Abstract
This paper proposes a geometrical analysis of the polyhedral feasible domains for the predictive control laws under constraints. The state vector is interpreted as a vector of parameters for the optimization problem to be solved at each sampling instant and its influence can be fully described by the use of parameterized polyhedra and their dual constraints/generators representation.
The construction of the associated explicit control laws at least for linear or quadratic cost functions can thus receive fully geometrical solutions. Convex nonlinear constraints can be approximated using a description based on the parameterized vertices. In the case of nonconvex regions the explicit solutions can be obtained using Voronoi partitions based on a collection of points distributed over the borders of the feasible domain.
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References
Scokaert, P.O., Mayne, D.Q., Rawlings, J.B.: Suboptimal model predictive control (feasibility implies stability). In: IEEE Transactions on Automatic Control. Volume 44. (1999) 648–654
Olaru, S., Dumur, D.: A parameterized polyhedra approach for explicit constrained predictive control. (In: 43rd IEEE Conference on Decision and Control, 2004.) 1580–1585 Vol.2
Motzkin, T.S., R.H.T.G., R.M., T.: The Double Description Method, republished in Theodore S. Motzkin: Selected Papers, (1983). Birkhauser (1953)
Schrijver, A.: Theory of Linear and Integer Programming. John Wiley and Sons, NY (1986)
Leverge, H.: A note on chernikova’s algorithm. In: Technical Report 635, IRISA, France (1994)
Loechner, V., Wilde, D.K.: Parameterized polyhedra and their vertices. International Journal of Parallel Programming V25 (1997) 525–549
Olaru, S., Dumur, D.: Compact explicit mpc with guarantee of feasibility for tracking. In: 44th IEEE Conference on Decision and Control, and European Control Conference. (2005) 969–974
Seron, M., Goodwin, G., Dona, J.D.: Characterisation of receding horizon control for constrained linear systems. In: Asian Journal of Control. Volume 5. (2003) 271–286
Bemporad, A., Morari, M., Dua, V., Pistikopoulos, E.: The Explicit Linear Quadratic Regulator for Constrained Systems. Automatica 38 (2002) 3–20
Goodwin, G., Seron, M., Dona, J.D.: Constrained Control and Estimation. Springer, Berlin (2004)
Borelli, F.: Constrained Optimal Control of Linear and Hybrid Systems. Springer-Verlag, Berlin (2003)
Tondel, P., Johansen, T., Bemporad, A.: Evaluation of piecewise affine control via binary search tree. Automatica 39 (2003) 945–950
Bemporad, A., Borrelli, F., Morari, M.: Robust Model Predictive Control: Piecewise Linear Explicit Solution. In: European Control Conference. (2001) 939–944
Kerrigan, E., Maciejowski, J.: Feedback min-max model predictive control using a single linear program: Robust stability and the explicit solution. International Journal of Robust and Nonlinear Control 14 (2004) 395–413
Olaru, S., Dumur, D.: On the continuity and complexity of control laws based on multiparametric linear programs. In: 45th IEEE Conference on Decision and Control. (2006)
Grancharova, A., Tondel, P., Johansen, T.A.: International Workshop on Assessment and Future Directions of Nonlinear Model Predictive Control. (2005)
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Olaru, S., Dumur, D., Dobre, S. (2009). On the Geometry of Predictive Control with Nonlinear Constraints. In: Filipe, J., Cetto, J.A., Ferrier, JL. (eds) Informatics in Control, Automation and Robotics. Lecture Notes in Electrical Engineering, vol 24. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85640-5_23
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DOI: https://doi.org/10.1007/978-3-540-85640-5_23
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