13,605 research outputs found
A Sums-of-Squares Extension of Policy Iterations
In order to address the imprecision often introduced by widening operators in
static analysis, policy iteration based on min-computations amounts to
considering the characterization of reachable value set of a program as an
iterative computation of policies, starting from a post-fixpoint. Computing
each policy and the associated invariant relies on a sequence of numerical
optimizations. While the early research efforts relied on linear programming
(LP) to address linear properties of linear programs, the current state of the
art is still limited to the analysis of linear programs with at most quadratic
invariants, relying on semidefinite programming (SDP) solvers to compute
policies, and LP solvers to refine invariants.
We propose here to extend the class of programs considered through the use of
Sums-of-Squares (SOS) based optimization. Our approach enables the precise
analysis of switched systems with polynomial updates and guards. The analysis
presented has been implemented in Matlab and applied on existing programs
coming from the system control literature, improving both the range of
analyzable systems and the precision of previously handled ones.Comment: 29 pages, 4 figure
Computationally efficient approximations of the joint spectral radius
The joint spectral radius of a set of matrices is a measure of the maximal
asymptotic growth rate that can be obtained by forming long products of
matrices taken from the set. This quantity appears in a number of application
contexts but is notoriously difficult to compute and to approximate. We
introduce in this paper a procedure for approximating the joint spectral radius
of a finite set of matrices with arbitrary high accuracy. Our approximation
procedure is polynomial in the size of the matrices once the number of matrices
and the desired accuracy are fixed
On suboptimal control design for hybrid automata using predictive control techniques
In this paper we propose an on-line design technique for the target control problem, when the system is modelled by hybrid automata. First, we compute off-line the shortest path, which has the minimum discrete cost, from an initial state to the given target set. Next, we derive a controller which successfully drives the system from the initial state to the target set while minimizing a cost function. The model predictive control (MPC) technique is used when the current state is not within a guard set, otherwise the mixed-integer predictive control (MIPC) technique is employed. An on-line, semi-explicit control algorithm is derived by combining the two techniques. Finally, as an application of the proposed control procedure, the high-speed and energy-saving control problem of the CPU processing isconsidered
The Maximal Positively Invariant Set: Polynomial Setting
This note considers the maximal positively invariant set for polynomial
discrete time dynamics subject to constraints specified by a basic
semialgebraic set. The note utilizes a relatively direct, but apparently
overlooked, fact stating that the related preimage map preserves basic
semialgebraic structure. In fact, this property propagates to underlying
set--dynamics induced by the associated restricted preimage map in general and
to its maximal trajectory in particular. The finite time convergence of the
corresponding maximal trajectory to the maximal positively invariant set is
verified under reasonably mild conditions. The analysis is complemented with a
discussion of computational aspects and a prototype implementation based on
existing toolboxes for polynomial optimization
Studying stellar binary systems with the Laser Interferometer Space Antenna using Delayed Rejection Markov chain Monte Carlo methods
Bayesian analysis of LISA data sets based on Markov chain Monte Carlo methods
has been shown to be a challenging problem, in part due to the complicated
structure of the likelihood function consisting of several isolated local
maxima that dramatically reduces the efficiency of the sampling techniques.
Here we introduce a new fully Markovian algorithm, a Delayed Rejection
Metropolis-Hastings Markov chain Monte Carlo method, to efficiently explore
these kind of structures and we demonstrate its performance on selected LISA
data sets containing a known number of stellar-mass binary signals embedded in
Gaussian stationary noise.Comment: 12 pages, 4 figures, accepted in CQG (GWDAW-13 proceedings
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