@article {2007,
	title = {Time optimal swing-up of the planar pendulum},
	journal = {46th IEEE Conference on Decision and Control (2007) 5389 - 5394},
	number = {SISSA;50/2006/M},
	year = {2007},
	abstract = {This paper presents qualitative and numerical results on the global structure of the time optimal trajectories of the planar pendulum on a cart.},
	doi = {10.1109/CDC.2007.4434688},
	url = {http://hdl.handle.net/1963/1867},
	author = {Mireille E. Broucke and Paolo Mason and Benedetto Piccoli}
}
@article {2006,
	title = {Classification of stable time-optimal controls on 2-manifolds},
	journal = {J. Math. Sci. 135 (2006) 3109-3124},
	number = {SISSA;20/2004/M},
	year = {2006},
	doi = {10.1007/s10958-006-0148-0},
	url = {http://hdl.handle.net/1963/2196},
	author = {Ugo Boscain and Igor Nikolaev and Benedetto Piccoli}
}
@article {2005,
	title = {Hybrid necessary principle},
	journal = {SIAM J. Control Optim. 43 (2005) 1867-1887},
	number = {SISSA;71/2002/M},
	year = {2005},
	note = {Proceedings of IFAC Conference on Analysis and Design of Hybrid Systems, Saint Malo, France},
	publisher = {SIAM},
	abstract = {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.},
	doi = {10.1137/S0363012903416219},
	url = {http://hdl.handle.net/1963/1641},
	author = {Mauro Garavello and Benedetto Piccoli}
}
@inbook {2005,
	title = {A short introduction to optimal control},
	booktitle = {Contr{\^o}le non lin{\'e}aire et applications: Cours donn{\'e}s {\`a} l\\\'{\'e}cole d\\\'{\'e}t{\'e} du Cimpa de l\\\'Universit{\'e} de Tlemcen /  Sari Tewfit [ed.]. - Paris:  Hermann, 2005},
	number = {SISSA;10/2004/M},
	year = {2005},
	isbn = {2 7056 6511 0},
	url = {http://hdl.handle.net/1963/2257},
	author = {Ugo Boscain and Benedetto Piccoli}
}
@article {2005,
	title = {Traffic flow on a road network},
	journal = {SIAM J. Math. Anal. 36 (2005) 1862-1886},
	number = {SISSA;13/2002/M},
	year = {2005},
	publisher = {SISSA Library},
	abstract = {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.},
	doi = {10.1137/S0036141004402683},
	url = {http://hdl.handle.net/1963/1584},
	author = {Giuseppe Maria Coclite and Benedetto Piccoli and Mauro Garavello}
}
@article {2003,
	title = {Hybrid optimal control: case study of a car with gears},
	journal = {Int. J. Control 76 (2003) 1272-1284},
	year = {2003},
	publisher = {Taylor and Francis},
	abstract = {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.},
	doi = {10.1080/0020717031000147520},
	url = {http://hdl.handle.net/1963/3022},
	author = {Ciro D{\textquoteright}Apice and Mauro Garavello and Rosanna Manzo and Benedetto Piccoli}
}
@article {2002,
	title = {Admissible Riemann solvers for genuinely nonlinear P-systems of mixed type},
	journal = {J. Differ. Equations, 2002, 180, 395},
	number = {SISSA;33/00/M},
	year = {2002},
	publisher = {SISSA Library},
	doi = {10.1006/jdeq.2001.4066},
	url = {http://hdl.handle.net/1963/1491},
	author = {Jean-Marc Mercier and Benedetto Piccoli}
}
@article {2002,
	title = {On the reachability of quantized control systems},
	journal = {IEEE Trans. Automat. Contr. 47 (2002) 546-563},
	number = {SISSA;43/00/M},
	year = {2002},
	publisher = {SISSA Library},
	abstract = {In this paper, we study control systems whose input sets are quantized, i.e., finite or regularly distributed on a mesh. We specifically focus on problems relating to the structure of the reachable set of such systems, which may turn out to be either dense or discrete. We report results on the reachable set of linear quantized systems, and on a particular but interesting class of nonlinear systems, i.e., nonholonomic chained-form systems. For such systems, we provide a complete characterization of the reachable set, and, in case the set is discrete, a computable method to completely and succinctly describe its structure. Implications and open problems in the analysis and synthesis of quantized control systems are addressed.},
