showing 5 related works from this author
Steering dynamical systems with finite plans and limited path length
2007
Complex dynamical systems can be steered by using symbolic input plans. These plans must have a finite descriptive length, and can be expressed by means of words chosen in an alphabet of symbols. In this way, such plans can be sent through a limited capacity channel to a remote system, where they are decoded in suitable control actions. The choice of this symbols is essential to efficiently encode steering plans. To this aim, in this paper, we state the problem of finding symbols maximizing the interval of points reachable by the system along paths with constrained length. We focus on the problem with two symbols, and compare the results with those produced by plans not accounting for the l…
Symbolic control for underactuated differentially flat systems
2006
In this paper we address the problem of generating input plans to steer complex dynamical systems in an obstacle-free environment. Plans considered admit a finite description length and are constructed by words on an alphabet of input symbols, which could be e.g. transmitted through a limited capacity channel to a remote system, where they can be decoded in suitable control actions. We show that, by suitable choice of the control encoding, finite plans can be efficiently built for a wide class of dynamical systems, computing arbitrarily close approximations of a desired equilibrium in polynomial time. Moreover, we illustrate by simulations the power of the proposed method, solving the steer…
Time optimal control of a satellite with two rotors
2001
International audience; The aim of this work is to investigate the structure of time-optimal trajectories for a control system modelizing a satellite with two rotors attached along its two fixed axes. Our results extend to the general case those obtained by Sussmann and Tang in an unpublished paper where they treat a particular case described below. We end up finding a sufficient family of four parameters trajectory types. The main tools used are the Pontryagin Maximum Principle, switching functions and envelope theory. © 2001 EUCA.
On Automaton Recognizability of Abnormal Extremals
2002
For a generic single-input planar control system $\dot x=F(x)+ u G(x),$ $x\in\mathbb{R}^2,$ $u\in [-1,1]$, $F(0)=0$, we analyze the properties of abnormal extremals for the minimum time stabilization to the origin. We prove that abnormal extremals are finite concatenations of bang arcs with switchings occurring on the set in which the vector fields F and G are collinear. Moreover, all the generic singularities of one parametric family of extremal trajectories near to abnormal extremals are studied. In particular, we prove that all possible sequences of these singularities, and hence all generic abnormal extremals, can be classified by a set of words recognizable by an automaton.
Regularization of chattering phenomena via bounded variation controls
2018
In control theory, the term chattering is used to refer to strong oscillations of controls, such as an infinite number of switchings over a compact interval of times. In this paper we focus on three typical occurences of chattering: the Fuller phenomenon, referring to situations where an optimal control switches an infinite number of times over a compact set; the Robbins phenomenon, concerning optimal control problems with state constraints, meaning that the optimal trajectory touches the boundary of the constraint set an infinite number of times over a compact time interval; the Zeno phenomenon, referring as well to an infinite number of switchings over a compact set, for hybrid optimal co…