196,728 research outputs found
Optimal Decentralized State-Feedback Control with Sparsity and Delays
This work presents the solution to a class of decentralized linear quadratic
state-feedback control problems, in which the plant and controller must satisfy
the same combination of delay and sparsity constraints. Using a novel
decomposition of the noise history, the control problem is split into
independent subproblems that are solved using dynamic programming. The approach
presented herein both unifies and generalizes many existing results
Optimal Control for LQG Systems on Graphs---Part I: Structural Results
In this two-part paper, we identify a broad class of decentralized
output-feedback LQG systems for which the optimal control strategies have a
simple intuitive estimation structure and can be computed efficiently. Roughly,
we consider the class of systems for which the coupling of dynamics among
subsystems and the inter-controller communication is characterized by the same
directed graph. Furthermore, this graph is assumed to be a multitree, that is,
its transitive reduction can have at most one directed path connecting each
pair of nodes. In this first part, we derive sufficient statistics that may be
used to aggregate each controller's growing available information. Each
controller must estimate the states of the subsystems that it affects (its
descendants) as well as the subsystems that it observes (its ancestors). The
optimal control action for a controller is a linear function of the estimate it
computes as well as the estimates computed by all of its ancestors. Moreover,
these state estimates may be updated recursively, much like a Kalman filter
Optimal Navigation Functions for Nonlinear Stochastic Systems
This paper presents a new methodology to craft navigation functions for
nonlinear systems with stochastic uncertainty. The method relies on the
transformation of the Hamilton-Jacobi-Bellman (HJB) equation into a linear
partial differential equation. This approach allows for optimality criteria to
be incorporated into the navigation function, and generalizes several existing
results in navigation functions. It is shown that the HJB and that existing
navigation functions in the literature sit on ends of a spectrum of
optimization problems, upon which tradeoffs may be made in problem complexity.
In particular, it is shown that under certain criteria the optimal navigation
function is related to Laplace's equation, previously used in the literature,
through an exponential transform. Further, analytical solutions to the HJB are
available in simplified domains, yielding guidance towards optimality for
approximation schemes. Examples are used to illustrate the role that noise, and
optimality can potentially play in navigation system design.Comment: Accepted to IROS 2014. 8 Page
Approximate Dynamic Programming via Sum of Squares Programming
We describe an approximate dynamic programming method for stochastic control
problems on infinite state and input spaces. The optimal value function is
approximated by a linear combination of basis functions with coefficients as
decision variables. By relaxing the Bellman equation to an inequality, one
obtains a linear program in the basis coefficients with an infinite set of
constraints. We show that a recently introduced method, which obtains convex
quadratic value function approximations, can be extended to higher order
polynomial approximations via sum of squares programming techniques. An
approximate value function can then be computed offline by solving a
semidefinite program, without having to sample the infinite constraint. The
policy is evaluated online by solving a polynomial optimization problem, which
also turns out to be convex in some cases. We experimentally validate the
method on an autonomous helicopter testbed using a 10-dimensional helicopter
model.Comment: 7 pages, 5 figures. Submitted to the 2013 European Control
Conference, Zurich, Switzerlan
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