	doi = {10.1109/9.995034},
	url = {http://hdl.handle.net/1963/1501},
	author = {Antonio Bicchi and Alessia Marigo and Benedetto Piccoli}
}
@article {2001,
	title = {Controllability for discrete systems with a finite control set},
	journal = {Math. Control Signals Systems 14 (2001) 173-193},
	number = {SISSA;148/97/M},
	year = {2001},
	publisher = {Springer},
	doi = {10.1007/PL00009881},
	url = {http://hdl.handle.net/1963/3114},
	author = {Yacine Chitour and Benedetto Piccoli}
}
@article {2001,
	title = {Extremal synthesis for generic planar systems},
	journal = {J. Dynam. Control Systems, 2001, 7, 209},
	number = {SISSA;45/00/M},
	year = {2001},
	publisher = {SISSA Library},
	doi = {10.1023/A:1013003204923},
	url = {http://hdl.handle.net/1963/1503},
	author = {Ugo Boscain and Benedetto Piccoli}
}
@article {2001,
	title = {Global continuous Riemann solver for nonlinear elasticity},
	journal = {Arch. Ration. Mech. An., 2001, 156, 89},
	number = {SISSA;35/00/M},
	year = {2001},
	publisher = {SISSA Library},
	doi = {10.1007/s002050100118},
	url = {http://hdl.handle.net/1963/1493},
	author = {Jean-Marc Mercier and Benedetto Piccoli}
}
@article {2001,
	title = {Morse properties for the minimum time function on 2-D manifolds},
	journal = {J. Dynam. Control Systems 7 (2001), no. 3, 385--423},
	number = {SISSA;84/00/M},
	year = {2001},
	publisher = {SISSA Library},
	doi = {10.1023/A:1013190914234},
	url = {http://hdl.handle.net/1963/1541},
	author = {Ugo Boscain and Benedetto Piccoli}
}
@article {2001,
	title = {Uniqueness of classical and nonclassical solutions for nonlinear hyperbolic systems},
	journal = {J. Differential Equations 172 (2001) 59-82},
	year = {2001},
	publisher = {Elsevier},
	doi = {10.1006/jdeq.2000.3869},
	url = {http://hdl.handle.net/1963/3113},
	author = {Paolo Baiti and Philippe G. LeFloch and Benedetto Piccoli}
}
@article {2000,
	title = {Abnormal extremals for minimum time on the plane},
	number = {SISSA;50/00/M},
	year = {2000},
	publisher = {SISSA Library},
	url = {http://hdl.handle.net/1963/1508},
	author = {Ugo Boscain and Benedetto Piccoli}
}
@article {2000,
	title = {Quantized control systems and discrete nonholonomy},
	journal = {Lagrangian and Hamiltonian Methods for Nonlinear Control : a proc. volume from the IFAC Workshop. Princeton, New Jersey, 16-18 March 2000 / ed. by N.E. Leonard, R. Ortega. - Oxford : Pergamon, 2000},
	number = {SISSA;44/00/M},
	year = {2000},
	publisher = {Elsevier},
	isbn = {0-08-043658-7},
	url = {http://hdl.handle.net/1963/1502},
	author = {Alessia Marigo and Benedetto Piccoli and Antonio Bicchi}
}
@inbook {2000,
	title = {Reachability Analysis for a Class of Quantized Control Systems},
	booktitle = {Proc. 39th IEEE Int. Conf. on Decision and Control 4 (2000) 3963-3968},
	year = {2000},
	publisher = {IEEE},
	organization = {IEEE},
	abstract = {We study control systems whose input sets are quantized. We specifically focus on problems relating to the structure of the reachable set of such systems, which may turn out to be either dense or discrete. We report on some results on the reachable set of linear quantized systems, and study in detail an interesting class of nonlinear systems, forming the discrete counterpart of driftless nonholonomic continuous systems. For such systems, we provide a complete characterization of the reachable set, and, in the case the set is discrete, a computable method to describe its lattice structure.},
