Enhanced Quadratic Programming via Pseudo-Transient Continuation: An Application to Model Predictive Control

In this letter, we present a novel fast solver for convex quadratic programs (QPs) based on pseudo-transient continuation (PTC). Tailored for real-time applications with strict computational requirements, our solver offers high execution speed and guaranteed global convergence to the optimal solution. PTC is a numerical technique that transforms multivariate nonlinear equations into autonomous systems that converge to the solution sought. In our approach, we recast the general QP Karush-Kuhn-Tucker (KKT) conditions into a system of equations and employ PTC to solve the latter to attain the optimal solution. Importantly, we provide theoretical guarantees demonstrating the global convergence of our PTC-based solver to the optimal solution of any given QP. To showcase the effectiveness of PTC, we employ it within the domain of Model Predictive Control (MPC). Numerical simulations are carried out on the MPC control of a quadrotor – a demanding dynamical system – highlighting excellent results in accurately executing the control task while ensuring lower computational times compared to conventional QP solvers.