Paper Info
Title
Free finite horizon LQR: A bilevel perspective and its application to model predictive control.
Abstract
We consider linear-quadratic optimal control problems with free final time and terminal state constraints and propose a solution procedure that is particularly useful for online feedback control in a model-predictive control (MPC) framework. The procedure avoids the standard time transformation, which transforms the problem into an equivalent but non-convex optimal control problem on a fixed time horizon. The transformed problem typically suffers from many local minima, which might cause instabilities in online optimization tasks like LQR or model-predictive control. To avoid this drawback of the time transformation we develop a method from the viewpoint of bilevel optimal control, which is beneficial especially in online control tasks. The novelty of the approach is the optimal final time tracking procedure, for which we exploit a property of the Hamiltonian function. To this end we show that within the continuous-time closed-loop controlled system the optimal final time linearly decreases in time, as one could intuitively expect. Finally, numerical experiments support the effectiveness of the proposed algorithm.
Year
DOI
Venue
2019
10.1016/j.automatica.2018.11.032
Automatica
Keywords
Field
DocType
Optimal control,Linear quadratic regulator,Free final time,Model predictive control
Drawback,Mathematical optimization,Optimal control,Control theory,Horizon,Model predictive control,Maxima and minima,Exploit,Hamiltonian mechanics,Mathematics,Standard time
Journal
Volume
Issue
ISSN
100
100
0005-1098
Citations 
PageRank 
References 
0
0.34
3
Authors
2
Name
Order
Citations
PageRank
Alberto De Marchi100.34
M. Gerdts25811.18