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Linearly-constrained Linear Quadratic Regulator from the viewpoint of kernel methods

Abstract : The linear quadratic regulator problem is central in optimal control and was investigated since the very beginning of control theory. Nevertheless, when it includes affine state constraints, it remains very challenging from the classical "maximum principle" perspective. In this study we present how matrix-valued reproducing kernels allow for an alternative viewpoint. We show that the quadratic objective paired with the linear dynamics encode the relevant kernel, defining a Hilbert space of controlled trajectories. Drawing upon kernel formalism, we introduce a strengthened continuous-time convex optimization problem which can be tackled exactly with finite dimensional solvers, and which solution is interior to the constraints. When refining a time-discretization grid, this solution can be made arbitrarily close to the solution of the state-constrained Linear Quadratic Regulator. We illustrate the implementation of this method on a path-planning problem.
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https://hal-enpc.archives-ouvertes.fr/hal-02977250
Contributeur : Pierre-Cyril Aubin-Frankowski <>
Soumis le : dimanche 28 mars 2021 - 11:42:15
Dernière modification le : mercredi 31 mars 2021 - 03:11:43

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  • HAL Id : hal-02977250, version 2

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Pierre-Cyril Aubin-Frankowski. Linearly-constrained Linear Quadratic Regulator from the viewpoint of kernel methods. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, inPress. ⟨hal-02977250v2⟩

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