Constructive Solution of Inverse Parametric Linear/Quadratic Programming Problems

Ngoc Anh Nguyen (1, 2) , Sorin Olaru (2, 3) , Pedro Rodriguez-Ayerbe (2) , Morten M Hovd (4) , Ion I Necoara (5)

1 CentraleSupélec
2 L2S - Laboratoire des signaux et systèmes
3 DISCO - Dynamical Interconnected Systems in COmplex Environments
4 ITK NTNU - Department of Engineering Cybernetics [Trondheim]
5 Department of Automatic Control and Systems Engineering [Bucharest]

Parametric convex programming has received a lot of attention, since it has many applications in chemical engineering, control engineering, signal processing , etc. Further, inverse optimality plays an important role in many contexts, e.g., image processing, motion planning. This paper introduces a constructive solution of the inverse optimality problem for the class of continuous piecewise affine functions. The main idea is based on the convex lifting concept. Accordingly, an algorithm to construct convex liftings of a given convexly liftable partition will be put forward. 2 N. A. Nguyen et al. uous piecewise affine function defined over a polytopic partition is the solution of a parametric linear/quadratic programming problem. Regarding linear model predic-tive control, it will be shown that any continuous piecewise affine control law can be obtained via a linear optimal control problem with the control horizon at most equal to 2 prediction steps.

Domaines: Automatique / Robotique

Ngoc Anh Nguyen, Sorin Olaru, Pedro Rodriguez-Ayerbe, Morten M Hovd, Ion I Necoara. Constructive Solution of Inverse Parametric Linear/Quadratic Programming Problems. Journal of Optimization Theory and Applications, 2016, 172 (2), pp.623-648. ⟨10.1007/s10957-016-0968-0⟩. ⟨hal-01408472⟩