A projected gradient and constraint linearization method for nonlinear model predictive control

A projected gradient and constraint linearization method for nonlinear model predictive control

Torrisi, Giampaolo (ETH Zürich)
Grammatico, S. (TU Delft Team Bart De Schutter)
Smith, Roy S. (ETH Zürich)
Morari, Manfred (University of Pennsylvania)

2018

Projected gradient descent denotes a class of iterative methods for solving optimization programs. In convex optimization, its computational complexity is relatively low whenever the projection onto the feasible set is relatively easy to compute. On the other hand, when the problem is nonconvex, e.g., because of nonlinear equality constraints, the projection becomes hard and thus impractical. In this paper, we propose a projected gradient method for nonlinear programs that only requires projections onto the linearization of the nonlinear constraints around the current iterate, similar to sequential quadratic programming (SQP). The proposed method falls neither into the class of projected gradient descent approaches, because the projection is not performed onto the original nonlinear manifold, nor into that of SQP, since second-order information is not used. For nonlinear smooth optimization problems, we assess local and global convergence to a Karush–Kuhn–Tucker point of the original problem. Further, we show that nonlinear model predictive control is a promising application of the proposed method, due to the sparsity of the resulting optimization problem.

First-order methods
Nonlinear model predictive control
Nonlinear programming
Sequential quadratic programming

http://resolver.tudelft.nl/uuid:6544e41b-80fb-4023-8ff6-0d95e2755c34

https://doi.org/10.1137/16M1098103

0363-0129

SIAM Journal on Control and Optimization, 56 (3), 1968-1999

Institutional Repository

journal article

© 2018 Giampaolo Torrisi, S. Grammatico, Roy S. Smith, Manfred Morari