TY - GEN
T1 - On the dual decomposition of linear quadratic optimal control problems for vehicular formations
AU - Fardad, Makan
AU - Lin, Fu
AU - Jovanović, Mihailo R.
PY - 2010
Y1 - 2010
N2 - We use the dual decomposition method along with the dual subgradient algorithm to decouple the linear quadratic optimal control problem for a system of single-integrator vehicles. This produces the optimal control law in a localized manner, in the sense that vehicles can iteratively compute their primal and dual variables by only communicating with their immediate neighbors. In particular, we demonstrate that each vehicle only needs to receive the primal variable of the vehicle ahead and the dual variable of the vehicle behind. We then assume a structured feedback gain relationship between the state and actuation signals, and reformulate the optimization problem to find the optimal feedback gains. We develop an algorithm whereby vehicles can compute structured feedback gains in a localized manner. Convergence properties of the latter algorithm are improved by employing a relaxed version of the augmented Lagrangian method, and numerical examples are provided to demonstrate the utility of our results.
AB - We use the dual decomposition method along with the dual subgradient algorithm to decouple the linear quadratic optimal control problem for a system of single-integrator vehicles. This produces the optimal control law in a localized manner, in the sense that vehicles can iteratively compute their primal and dual variables by only communicating with their immediate neighbors. In particular, we demonstrate that each vehicle only needs to receive the primal variable of the vehicle ahead and the dual variable of the vehicle behind. We then assume a structured feedback gain relationship between the state and actuation signals, and reformulate the optimization problem to find the optimal feedback gains. We develop an algorithm whereby vehicles can compute structured feedback gains in a localized manner. Convergence properties of the latter algorithm are improved by employing a relaxed version of the augmented Lagrangian method, and numerical examples are provided to demonstrate the utility of our results.
KW - Distributed optimization
KW - Dual decomposition
KW - Localized cooperative control
KW - Multi-vehicle systems
KW - Subgradient algorithm
UR - http://www.scopus.com/inward/record.url?scp=79953132306&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79953132306&partnerID=8YFLogxK
U2 - 10.1109/CDC.2010.5717487
DO - 10.1109/CDC.2010.5717487
M3 - Conference contribution
AN - SCOPUS:79953132306
SN - 9781424477456
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 6287
EP - 6292
BT - 2010 49th IEEE Conference on Decision and Control, CDC 2010
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 49th IEEE Conference on Decision and Control, CDC 2010
Y2 - 15 December 2010 through 17 December 2010
ER -