Paper Info
Title
Structure preserving integrators for solving (non-)linear quadratic optimal control problems with applications to describe the flight of a quadrotor.
Abstract
We present structure preserving integrators for solving linear quadratic optimal control problems. The goal is to build methods which can also be used for the integration of nonlinear problems if they are previously linearized. The equations are solved using an iterative method on a fixed mesh with the constraint that at each iteration one can only use results obtained in previous iterations on that fixed mesh. On the other hand, this problem requires the numerical integration of matrix Riccati differential equations whose exact solution is a symmetric positive definite time-dependent matrix which controls the stability of the equation for the state. This property is not preserved, in general, by the numerical methods. We analyze how to build methods for the linear problem taking into account the previous constraints, and we propose second order exponential methods based on the Magnus series expansion which unconditionally preserve positivity for this problem and analyze higher order Magnus integrators. The performance of the algorithms is illustrated with the stabilization of a quadrotor which is an unmanned aerial vehicle.
Year
DOI
Venue
2014
10.1016/j.cam.2013.09.061
J. Computational Applied Mathematics
Keywords
Field
DocType
nonlinear problem,matrix riccati differential equation,fixed mesh,magnus integrator,numerical method,numerical integration,linear quadratic optimal control,magnus series expansion,higher order,linear problem
Mathematical optimization,Optimal control,Nonlinear system,Exponential integrator,Matrix (mathematics),Iterative method,Magnus expansion,Control theory,Mathematical analysis,Numerical analysis,Linear-quadratic regulator,Mathematics
Journal
Volume
ISSN
Citations 
262
0377-0427
10
PageRank 
References 
Authors
0.71
4
3
Name
Order
Citations
PageRank
Philipp Bader1163.20
Sergio Blanes25210.17
Enrique Ponsoda3267.00