3 research outputs found
Motion planning and stabilization of nonholonomic systems using gradient flow approximations
Nonlinear control-affine systems with time-varying vector fields are
considered in the paper. We propose a unified control design scheme with
oscillating inputs for solving the trajectory tracking and stabilization
problems. This methodology is based on the approximation of a gradient like
dynamics by trajectories of the designed closed-loop system. As an intermediate
outcome, we characterize the asymptotic behavior of solutions of the considered
class of nonlinear control systems with oscillating inputs under rather general
assumptions on the generating potential function. These results are applied to
examples of nonholonomic trajectory tracking and obstacle avoidance.Comment: submitte
Algebraic Structures and Stochastic Differential Equations driven by Levy processes
We construct an efficient integrator for stochastic differential systems
driven by Levy processes. An efficient integrator is a strong approximation
that is more accurate than the corresponding stochastic Taylor approximation,
to all orders and independent of the governing vector fields. This holds
provided the driving processes possess moments of all orders and the vector
fields are sufficiently smooth. Moreover the efficient integrator in question
is optimal within a broad class of perturbations for half-integer global root
mean-square orders of convergence. We obtain these results using the
quasi-shuffle algebra of multiple iterated integrals of independent Levy
processes.Comment: 41 pages, 11 figure