Nonlinear Model Predictive ControlFast Algorithms and Implementation
The problem of an efficient implementation of a Model Predictive Control (MPC) algorithm is addressed in this dissertation. The nominal problem formulation for the MPC control law involves the solution, for each sample time, to an optimization problem that is, in general, nonlinear and hard to be solved. The sample time must be greater than the time required to solve the optimization problem and, as a consequence, MPC cannot be directly applied to system with a fast dynamics. To overcome this problem, two possible approaches are proposed here: a set-membership (SM) based technique and a approximation of the optimization solver. The proposed SM based technique, substantially, allows to avoid solving the optimization problem on-line at each sample time. The control move is computed by means of a set of pre-computed solutions to the optimization problem for a given number of different system state values. This approach is potentially applicable to every kind of system, with the disadvantage to require a large amount of memory needed to store the data for the approximation. By focusing on the case of the linear MPC, other approximations can be used to obtain a fast implementation of a MPC controller with no pre-computed solutions. A modified interior-point algorithm which guarantee execution time in the order of a millisecond is described in this thesis. The effectiveness of the proposed techniques is shown through examples from real world applications. The examples were chosen from the set of such applications whose properties that prevent the applicability of the nominal predictive controller. The obtained simulations results shown the effectiveness of the proposed approximation techniques.
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