TY - JOUR
T1 - Time optimal swing-up of the planar pendulum
JF - 46th IEEE Conference on Decision and Control (2007) 5389 - 5394
Y1 - 2007
A1 - Mireille E. Broucke
A1 - Paolo Mason
A1 - Benedetto Piccoli
AB - This paper presents qualitative and numerical results on the global structure of the time optimal trajectories of the planar pendulum on a cart.
UR - http://hdl.handle.net/1963/1867
U1 - 2355
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Classification of stable time-optimal controls on 2-manifolds
JF - J. Math. Sci. 135 (2006) 3109-3124
Y1 - 2006
A1 - Ugo Boscain
A1 - Igor Nikolaev
A1 - Benedetto Piccoli
UR - http://hdl.handle.net/1963/2196
U1 - 2048
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
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 - CHAP
T1 - A short introduction to optimal control
T2 - Contrôle non linéaire et applications: Cours donnés à l\\\'école d\\\'été du Cimpa de l\\\'Université de Tlemcen / Sari Tewfit [ed.]. - Paris: Hermann, 2005
Y1 - 2005
A1 - Ugo Boscain
A1 - Benedetto Piccoli
JF - Contrôle non linéaire et applications: Cours donnés à l\\\'école d\\\'été du Cimpa de l\\\'Université de Tlemcen / Sari Tewfit [ed.]. - Paris: Hermann, 2005
SN - 2 7056 6511 0
UR - http://hdl.handle.net/1963/2257
U1 - 1990
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 -
TY - JOUR
T1 - Admissible Riemann solvers for genuinely nonlinear P-systems of mixed type
JF - J. Differ. Equations, 2002, 180, 395
Y1 - 2002
A1 - Jean-Marc Mercier
A1 - Benedetto Piccoli
PB - SISSA Library
UR - http://hdl.handle.net/1963/1491
U1 - 2672
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - On the reachability of quantized control systems
JF - IEEE Trans. Automat. Contr. 47 (2002) 546-563
Y1 - 2002
A1 - Antonio Bicchi
A1 - Alessia Marigo
A1 - Benedetto Piccoli
AB - 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.
PB - SISSA Library
UR - http://hdl.handle.net/1963/1501
U1 - 2662
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Controllability for discrete systems with a finite control set
JF - Math. Control Signals Systems 14 (2001) 173-193
Y1 - 2001
A1 - Yacine Chitour
A1 - Benedetto Piccoli
PB - Springer
UR - http://hdl.handle.net/1963/3114
U1 - 1219
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Extremal synthesis for generic planar systems
JF - J. Dynam. Control Systems, 2001, 7, 209
Y1 - 2001
A1 - Ugo Boscain
A1 - Benedetto Piccoli
PB - SISSA Library
UR - http://hdl.handle.net/1963/1503
U1 - 2660
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Global continuous Riemann solver for nonlinear elasticity
JF - Arch. Ration. Mech. An., 2001, 156, 89
Y1 - 2001
A1 - Jean-Marc Mercier
A1 - Benedetto Piccoli
PB - SISSA Library
UR - http://hdl.handle.net/1963/1493
U1 - 2670
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Morse properties for the minimum time function on 2-D manifolds
JF - J. Dynam. Control Systems 7 (2001), no. 3, 385--423
Y1 - 2001
A1 - Ugo Boscain
A1 - Benedetto Piccoli
PB - SISSA Library
UR - http://hdl.handle.net/1963/1541
U1 - 2622
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Uniqueness of classical and nonclassical solutions for nonlinear hyperbolic systems
JF - J. Differential Equations 172 (2001) 59-82
Y1 - 2001
A1 - Paolo Baiti
A1 - Philippe G. LeFloch
A1 - Benedetto Piccoli
PB - Elsevier
UR - http://hdl.handle.net/1963/3113
U1 - 1220
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Abnormal extremals for minimum time on the plane
Y1 - 2000
A1 - Ugo Boscain
A1 - Benedetto Piccoli
PB - SISSA Library
UR - http://hdl.handle.net/1963/1508
U1 - 2655
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Quantized control systems and discrete nonholonomy
JF - 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
Y1 - 2000
A1 - Alessia Marigo
A1 - Benedetto Piccoli
A1 - Antonio Bicchi
PB - Elsevier
SN - 0-08-043658-7
UR - http://hdl.handle.net/1963/1502
U1 - 2661
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - CHAP
T1 - Reachability Analysis for a Class of Quantized Control Systems
T2 - Proc. 39th IEEE Int. Conf. on Decision and Control 4 (2000) 3963-3968
Y1 - 2000
A1 - Alessia Marigo
A1 - Benedetto Piccoli
A1 - Antonio Bicchi
AB - 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.
