Forward Approximate Solution for Linear Quadratic Tracking

TL;DR

This paper introduces a forward, local-in-time approximation method for solving Linear Quadratic Tracking problems, offering a computationally efficient alternative to model predictive control with comparable performance.

Contribution

It presents a novel approximation strategy that is forward and local in time, leveraging the value function and time reversal to efficiently solve LQT problems.

Findings

The proposed method performs comparably to optimal solutions.

It significantly reduces computational burden compared to MPC.

Experimental results validate the effectiveness of the approach.

Abstract

In this paper, we discuss an approximation strategy for solving the Linear Quadratic Tracking that is both forward and local in time. We exploit the known form of the value function along with a time reversal transformation that nicely addresses the boundary condition consistency. We provide the results of an experimental investigation with the aim of showing how the proposed solution performs with respect to the optimal solution. Finally, we also show that the proposed solution turns out to be a valid alternative to model predictive control strategies, whose computational burden is dramatically reduced.