%0 Journal Article %J SIAM J. Control Optim. 43 (2005) 1867-1887 %D 2005 %T Hybrid necessary principle %A Mauro Garavello %A Benedetto Piccoli %X 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. %B SIAM J. Control Optim. 43 (2005) 1867-1887 %I SIAM %G en %U http://hdl.handle.net/1963/1641 %1 2477 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:44Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002 %R 10.1137/S0363012903416219 %0 Journal Article %J SIAM J. Math. Anal. 36 (2005) 1862-1886 %D 2005 %T Traffic flow on a road network %A Giuseppe Maria Coclite %A Benedetto Piccoli %A Mauro Garavello %X 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. %B SIAM J. Math. Anal. 36 (2005) 1862-1886 %I SISSA Library %G en %U http://hdl.handle.net/1963/1584 %1 2534 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:54Z (GMT). No. of bitstreams: 1\\nmath.AP0202146.pdf: 256961 bytes, checksum: 51f64ff00e916dd87d3dd6df41903d23 (MD5)\\n Previous issue date: 2002 %R 10.1137/S0036141004402683 %0 Journal Article %J Int. J. Control 76 (2003) 1272-1284 %D 2003 %T Hybrid optimal control: case study of a car with gears %A Ciro D'Apice %A Mauro Garavello %A Rosanna Manzo %A Benedetto Piccoli %X 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. %B Int. J. Control 76 (2003) 1272-1284 %I Taylor and Francis %G en_US %U http://hdl.handle.net/1963/3022 %1 1311 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-02T15:37:32Z\\nNo. of bitstreams: 1\\ndgb.pdf: 374355 bytes, checksum: 5c6cc02be9e07396a29d5c6ff22db238 (MD5) %R 10.1080/0020717031000147520