00512nas a2200121 4500008004300000245004900043210004800092520014900140100002500289700001700314700002300331856003600354 2007 en_Ud 00aTime optimal swing-up of the planar pendulum0 aTime optimal swingup of the planar pendulum3 aThis paper presents qualitative and numerical results on the global structure of the time optimal trajectories of the planar pendulum on a cart.1 aBroucke, Mireille E.1 aMason, Paolo1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/186700378nas a2200109 4500008004300000245006600043210006400109100001700173700001900190700002300209856003600232 2006 en_Ud 00aClassification of stable time-optimal controls on 2-manifolds0 aClassification of stable timeoptimal controls on 2manifolds1 aBoscain, Ugo1 aNikolaev, Igor1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/219600679nas a2200121 4500008004100000245003100041210003100072260000900103520036500112100002100477700002300498856003600521 2005 en d00aHybrid necessary principle0 aHybrid necessary principle bSIAM3 aWe 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.1 aGaravello, Mauro1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/164100333nas a2200109 4500008004300000020001800043245004400061210004200105100001700147700002300164856003600187 2005 en_Ud a2 7056 6511 000aA short introduction to optimal control0 ashort introduction to optimal control1 aBoscain, Ugo1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/225701069nas a2200133 4500008004100000245003500041210003500076260001800111520069800129100002800827700002300855700002100878856003600899 2005 en d00aTraffic flow on a road network0 aTraffic flow on a road network bSISSA Library3 aThis 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.1 aCoclite, Giuseppe Maria1 aPiccoli, Benedetto1 aGaravello, Mauro uhttp://hdl.handle.net/1963/158400868nas a2200145 4500008004300000245005900043210005800102260002300160520042200183100001800605700002100623700001900644700002300663856003600686 2003 en_Ud 00aHybrid optimal control: case study of a car with gears0 aHybrid optimal control case study of a car with gears bTaylor and Francis3 aThe 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.1 aD'Apice, Ciro1 aGaravello, Mauro1 aManzo, Rosanna1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/302200399nas a2200109 4500008004100000245007900041210006900120260001800189100002300207700002300230856003600253 2002 en d00aAdmissible Riemann solvers for genuinely nonlinear P-systems of mixed type0 aAdmissible Riemann solvers for genuinely nonlinear Psystems of m bSISSA Library1 aMercier, Jean-Marc1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/149101129nas a2200133 4500008004100000245005300041210004600094260001800140520073800158100002000896700002000916700002300936856003600959 2002 en d00aOn the reachability of quantized control systems0 areachability of quantized control systems bSISSA Library3 aIn 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.1 aBicchi, Antonio1 aMarigo, Alessia1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/150100379nas a2200109 4500008004300000245006700043210006700110260001300177100002000190700002300210856003600233 2001 en_Ud 00aControllability for discrete systems with a finite control set0 aControllability for discrete systems with a finite control set bSpringer1 aChitour, Yacine1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/311400345nas a2200109 4500008004100000245005000041210005000091260001800141100001700159700002300176856003600199 2001 en d00aExtremal synthesis for generic planar systems0 aExtremal synthesis for generic planar systems bSISSA Library1 aBoscain, Ugo1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/150300375nas a2200109 4500008004100000245006200041210006200103260001800165100002300183700002300206856003600229 2001 en d00aGlobal continuous Riemann solver for nonlinear elasticity0 aGlobal continuous Riemann solver for nonlinear elasticity bSISSA Library1 aMercier, Jean-Marc1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/149300380nas a2200109 4500008004100000245006800041210006700109260001800176100001700194700002300211856003600234 2001 en d00aMorse properties for the minimum time function on 2-D manifolds0 aMorse properties for the minimum time function on 2D manifolds bSISSA Library1 aBoscain, Ugo1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/154100436nas a2200121 4500008004300000245008800043210006900131260001300200100001700213700002500230700002300255856003600278 2001 en_Ud 00aUniqueness of classical and nonclassical solutions for nonlinear hyperbolic systems0 aUniqueness of classical and nonclassical solutions for nonlinear bElsevier1 aBaiti, Paolo1 aLeFloch, Philippe G.1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/311300351nas a2200109 