints related to the predicted process state variables are formulated as soft ones to guarantee computational safety. Furthermore, in order to obtain a computationally simple procedure, the process dynamics and the fuel utilization model are linearized on-line and used for prediction in MPC. It leads to a quadratic programming MPC task, the necessity of nonlinear optimization performed in real-time is eliminated. In order to stress advantages of the discussed computationally uncomplicated MPC method it is compared with the basic scheme with on-line nonlinear optimization in terms of control quality and computational time. Additionally, effectiveness of the MPC algorithm is discussed in presence of modeling errors and measurement noise. Finally, additional constraints imposed on the rate of change of the manipulated variables are considered.

This work is concerned with the tuning of the parameters of Model Predictive Control (MPC) algorithms when used for industrial tasks, i.e., compensation of disturbances that affect the process (process uncontrolled inputs and measurement noises). The discussed simulation optimisation tuning procedure is quite computationally simple since the consecutive parameters are optimised separately, and it requires only a very limited number of simulations. It makes it possible to perform a multicriteria control assessment as a few control quality measures may be taken into account. The effectiveness of the tuning method is demonstrated for a multivariable distillation column. Two cases are considered: a perfect model case and a more practical case in which the model is characterised by some error. It is shown that the discussed tuning approach makes it possible to obtain very good control quality, much better than in the most common case in which all tuning parameters are constant.

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