"FMPC: A Fast Implementation of Model Predictive Control,
and its application to Semi-Active Suspension Control"
Prof. Mario Milanese, Politecnico di Torino, Italy
Model Predictive Control (MPC) is a model based control technique especially suited in dealing with input and/or state constraints. The online application of the procedure requires the solution of the an optimization problem at each sampling time, a task that can limit its use for systems with fast dynamics.
This motivates the recent research efforts devoted to develop computationally tractable MPC solutions. Indeed the control move at time results to be a continuous nonlinear static function of the system state. In [1], [2] explicit piece-wise linear solutions of the MPC problem have been introduced to compute the function in case of linear systems. They are based on a state space partition in polyhedral regions inside which the control law is an affine function of the system state that can be precomputed, stored, and implemented online. While such approach is quite attractive, as the online optimization is avoided, it may have serious limitations as, at each sampling time, the polyhedral region the initial state lies in, has to be determined. However, the number of subregions typically has a very fast increase with the dimension of state space and of the control horizon , leading to large computational complexity even for moderate values of state dimension and control horizon.
A different approach has been introduced in [3] and [4], where a neural approximation of the static function is considered, based on the offline computation of the values of the function at a given number of states. The problems with such an approach are the trapping in local minima during the learning phase and the difficulty of handling the constraints in the image set of the function to be approximated. In the lecture, the Set Membership method proposed in [5] is presented for the approximation of the static function from the the offline computation of the values of the function at a given number of states. An approximating function is obtained fulfilling input and/or state constraint and whose computational time is independent on the MPC control horizon. The approach allows also to deal with Nonlinear Model Predictive Control (NMPC) problems. The effectiveness of the proposed methodology is shown by the application to a semi-active suspension control design [6].
References
[1] A. Bemporad, M. Morari, V. Dua, and E. N. Pistikopoulos, "The explicit linear quadratic regulator for constrained systems," Automatica, vol. 38, pp. 3-20, 2002. [2] M. M. Seron, G. C. Goodwin, and J. A. De Dona, "Characterization of receding horizon control for constrained linear systems," Asian J. Control, vol. 5, no. 2, pp. 271-286, 2003. [3] T. Parisini and R. Zoppoli, "A receding-horizon regulator for nonlinear systems and a neural approximation," Automatica, vol. 31, no. 10, pp. 1443-1451, 1995. [4] D. R. Ramirez, M. R. Arahal, and E. F. Camacho, "Min-max predictive control of a heat exchanger using a neural network solver," IEEE Trans. Contr. Syst. Technol., vol. 12, no. 5, pp. 776-786, Sep. 2004. [5]. Canale and M. Milanese, "FMPC: A fast implementation of model predictive control techniques," Proc. 16th IFACWorld Congr., Prague, Czech Republic, 2005. [6] M. Canale, M. Milanese, C. Novara, "Semi-active suspension control using Fast Model Predictive Techniques", IEEE Transactions on Control Systems Technology, vol. 14, no. 6, pp. 1034-1046, 2006.
Two OPTEC professors have been awarded three "Gouden Krijtjes", the yearly teaching awards given by the organization of engineering students (vtk). Prof. Lombaert was awarded the prize for the best course in civil engineering, and Prof. Diehl the prizes for the best professor and the best course in mathematical engineering (where he teaches numerical optimization). They received these awards at the yearly "proffentap" where experienced students taught them how to draft beer professionally.