JF - Proc. 39th IEEE Int. Conf. on Decision and Control 4 (2000) 3963-3968
PB - IEEE
UR - http://hdl.handle.net/1963/3518
U1 - 746
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Regular Synthesis and Sufficiency Conditions for Optimality
JF - SIAM J. Control Optim. 39 (2000) 359-410
Y1 - 2000
A1 - Benedetto Piccoli
A1 - Hector J. Sussmann
AB - 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.
PB - SIAM
UR - http://hdl.handle.net/1963/3213
U1 - 1088
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - BOOK
T1 - Well-posedness of the Cauchy problem for n x n systems of conservation laws
T2 - Mem. Amer. Math. Soc. 146 (2000), no. 694, 134 p.
Y1 - 2000
A1 - Alberto Bressan
A1 - Graziano Crasta
A1 - Benedetto Piccoli
JF - Mem. Amer. Math. Soc. 146 (2000), no. 694, 134 p.
PB - American Mathematical Society
UR - http://hdl.handle.net/1963/3495
N1 - Chapter 1 and 2
U1 - 769
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Nonclassical Shocks and the Cauchy Problem for Nonconvex Conservation Laws
JF - J. Differential Equations 151 (1999) 345-372
Y1 - 1999
A1 - Debora Amadori
A1 - Paolo Baiti
A1 - Philippe G. LeFloch
A1 - Benedetto Piccoli
AB - 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.
PB - Elsevier
UR - http://hdl.handle.net/1963/3312
U1 - 1018
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Projection singularities of extremals for planar systems
Y1 - 1999
A1 - Ugo Boscain
A1 - Benedetto Piccoli
PB - SISSA Library
UR - http://hdl.handle.net/1963/1304
U1 - 3151
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - A generic classification of time-optimal planar stabilizing feedbacks
JF - SIAM J. Control Optim. 36 (1998) 12-32
Y1 - 1998
A1 - Alberto Bressan
A1 - Benedetto Piccoli
AB - 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.
PB - SISSA Library
UR - http://hdl.handle.net/1963/998
U1 - 2858
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Geometric control approach to synthesis theory
JF - Rend. Sem. Mat. Univ. Politec. Torino 56 (1998), no. 4, 53-68 (2001)
Y1 - 1998
A1 - Ugo Boscain
A1 - Benedetto Piccoli
PB - SISSA Library
UR - http://hdl.handle.net/1963/1277
U1 - 3178
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Infinite time regular synthesis
JF - ESAIM: COCV 3 (1998) 381-405
Y1 - 1998
A1 - Benedetto Piccoli
AB - 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.
PB - EDP Sciences
UR - http://hdl.handle.net/1963/3517
U1 - 747
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Structural stability for time-optimal planar sytheses
JF - Dynam. Contin. Discrete Impuls. Systems 3 (1997), no. 3, 335--371
Y1 - 1997
A1 - Alberto Bressan
A1 - Benedetto Piccoli
PB - SISSA Library
UR - http://hdl.handle.net/1963/997
U1 - 2859
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Viscosity solutions and uniquenessfor systems of inhomogeneous balance laws
JF - Discrete Contin. Dynam. Systems 3 (1997), no. 4, 477--5
Y1 - 1997
A1 - Graziano Crasta
A1 - Benedetto Piccoli
PB - SISSA Library
UR - http://hdl.handle.net/1963/969
U1 - 3485
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Some control problems for the pendulum
JF - Proceedings of the 34th IEEE Conference on Decision and Control 4 (1995) 3313-3318
Y1 - 1995
A1 - Benedetto Piccoli
AB - 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.
PB - IEEE
UR - http://hdl.handle.net/1963/982
U1 - 2874
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -