Section: New Results
Inverse optimality results for constrained control
Participants : Sorin Olaru, Ngoc Anh Nguyen [L2S] , Pedro Rodriguez [L2S] , Morten Hovd [NTNU Trondheim, Norway] , Ioan Necoara [Univ. Politehnica Bucharest, Romania] .
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. In this context we introduced  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 have been put forward. Continuous piecewise affine function defined over a polytopic partition of the state space are known to be obtained as the solution of a parametric linear/quadratic programming problem. Regarding linear model predictive control, is 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.