In this talk I will consider a particular class of dynamical systems, which are characterized by having a continuous state space but a discrete input and/or output set, due e.g. to quantization or logic commands. Such systems arise naturally in some applications, and present some system-theoretic peculiarities which, in some specific cases, have useful implications. As it turns out, the study of quantized systems offers motivations for purposefully introducing control discretization even for classical continuous systems. In particular, I will consider the problem of steering physical plants, consisting of dynamic systems capable of complex behaviours, by hierarchically abstracted levels of decision, planning and supervision, i.e. by logic control. The main concern here is to build efficient finite-length plans to steer a complex dynamical system among equilibria in its state space. Steering efficiency is considered as the possibility of compactly representing the set of reachable states, and quickly computing plans to move among them. By introducing suitable control encodings for a symbolic input language, the goal of efficient finite-length steering can be achieved for some general and important classes of dynamical systems. Applications to planning for multitrailer vehicles and underactuated mechanical systems will be discussed.
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