4500008004100000245005300041210005300094260001800147100001700165700002300182856003600205 2000 en d00aAbnormal extremals for minimum time on the plane0 aAbnormal extremals for minimum time on the plane bSISSA Library1 aBoscain, Ugo1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/150800415nas a2200133 4500008004100000020001800041245005500059210005500114260001300169100002000182700002300202700002000225856003600245 2000 en d a0-08-043658-700aQuantized control systems and discrete nonholonomy0 aQuantized control systems and discrete nonholonomy bElsevier1 aMarigo, Alessia1 aPiccoli, Benedetto1 aBicchi, Antonio uhttp://hdl.handle.net/1963/150201019nas a2200133 4500008004300000245006700043210006700110260000900177520060000186100002000786700002300806700002000829856003600849 2000 en_Ud 00aReachability Analysis for a Class of Quantized Control Systems0 aReachability Analysis for a Class of Quantized Control Systems bIEEE3 aWe 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.1 aMarigo, Alessia1 aPiccoli, Benedetto1 aBicchi, Antonio uhttp://hdl.handle.net/1963/351801450nas a2200121 4500008004300000245006400043210006400107260000900171520106500180100002301245700002401268856003601292 2000 en_Ud 00aRegular Synthesis and Sufficiency Conditions for Optimality0 aRegular Synthesis and Sufficiency Conditions for Optimality bSIAM3 aWe 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.1 aPiccoli, Benedetto1 aSussmann, Hector J. uhttp://hdl.handle.net/1963/321300449nam a2200121 4500008004300000245008000043210006900123260003400192100002100226700002100247700002300268856003600291 2000 en_Ud 00aWell-posedness of the Cauchy problem for n x n systems of conservation laws0 aWellposedness of the Cauchy problem for n x n systems of conserv bAmerican Mathematical Society1 aBressan, Alberto1 aCrasta, Graziano1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/349501145nas a2200145 4500008004300000245007900043210006900122260001300191520067400204100002000878700001700898700002500915700002300940856003600963 1999 en_Ud 00aNonclassical Shocks and the Cauchy Problem for Nonconvex Conservation Laws0 aNonclassical Shocks and the Cauchy Problem for Nonconvex Conserv bElsevier3 aThe 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.1 aAmadori, Debora1 aBaiti, Paolo1 aLeFloch, Philippe G.1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/331200367nas a2200109 4500008004100000245006100041210006100102260001800163100001700181700002300198856003600221 1999 en d00aProjection singularities of extremals for planar systems0 aProjection singularities of extremals for planar systems bSISSA Library1 aBoscain, Ugo1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/130401087nas a2200121 4500008004100000245007400041210006900115260001800184520068400202100002100886700002300907856003500930 1998 en d00aA generic classification of time-optimal planar stabilizing feedbacks0 ageneric classification of timeoptimal planar stabilizing feedbac bSISSA Library3 aConsider 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.1 aBressan, Alberto1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/99800347nas a2200109 4500008004100000245005100041210005100092260001800143100001700161700002300178856003600201 1998 en d00aGeometric control approach to synthesis theory0 aGeometric control approach to synthesis theory bSISSA Library1 aBoscain, Ugo1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/127701111nas a2200109 4500008004300000245003600043210003600079260001700115520081000132100002300942856003600965 1998 en_Ud 00aInfinite time regular synthesis0 aInfinite time regular synthesis bEDP Sciences3 aIn 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.1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/351700363nas a2200109 4500008004100000245005800041210005700099260001800156100002100174700002300195856003500218 1997 en d00aStructural stability for time-optimal planar sytheses0 aStructural stability for timeoptimal planar sytheses bSISSA Library1 aBressan, Alberto1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/99700397nas a2200109 4500008004100000245008000041210006900121260001800190100002100208700002300229856003500252 1997 en d00aViscosity solutions and uniquenessfor systems of inhomogeneous balance laws0 aViscosity solutions and uniquenessfor systems of inhomogeneous b bSISSA Library1 aCrasta, Graziano1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/96900558nas a2200109 4500008004100000245004300041210004300084260000900127520025400136100002300390856003500413 1995 en d00aSome control problems for the pendulum0 aSome control problems for the pendulum bIEEE3 aThe 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.1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/982