Nonlinear Robust and Optimal Control via Proper Orthogonal Decomposition

Didier Georges (1)

1 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité

In this paper, a methodology based on proper orthogonal decomposition (POD) for computing approximate closed-loop optimal or robust control laws for finite-dimensional nonlinear systems is proposed. The solution can be obtained on any arbitrary domain of the state space represented by a multidimensional grid. The method only requires the computation of a limited number of well-conditioned two-point boundary value problems and a simple backwards integration of a reduced model of the Hamilton-Jacobi-Bellman or Hamilton-Jacobi-Isaacs equation associated to the control problem. Two illustrative examples demonstrate the effectiveness of the approach.

Mots clés: Hamilton; Jacobi; Bellman(Isaacs) equation; Robust control; optimal control; proper orthogonal decomposition; Galerkin method

Domaines: Automatique / Robotique

Didier Georges. Nonlinear Robust and Optimal Control via Proper Orthogonal Decomposition. NOLCOS 2013 - 9th IFAC Symposium on Nonlinear Control Systems, Sep 2013, Toulouse, France. ⟨10.3182/20130904-3-FR-2041.00210⟩. ⟨hal-00834339⟩