	doi = {10.1109/CDC.2000.912333},
	url = {http://hdl.handle.net/1963/3518},
	author = {Alessia Marigo and Benedetto Piccoli and Antonio Bicchi}
}
@article {2000,
	title = {Regular Synthesis and Sufficiency Conditions for Optimality},
	journal = {SIAM J. Control Optim. 39 (2000) 359-410},
	number = {SISSA;68/96/M},
	year = {2000},
	publisher = {SIAM},
	abstract = {We propose a definition of \\\"regular synthesis\\\" that is more general than those suggested by other authors such as Boltyanskii and Brunovsky, and an even more general notion of \\\"regular presynthesis.\\\" We give a complete proof of the corresponding sufficiency theorem, a slightly weaker version of which had been stated in an earlier article, with only a rough outline of the proof. We illustrate the strength of our result by showing that the optimal synthesis for the famous Fuller problem satisfies our hypotheses. We also compare our concept of synthesis with the simpler notion of a \\\"family of solutions of the closed-loop equation arising from an optimal feedback law,\\\" and show by means of examples why the latter is inadequate, and why the difficulty cannot be resolved byusing other concepts of solution--such as Filippov solutions, or the limits of sample-and-hold solutions recently proposed as feedback solutions by Clarke, Ledyaev, Subbotin and Sontag -for equations with a non-Lipschitz and possibly discontinuous right-hand side.},
	doi = {10.1137/S0363012999322031},
	url = {http://hdl.handle.net/1963/3213},
	author = {Benedetto Piccoli and Hector J. Sussmann}
}
@book {2000,
	title = {Well-posedness of the Cauchy problem for n x n systems of conservation laws},
	series = {Mem. Amer. Math. Soc. 146 (2000), no. 694, 134 p.},
	number = {SISSA;184/96/M},
	year = {2000},
	note = {Chapter 1 and 2},
	publisher = {American Mathematical Society},
	organization = {American Mathematical Society},
	url = {http://hdl.handle.net/1963/3495},
	author = {Alberto Bressan and Graziano Crasta and Benedetto Piccoli}
}
@article {1999,
	title = {Nonclassical Shocks and the Cauchy Problem for Nonconvex Conservation Laws},
	journal = {J. Differential Equations 151 (1999) 345-372},
	number = {SISSA;139/97/M},
	year = {1999},
	publisher = {Elsevier},
	abstract = {The Riemann problem for a conservation law with a nonconvex (cubic) flux can be solved in a class of admissible nonclassical solutions that may violate the Oleinik entropy condition but satisfy a single entropy inequality and a kinetic relation. We use such a nonclassical Riemann solver in a front tracking algorithm, and prove that the approximate solutions remain bounded in the total variation norm. The nonclassical shocks induce an increase of the total variation and, therefore, the classical measure of total variation must be modified accordingly. We prove that the front tracking scheme converges strongly to a weak solution satisfying the entropy inequality.},
	doi = {10.1006/jdeq.1998.3513},
	url = {http://hdl.handle.net/1963/3312},
	author = {Debora Amadori and Paolo Baiti and Philippe G. LeFloch and Benedetto Piccoli}
}
@article {1999,
	title = {Projection singularities of extremals for planar systems},
	number = {SISSA;90/99/M},
	year = {1999},
	publisher = {SISSA Library},
	url = {http://hdl.handle.net/1963/1304},
	author = {Ugo Boscain and Benedetto Piccoli}
}
@article {1998,
	title = {A generic classification of time-optimal planar stabilizing feedbacks},
