Dynamics-compatible potential fields using stochastic perturbations

Suboptimal stabilizing controllers for linearly solvable system

“…Let d be the maximum degree of Ψ l , Ψ u and polynomials in S and T , and denote (Ψ d u , Ψ d l , S d , T d , d ) as a solution to (13) when the maximum polynomial degree is fixed at d. The hierarchy of SOS programs with increasing polynomial degree produces a sequence of possibly empty solutions…”

“…Hence, V u is also a positive definite function. The second and third to last constraints in (13) ensures that Ψ l is nonincreasing.…”

“…To quantify the performance of the controller, a Monte Carlo experiment is performed. For each polynomial degree that is feasible, the controller obtained from Ψ l in optimization (13) is implemented in 20 simulations of the system subject to random samples of Gaussian white noise with Σ = 1. The initial condition is fixed at x 0 = −0.5 and t = 0.…”

“…This line of research has recently been the subject of focused study by Kappen [7] and Todorov [8]. These results have been developed in a number of compelling directions [9]- [13].…”

Navigation Functions With Time-Varying Destination Manifolds in Star Worlds

“…Alternative to harmonic functions, yet still within the class level-set based methods, are fast marching methods [32], which produce scalar fields by solving numerically a Hamilton-Jacobi pde (cf. [33] for a different way of approaching a level-set construction). The main issue with these methods, in addition to the difficulty of harmonic functions to handle complex obstacle geometries, is related to the complexity of solving the associated PDE.…”