1,742 research outputs found
A Correctness Result for Synthesizing Plans With Loops in Stochastic Domains
Finite-state controllers (FSCs), such as plans with loops, are powerful and
compact representations of action selection widely used in robotics, video
games and logistics. There has been steady progress on synthesizing FSCs in
deterministic environments, but the algorithmic machinery needed for lifting
such techniques to stochastic environments is not yet fully understood. While
the derivation of FSCs has received some attention in the context of discounted
expected reward measures, they are often solved approximately and/or without
correctness guarantees. In essence, that makes it difficult to analyze
fundamental concerns such as: do all paths terminate, and do the majority of
paths reach a goal state?
In this paper, we present new theoretical results on a generic technique for
synthesizing FSCs in stochastic environments, allowing for highly granular
specifications on termination and goal satisfaction
Synthesis of Minimal Error Control Software
Software implementations of controllers for physical systems are at the core
of many embedded systems. The design of controllers uses the theory of
dynamical systems to construct a mathematical control law that ensures that the
controlled system has certain properties, such as asymptotic convergence to an
equilibrium point, while optimizing some performance criteria. However, owing
to quantization errors arising from the use of fixed-point arithmetic, the
implementation of this control law can only guarantee practical stability:
under the actions of the implementation, the trajectories of the controlled
system converge to a bounded set around the equilibrium point, and the size of
the bounded set is proportional to the error in the implementation. The problem
of verifying whether a controller implementation achieves practical stability
for a given bounded set has been studied before. In this paper, we change the
emphasis from verification to automatic synthesis. Using synthesis, the need
for formal verification can be considerably reduced thereby reducing the design
time as well as design cost of embedded control software.
We give a methodology and a tool to synthesize embedded control software that
is Pareto optimal w.r.t. both performance criteria and practical stability
regions. Our technique is a combination of static analysis to estimate
quantization errors for specific controller implementations and stochastic
local search over the space of possible controllers using particle swarm
optimization. The effectiveness of our technique is illustrated using examples
of various standard control systems: in most examples, we achieve controllers
with close LQR-LQG performance but with implementation errors, hence regions of
practical stability, several times as small.Comment: 18 pages, 2 figure
Abstract Learning Frameworks for Synthesis
We develop abstract learning frameworks (ALFs) for synthesis that embody the
principles of CEGIS (counter-example based inductive synthesis) strategies that
have become widely applicable in recent years. Our framework defines a general
abstract framework of iterative learning, based on a hypothesis space that
captures the synthesized objects, a sample space that forms the space on which
induction is performed, and a concept space that abstractly defines the
semantics of the learning process. We show that a variety of synthesis
algorithms in current literature can be embedded in this general framework.
While studying these embeddings, we also generalize some of the synthesis
problems these instances are of, resulting in new ways of looking at synthesis
problems using learning. We also investigate convergence issues for the general
framework, and exhibit three recipes for convergence in finite time. The first
two recipes generalize current techniques for convergence used by existing
synthesis engines. The third technique is a more involved technique of which we
know of no existing instantiation, and we instantiate it to concrete synthesis
problems
Distributed Implementation of Message Sequence Charts
International audienc
Synthesizing a Lego Forklift Controller in GR(1): A Case Study
Reactive synthesis is an automated procedure to obtain a
correct-by-construction reactive system from a given specification. GR(1) is a
well-known fragment of linear temporal logic (LTL) where synthesis is possible
using a polynomial symbolic algorithm. We conducted a case study to learn about
the challenges that software engineers may face when using GR(1) synthesis for
the development of a reactive robotic system. In the case study we developed
two variants of a forklift controller, deployed on a Lego robot. The case study
employs LTL specification patterns as an extension of the GR(1) specification
language, an examination of two specification variants for execution
scheduling, traceability from the synthesized controller to constraints in the
specification, and generated counter strategies to support understanding
reasons for unrealizability. We present the specifications we developed, our
observations, and challenges faced during the case study.Comment: In Proceedings SYNT 2015, arXiv:1602.0078
Exponential stabilization of driftless nonlinear control systems using homogeneous feedback
This paper focuses on the problem of exponential stabilization of controllable, driftless systems using time-varying, homogeneous feedback. The analysis is performed with respect to a homogeneous norm in a nonstandard dilation that is compatible with the algebraic structure of the control Lie algebra. It can be shown that any continuous, time-varying controller that achieves exponential stability relative to the Euclidean norm is necessarily non-Lipschitz. Despite these restrictions, we provide a set of constructive, sufficient conditions for extending smooth, asymptotic stabilizers to homogeneous, exponential stabilizers. The modified feedbacks are everywhere continuous, smooth away from the origin, and can be extended to a large class of systems with torque inputs. The feedback laws are applied to an experimental mobile robot and show significant improvement in convergence rate over smooth stabilizers
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