TY - JOUR
T1 - Hybrid necessary principle
JF - SIAM J. Control Optim. 43 (2005) 1867-1887
Y1 - 2005
A1 - Mauro Garavello
A1 - Benedetto Piccoli
AB - We consider a hybrid control system and general optimal control problems for this system. We suppose that the switching strategy imposes restrictions on control sets and we provide necessary conditions for an optimal hybrid trajectory, stating a hybrid necessary principle (HNP). Our result generalizes various necessary principles available in the literature.
PB - SIAM
UR - http://hdl.handle.net/1963/1641
N1 - Proceedings of IFAC Conference on Analysis and Design of Hybrid Systems, Saint Malo, France
U1 - 2477
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Traffic flow on a road network
JF - SIAM J. Math. Anal. 36 (2005) 1862-1886
Y1 - 2005
A1 - Giuseppe Maria Coclite
A1 - Benedetto Piccoli
A1 - Mauro Garavello
AB - This paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from conservation of the number of cars,\\ndefined on a road network that is a collection of roads with junctions. The evolution problem is underdetermined at junctions, hence we choose to have some fixed rules for the distribution of traffic plus an optimization criteria for the flux. We prove existence, uniqueness and stability of solutions to the Cauchy problem. Our method is based on wave front tracking approach, see [6], and works also for boundary data and time dependent coefficients of traffic distribution at junctions, so including traffic lights.
PB - SISSA Library
UR - http://hdl.handle.net/1963/1584
U1 - 2534
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Hybrid optimal control: case study of a car with gears
JF - Int. J. Control 76 (2003) 1272-1284
Y1 - 2003
A1 - Ciro D'Apice
A1 - Mauro Garavello
A1 - Rosanna Manzo
A1 - Benedetto Piccoli
AB - The purpose of this paper is to show the use of some analytical tools for hybrid optimal control. We illustrate both the hybrid maximum principle and the hybrid necessary principle at work on a simple example of a car with gears. The model is sufficiently rich to generate non-trivial optimization problems and the obtained results match with intuition. Finally, computer simulations confirm the theoretical analysis.
PB - Taylor and Francis
UR - http://hdl.handle.net/1963/3022
U1 - 1311
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -