A numerical procedure for computing the solution to the continuous-time infinite-horizon constrained linear quadratic regulator was presented in [1], which is based successive strictly convex QP problems where the decision variables are the control input value and slope at selected grid points. Each QP generates an upper bund to the optimal cost, and the accuracy is increased by using gradually refined grids computed offline to avoid any online integration. In this work we propose an adaptive method to gradually refine the grid where it is most needed, still without having to perform integration online, and we address the convergence properties of such algorithm as the number of grid points is increased. By means of suitable optimality functions, each iteration given the current upper bound cost, we compute: (i) a lower bound approximation of the optimal cost which can be used to stop the algorithm within a guaranteed tolerance; (ii) for each grid interval, an estimate of the cost reduction that can obtained by bisecting it.

On the convergence of numerical solutions to the continuous-time constrained LQR problem

PANNOCCHIA, GABRIELE;
2012

Abstract

A numerical procedure for computing the solution to the continuous-time infinite-horizon constrained linear quadratic regulator was presented in [1], which is based successive strictly convex QP problems where the decision variables are the control input value and slope at selected grid points. Each QP generates an upper bund to the optimal cost, and the accuracy is increased by using gradually refined grids computed offline to avoid any online integration. In this work we propose an adaptive method to gradually refine the grid where it is most needed, still without having to perform integration online, and we address the convergence properties of such algorithm as the number of grid points is increased. By means of suitable optimality functions, each iteration given the current upper bound cost, we compute: (i) a lower bound approximation of the optimal cost which can be used to stop the algorithm within a guaranteed tolerance; (ii) for each grid interval, an estimate of the cost reduction that can obtained by bisecting it.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/158254
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