Linearly Constrained Linear Quadratic Regulator from the Viewpoint of Kernel Methods

The linear quadratic regulator problem is central in optimal control and has been investigated since the very beginning of theory. Nevertheless, when it includes affine state constraints, remains challenging from classical “maximum principle” perspective. In this study we present how matrix-valued reproducing kernels allow for an alternative viewpoint. We show that objective paired with dynamics encode relevant kernel, defining a Hilbert space controlled trajectories. Drawing upon kernel formalism, introduce strengthened continuous-time convex optimization which can be tackled exactly finite-dimensional solvers, solution interior to constraints. When refining time-discretization grid, made arbitrarily close state-constrained regulator. illustrate implementation method on path-planning problem.