@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}
}
@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}
}
