ISSN:
1573-2878
Keywords:
Controllability
;
reachability
;
disturbed systems
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract This paper addresses the problem of state controllability in the presence of additive disturbances. In contrast to the stochastic controllability problem, the formulation given here does not require a probabilistic description of the uncertainty. Instead, the objective is to steer the state to the target in a so-called guaranteed sense. That is, one only assumes the availability of ana priori bounding setQ for the values of the uncertainty. Within this context, the goal is to decide whether one can find a control, having values restricted to a set Ω, which guarantees the transfer of the state to a prespecified target. Hence, we are led to define the notion of (Ω,Q)-controllability. The main result of this paper is given in Theorem 4.1. Loosely speaking, this theorem gives criteria for (Ω,Q)-controllability, which involve looking at the convergence properties of certain scalar-valued time functions which are created from the known data. In order to achieve this result, it is first shown that the given system (S x with its targetX(·) can be associated with another system (S Y) having targetY(·). Although (S x) has disturbances in its dynamical description, (S Y) is disturbance-free. Moreover, it is shown that (S x) is (Ω,Q)-controllable toX(·) if and only if (S Y) is Ω-controllable toY(·). After transforming the pair [(S x),X(·)] into [(S Y,Y(·)], one can use the known results (e.g., Ref. 1) on Ω-controllability of deterministic systems to determine the controllability properties of the system with disturbances. This line of thought motivates calling (S Y) the associated disturbance-free system. Finally, it is also shown how the required calculations can be greatly simplified for the special case of a polyhedral target.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00934486
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