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In this paper, we consider controllability of discrete-time polynomial systems. First, we present a forward accessibility (local reachability) condition that can be verified in finite time, in contrast to conventional conditions. Second, we give a backward accessibility (local controllability) condition for an invertible system and a condition to verify invertibility. Finally, we derive sufficient conditions to test whether the forward accessible system is reachable and to test the backward accessible system is controllable. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to compute a class of polynomial vector fields, whose associated dynamical system has a given affine variety as attractive and invariant set, a given point in such an affine variety as invariant and attractive and another given affine variety as invariant set, solving the application of this technique in the robotic area. This objective is reached by using some tools taken from algebraic geometry. Practical examples of how these vector fields can be computed are reported. Moreover, by using these techniques, two feedback control laws, respectively, for a unicycle-like mobile robot and for a car-like mobile robot, which make them move, within the workspace, approaching to a selected algebraic curve, are given. [ABSTRACT FROM PUBLISHER]

The primary goal of this paper is to describe the classes of all polynomial vector fields such that the associated dynamical system admits some polynomial Lyapunov functionv(x). By fixing or constraining the time derivative ofv(x) in different ways, several different cases are studied. Hints are given about how to use the results for stability analysis and for non-polynomial systems. [ABSTRACT FROM PUBLISHER]