%0 Journal Article %J 46th IEEE Conference on Decision and Control (2007) 5389 - 5394 %D 2007 %T Time optimal swing-up of the planar pendulum %A Mireille E. Broucke %A Paolo Mason %A Benedetto Piccoli %X This paper presents qualitative and numerical results on the global structure of the time optimal trajectories of the planar pendulum on a cart. %B 46th IEEE Conference on Decision and Control (2007) 5389 - 5394 %G en_US %U http://hdl.handle.net/1963/1867 %1 2355 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-10-11T06:54:22Z\\nNo. of bitstreams: 1\\n50-2006M.pdf: 688756 bytes, checksum: d32f46138cc2e7400dfec38315fdb24a (MD5) %R 10.1109/CDC.2007.4434688 %0 Journal Article %J J. Math. Sci. 135 (2006) 3109-3124 %D 2006 %T Classification of stable time-optimal controls on 2-manifolds %A Ugo Boscain %A Igor Nikolaev %A Benedetto Piccoli %B J. Math. Sci. 135 (2006) 3109-3124 %G en_US %U http://hdl.handle.net/1963/2196 %1 2048 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-11T07:48:50Z\\nNo. of bitstreams: 1\\nboscain-paper.pdf: 322031 bytes, checksum: 560c6fdce3f93d196d1cc9d9c4115edb (MD5) %R 10.1007/s10958-006-0148-0 %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 Book Section %B 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 %D 2005 %T A short introduction to optimal control %A Ugo Boscain %A Benedetto Piccoli %B 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 %@ 2 7056 6511 0 %G en_US %U http://hdl.handle.net/1963/2257 %1 1990 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-18T11:30:24Z\\nNo. of bitstreams: 1\\nNotes-OptCont.pdf: 442775 bytes, checksum: 196e4d9cc52950dd18cf17feb0e89808 (MD5) %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 %0 Journal Article %J J. Differ. Equations, 2002, 180, 395 %D 2002 %T Admissible Riemann solvers for genuinely nonlinear P-systems of mixed type %A Jean-Marc Mercier %A Benedetto Piccoli %B J. Differ. Equations, 2002, 180, 395 %I SISSA Library %G en %U http://hdl.handle.net/1963/1491 %1 2672 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:09Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1006/jdeq.2001.4066 %0 Journal Article %J IEEE Trans. Automat. Contr. 47 (2002) 546-563 %D 2002 %T On the reachability of quantized control systems %A Antonio Bicchi %A Alessia Marigo %A Benedetto Piccoli %X 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. %B IEEE Trans. Automat. Contr. 47 (2002) 546-563 %I SISSA Library %G en %U http://hdl.handle.net/1963/1501 %1 2662 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:18Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1109/9.995034 %0 Journal Article %J Math. Control Signals Systems 14 (2001) 173-193 %D 2001 %T Controllability for discrete systems with a finite control set %A Yacine Chitour %A Benedetto Piccoli %B Math. Control Signals Systems 14 (2001) 173-193 %I Springer %G en_US %U http://hdl.handle.net/1963/3114 %1 1219 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-15T10:33:44Z\\nNo. of bitstreams: 1\\ncontrollability.pdf: 247896 bytes, checksum: 6f94f9b27348f59bb506c1e79beba6e1 (MD5) %R 10.1007/PL00009881 %0 Journal Article %J J. Dynam. Control Systems, 2001, 7, 209 %D 2001 %T Extremal synthesis for generic planar systems %A Ugo Boscain %A Benedetto Piccoli %B J. Dynam. Control Systems, 2001, 7, 209 %I SISSA Library %G en %U http://hdl.handle.net/1963/1503 %1 2660 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:19Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1023/A:1013003204923 %0 Journal Article %J Arch. Ration. Mech. An., 2001, 156, 89 %D 2001 %T Global continuous Riemann solver for nonlinear elasticity %A Jean-Marc Mercier %A Benedetto Piccoli %B Arch. Ration. Mech. An., 2001, 156, 89 %I SISSA Library %G en %U http://hdl.handle.net/1963/1493 %1 2670 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:11Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1007/s002050100118 %0 Journal Article %J J. Dynam. Control Systems 7 (2001), no. 3, 385--423 %D 2001 %T Morse properties for the minimum time function on 2-D manifolds %A Ugo Boscain %A Benedetto Piccoli %B J. Dynam. Control Systems 7 (2001), no. 3, 385--423 %I SISSA Library %G en %U http://hdl.handle.net/1963/1541 %1 2622 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:51Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1023/A:1013190914234 %0 Journal Article %J J. Differential Equations 172 (2001) 59-82 %D 2001 %T Uniqueness of classical and nonclassical solutions for nonlinear hyperbolic systems %A Paolo Baiti %A Philippe G. LeFloch %A Benedetto Piccoli %B J. Differential Equations 172 (2001) 59-82 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3113 %1 1220 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-15T10:27:54Z\\nNo. of bitstreams: 1\\nuniqueness.pdf: 278381 bytes, checksum: d70f89c690a2695e7b44e73737a6aff8 (MD5) %R 10.1006/jdeq.2000.3869 %0 Journal Article %D 2000 %T Abnormal extremals for minimum time on the plane %A Ugo Boscain %A Benedetto Piccoli %I SISSA Library %G en %U http://hdl.handle.net/1963/1508 %1 2655 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:23Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %0 Journal Article %J 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 %D 2000 %T Quantized control systems and discrete nonholonomy %A Alessia Marigo %A Benedetto Piccoli %A Antonio Bicchi %B 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 %I Elsevier %@ 0-08-043658-7 %G en %U http://hdl.handle.net/1963/1502 %1 2661 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:18Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %0 Book Section %B Proc. 39th IEEE Int. Conf. on Decision and Control 4 (2000) 3963-3968 %D 2000 %T Reachability Analysis for a Class of Quantized Control Systems %A Alessia Marigo %A Benedetto Piccoli %A Antonio Bicchi %X 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. %B Proc. 39th IEEE Int. Conf. on Decision and Control 4 (2000) 3963-3968 %I IEEE %G en_US %U http://hdl.handle.net/1963/3518 %1 746 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-18T10:49:16Z\\nNo. of bitstreams: 1\\nquantized-CDC00.pdf: 249884 bytes, checksum: b54871be602650ae79a8f293167c1a1c (MD5) %R 10.1109/CDC.2000.912333 %0 Journal Article %J SIAM J. Control Optim. 