2,705 research outputs found
Robust Control of Uncertain Markov Decision Processes with Temporal Logic Specifications
We present a method for designing robust controllers for dynamical systems with linear temporal logic specifications. We abstract the original system by a finite Markov Decision Process (MDP) that has transition probabilities in a specified uncertainty set. A robust control policy for the MDP is generated that maximizes the worst-case probability of satisfying the specification over all transition probabilities in the uncertainty set. To do this, we use a procedure from probabilistic model checking to combine the system model with an automaton representing the specification. This new MDP is then transformed into an equivalent form that satisfies assumptions for stochastic shortest path dynamic programming. A robust version of dynamic programming allows us to solve for a -suboptimal robust control policy with time complexity times that for the non-robust case. We then implement this control policy on the original dynamical system
On the Minimal Revision Problem of Specification Automata
As robots are being integrated into our daily lives, it becomes necessary to
provide guarantees on the safe and provably correct operation. Such guarantees
can be provided using automata theoretic task and mission planning where the
requirements are expressed as temporal logic specifications. However, in
real-life scenarios, it is to be expected that not all user task requirements
can be realized by the robot. In such cases, the robot must provide feedback to
the user on why it cannot accomplish a given task. Moreover, the robot should
indicate what tasks it can accomplish which are as "close" as possible to the
initial user intent. This paper establishes that the latter problem, which is
referred to as the minimal specification revision problem, is NP complete. A
heuristic algorithm is presented that can compute good approximations to the
Minimal Revision Problem (MRP) in polynomial time. The experimental study of
the algorithm demonstrates that in most problem instances the heuristic
algorithm actually returns the optimal solution. Finally, some cases where the
algorithm does not return the optimal solution are presented.Comment: 23 pages, 16 figures, 2 tables, International Joural of Robotics
Research 2014 Major Revision (submitted
Braids of entangled particle trajectories
In many applications, the two-dimensional trajectories of fluid particles are
available, but little is known about the underlying flow. Oceanic floats are a
clear example. To extract quantitative information from such data, one can
measure single-particle dispersion coefficients, but this only uses one
trajectory at a time, so much of the information on relative motion is lost. In
some circumstances the trajectories happen to remain close long enough to
measure finite-time Lyapunov exponents, but this is rare. We propose to use
tools from braid theory and the topology of surface mappings to approximate the
topological entropy of the underlying flow. The procedure uses all the
trajectory data and is inherently global. The topological entropy is a measure
of the entanglement of the trajectories, and converges to zero if they are not
entangled in a complex manner (for instance, if the trajectories are all in a
large vortex). We illustrate the techniques on some simple dynamical systems
and on float data from the Labrador sea.Comment: 24 pages, 21 figures. PDFLaTeX with RevTeX4 macros. Matlab code
included with source. Fixed an inconsistent convention problem. Final versio
4d/2d -> 3d/1d: A song of protected operator algebras
Superconformal field theories (SCFT) are known to possess solvable yet nontrivial sectors in their full operator algebras. Two prime examples are the chiral algebra sector on a two dimensional plane in four dimensional N=2 SCFTs, and the topological quantum mechanics (TQM) sector on a line in three dimensional N=4 SCFTs. Under Weyl transformation, they respectively map to operator algebras on a great torus in S^1ĆS^3 and a great circle in S^3, and are naturally related by reduction along the S^1 factor, which amounts to taking the Cardy (high-temperature) limit of the four dimensional theory on S1ĆS3. We elaborate on this relation by explicit examples that involve both Lagrangian and non-Lagrangian theories in four dimensions, where the chiral algebra sector is generally described by a certain W-algebra, while the three dimensional descendant SCFT always has a (mirror) Lagrangian description. By taking into account a subtle R-symmetry mixing, we provide explicit dictionaries between selected operator product expansion (OPE) data in the four and three dimensional SCFTs, which we verify in the examples using recent localization results in four and three dimensions. Our methods thus provide nontrivial support for various chiral algebra proposals in the literature. Along the way, we also identify three dimensional mirrors for Argyres-Douglas theories of type (A1,D2n+1) reduced on S^1, and find more evidence for earlier proposals in the case of (A_1,A_(2nā2)), which both realize certain superconformal boundary conditions for the four dimensional N=4 super-Yang-Mills. This is a companion paper to arXiv:1911.05741
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