By (Eds.) C. Bachas, J. Maldacena, K. S. Narain, S. Randjbar-Daemi
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Piecewise linear quadratic optimal control. IEEE Transactions on Automatic Control, 45:629–637, 2000. , Olaru, S. Comments – Remarks 35 Preprints of the NIL workshop Jan 10–15, 2011, Bratislava, Slovakia Nguyen, H. , Hovd, M. Patchy approximate explicit model predictive control Hoai Nam Nguyen ∗ Sorin Olaru ∗∗ Morten Hovd ∗∗∗ ∗ Automatic Control Department, Supelec, 3 rue Joliot Curie, 91192 France ∗∗ Automatic Control Department, Supelec, 3 rue Joliot Curie, 91192 France ∗∗∗ Engineering Cybernetics Department, Norwegian University of Science and Technology, N-7491 Trondheim, Norway Abstract: Multiparametric quadratic programming (MPQP) can be used to construct an offline solution to constrained linear model predictive control.
The relaxations (19) and (20) do Equation (9) is fulﬁlled simply by deﬁning P¯i to be a symmetric (matrix valued) variable. , Olaru, S. fulﬁll these requirements, and have proven eﬀective for problems of modest size. However, the resulting relaxation functions are somewhat arbitrary, and there is a possibility that more careful speciﬁcation of the functional form of the relaxations can be beneﬁcial. is inside the polytopic cone, such that any ray originating at the origin which is orthogonal to rm is fully outside the polytopic cone.
These simplices have following properties: In the sequel any inequality constraint is said to be active for some x if it holds with equality at the optimum. • Xfk has nonempty interior, • Int(Xfk ∩ Xfl ) = ∅ if k = l, • k Xfk = Xf , The following theorem gives an explicit representation of the optimal piecewise affine function of state. Theorem 3. Consider the problem (8) and arbitrary fixed set of active constraints. Denote G, W ans S the submatrices containing the corresponding rows of G, S and W.
2001 Spring School on Superstrings and Related Matters by (Eds.) C. Bachas, J. Maldacena, K. S. Narain, S. Randjbar-Daemi