39 (2000) 359-410 %D 2000 %T Regular Synthesis and Sufficiency Conditions for Optimality %A Benedetto Piccoli %A Hector J. Sussmann %X 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. %B SIAM J. Control Optim. 39 (2000) 359-410 %I SIAM %G en_US %U http://hdl.handle.net/1963/3213 %1 1088 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-30T10:03:13Z\\nNo. of bitstreams: 1\\npiccolisussmann.pdf: 302609 bytes, checksum: 5cd7041b7e00172b4670a5e17f815e63 (MD5) %R 10.1137/S0363012999322031 %0 Book %B Mem. Amer. Math. Soc. 146 (2000), no. 694, 134 p. %D 2000 %T Well-posedness of the Cauchy problem for n x n systems of conservation laws %A Alberto Bressan %A Graziano Crasta %A Benedetto Piccoli %B Mem. Amer. Math. Soc. 146 (2000), no. 694, 134 p. %I American Mathematical Society %G en_US %U http://hdl.handle.net/1963/3495 %1 769 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-06T11:34:33Z\\nNo. of bitstreams: 1\\nbcpams.pdf: 323551 bytes, checksum: 9bc3f06472e13a47266da010edb58ba1 (MD5) %0 Journal Article %J J. Differential Equations 151 (1999) 345-372 %D 1999 %T Nonclassical Shocks and the Cauchy Problem for Nonconvex Conservation Laws %A Debora Amadori %A Paolo Baiti %A Philippe G. LeFloch %A Benedetto Piccoli %X 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. %B J. Differential Equations 151 (1999) 345-372 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3312 %1 1018 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-11-20T11:49:26Z\\nNo. of bitstreams: 1\\nNonclassical_shocks.pdf: 261875 bytes, checksum: bd41bb6490895996b965941b1eeb6797 (MD5) %R 10.1006/jdeq.1998.3513 %0 Journal Article %D 1999 %T Projection singularities of extremals for planar systems %A Ugo Boscain %A Benedetto Piccoli %I SISSA Library %G en %U http://hdl.handle.net/1963/1304 %1 3151 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:56:02Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %0 Journal Article %J SIAM J. Control Optim. 36 (1998) 12-32 %D 1998 %T A generic classification of time-optimal planar stabilizing feedbacks %A Alberto Bressan %A Benedetto Piccoli %X 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. %B SIAM J. Control Optim. 36 (1998) 12-32 %I SISSA Library %G en %U http://hdl.handle.net/1963/998 %1 2858 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:41:28Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %R 10.1137/S0363012995291117 %0 Journal Article %J Rend. Sem. Mat. Univ. Politec. Torino 56 (1998), no. 4, 53-68 (2001) %D 1998 %T Geometric control approach to synthesis theory %A Ugo Boscain %A Benedetto Piccoli %B Rend. Sem. Mat. Univ. Politec. Torino 56 (1998), no. 4, 53-68 (2001) %I SISSA Library %G en %U http://hdl.handle.net/1963/1277 %1 3178 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:40Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %0 Journal Article %J ESAIM: COCV 3 (1998) 381-405 %D 1998 %T Infinite time regular synthesis %A Benedetto Piccoli %X 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. %B ESAIM: COCV 3 (1998) 381-405 %I EDP Sciences %G en_US %U http://hdl.handle.net/1963/3517 %1 747 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-18T10:02:14Z\\nNo. of bitstreams: 1\\ncocv-Vol3.18.pdf: 313695 bytes, checksum: 34061a9e90f00985dc33afbf45ab584c (MD5) %R 10.1051/cocv:1998117 %0 Journal Article %J Dynam. Contin. Discrete Impuls. Systems 3 (1997), no. 3, 335--371 %D 1997 %T Structural stability for time-optimal planar sytheses %A Alberto Bressan %A Benedetto Piccoli %B Dynam. Contin. Discrete Impuls. Systems 3 (1997), no. 3, 335--371 %I SISSA Library %G en %U http://hdl.handle.net/1963/997 %1 2859 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:41:28Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Journal Article %J Discrete Contin. Dynam. Systems 3 (1997), no. 4, 477--5 %D 1997 %T Viscosity solutions and uniquenessfor systems of inhomogeneous balance laws %A Graziano Crasta %A Benedetto Piccoli %B Discrete Contin. Dynam. Systems 3 (1997), no. 4, 477--5 %I SISSA Library %G en %U http://hdl.handle.net/1963/969 %1 3485 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:41:06Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Journal Article %J Proceedings of the 34th IEEE Conference on Decision and Control 4 (1995) 3313-3318 %D 1995 %T Some control problems for the pendulum %A Benedetto Piccoli %X 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. %B Proceedings of the 34th IEEE Conference on Decision and Control 4 (1995) 3313-3318 %I IEEE %G en %U http://hdl.handle.net/1963/982 %1 2874 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:41:16Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %R 10.1109/CDC.1995.478998