Proportional-Integral Projected Gradient Method for Model Predictive Control

Abstract

Conic optimization is the minimization of a differentiable convex objective function subject to conic constraints. We propose a novel primal-dual first-order method for conic optimization, named proportional-integral projected gradient method (PIPG). PIPG ensures that both the primal-dual gap and the constraint violation converge to zero at the rate of Op1{kq, where k is the number of iterations. If the objective function is strongly convex, PIPG improves the convergence rate of the primal-dual gap to Op1{k 2 q. Further, unlike any existing first-order methods, PIPG also improves the convergence rate of the constraint violation to Op1{k 3 q. We demonstrate the application of PIPG in constrained optimal control problems.

Model predictive control of discrete-time linear systems by ADMM with applications to turbofan engine control problems

“…Therefore, computational efficiency is crucial for solving MPC problems. There have been many improved works in this area, for example, the extended Newton Raphson algorithm [16], the gradient algorithm [17], and the ADMM algorithm (the common MPC problems: the Lasso MPC problem for time-varying systems [18], the MPCT problem [19], the MPC problem for systems with feedback gain [20], the BCMPC problem [21], and the symmetric MPC problem [22]).…”

A type system for Julia

“…user code One Julia use case is to write concrete analyses, where specific values and types are known. To evaluate the utility of the type checker on such code, I considered an implementation of the PIPG algorithm [83]. This program determines the flight path of a quadcopter that avoids two obstacles in its path using numerical optimization.…”