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 - 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 -