	journal = {SIAM J. Control Optim. 36 (1998) 12-32},
	number = {SISSA;96/95/M},
	year = {1998},
	publisher = {SISSA Library},
	abstract = {Consider the problem of stabilization at the origin in minimum time for a planar control system affine with respect to the control. For a family of generic vector fields, a topological equivalence relation on the corresponding time-optimal feedback synthesis was introduced in a previous paper [Dynamics of Continuous, Discrete and Impulsive Systems, 3 (1997), pp. 335--371]. The set of equivalence classes can be put in a one-to-one correspondence with a discrete family of graphs. This provides a classification of the global structure of generic time-optimal stabilizing feedbacks in the plane, analogous to the classification of smooth dynamical systems developed by Peixoto.},
	doi = {10.1137/S0363012995291117},
	url = {http://hdl.handle.net/1963/998},
	author = {Alberto Bressan and Benedetto Piccoli}
}
@article {1998,
	title = {Geometric control approach to synthesis theory},
	journal = {Rend. Sem. Mat. Univ. Politec. Torino 56 (1998), no. 4, 53-68 (2001)},
	number = {SISSA;63/99/M},
	year = {1998},
	publisher = {SISSA Library},
	url = {http://hdl.handle.net/1963/1277},
	author = {Ugo Boscain and Benedetto Piccoli}
}
@article {1998,
	title = {Infinite time regular synthesis},
	journal = {ESAIM: COCV  3 (1998) 381-405},
	year = {1998},
	publisher = {EDP Sciences},
	abstract = {In this paper we provide a new sufficiency theorem for regular syntheses. The concept of regular synthesis is discussed in [12], where a sufficiency theorem for finite time syntheses is proved. There are interesting examples of optimal syntheses that are very regular, but whose trajectories have time domains not necessarily bounded. The regularity assumptions of the main theorem in [12] are verified by every piecewise smooth feedback control generating extremal trajectories that reach the target in finite time with a finite number of switchings. In the case of this paper the situation is even more complicate, since we admit both trajectories with finite and infinite time. We use weak differentiability assumptions on the synthesis and weak continuity assumptions on the associated value function.},
	doi = {10.1051/cocv:1998117},
	url = {http://hdl.handle.net/1963/3517},
	author = {Benedetto Piccoli}
}
@article {1997,
	title = {Structural stability for time-optimal planar sytheses},
	journal = {Dynam. Contin. Discrete Impuls. Systems 3 (1997), no. 3, 335--371},
	number = {SISSA;95/95/M},
	year = {1997},
	publisher = {SISSA Library},
	url = {http://hdl.handle.net/1963/997},
	author = {Alberto Bressan and Benedetto Piccoli}
}
@article {1997,
	title = {Viscosity solutions and uniquenessfor systems of inhomogeneous balance laws},
	journal = {Discrete Contin. Dynam. Systems 3 (1997), no. 4, 477--5},
	number = {SISSA;67/95/M},
	year = {1997},
	publisher = {SISSA Library},
	url = {http://hdl.handle.net/1963/969},
	author = {Graziano Crasta and Benedetto Piccoli}
}
@article {1995,
	title = {Some control problems for the pendulum},
	journal = {Proceedings of the 34th IEEE Conference on Decision and Control 4 (1995) 3313-3318},
	number = {SISSA;80/95/M},
	year = {1995},
	publisher = {IEEE},
	abstract = {The aim of this paper is to illustrate some geometric techniques for the study of nonlinear systems. The pendulum on one hand is good for its simplicity, on the other it presents many of the difficulties one can encounter treating nonlinear systems.},
	doi = {10.1109/CDC.1995.478998},
	url = {http://hdl.handle.net/1963/982},
	author = {Benedetto Piccoli}
}
