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A polynomial-time algorithm for determining quadratic Lyapunov functions for nonlinear systems
polynomial-time algorithm determining quadratic Lyapunov functions nonlinear systems
2015/7/13
We consider nonlinear systems dx/dt=f(x(t)) where Df(x(t)) is known to lie in the convex hull of L n times n matrices A_1,ldots,A_L. For such systems, quadratic Lyapunov functions can be determined us...
Quadratic Stabilization and Control of Piecewise-Linear Systems
Piecewise-linear systems quadratic stabilization linear matrix inequality (LMI)
2015/7/13
We consider analysis and controller synthesis of piecewise-linear systems. The method is based on constructing quadratic and piecewise-quadratic Lyapunov functions that prove stability and performance...
Fast Evaluation of Quadratic Control-Lyapunov Policy
Fast Evaluation Quadratic Control-Lyapunov Policy
2015/7/9
The evaluation of a control-Lyapunov policy, with quadratic Lyapunov function, requires the solution of a quadratic program (QP) at each time step. For small problems this QP can be solved explicitly;...
Quadratic Approximate Dynamic Programming for Input-Affine Systems
approximate dynamic programming stochastic control convex optimization
2015/7/9
We consider the use of quadratic approximate value functions for stochastic control problems with input-affine dynamics and convex stage cost and constraints. Evaluating the approximate dynamic progra...
USER’S GUIDE FOR QPOPT 1.0: A FORTRAN PACKAGE FOR QUADRATIC PROGRAMMING
Quadratic programming linear programming linear constraints
2015/7/3
QPOPT is a set of Fortran subroutines for minimizing a general quadratic function
subject to linear constraints and simple upper and lower bounds. QPOPT may also be
used for linear programming and f...
STABLE REDUCTION TO KKT SYSTEMS IN BARRIER METHODS FOR LINEAR AND QUADRATIC PROGRAMMING
interior methods barrier methods linear programming
2015/7/3
We discuss methods for solving the key linear equations within primal-dual barrier
methods for linear and quadratic programming. Following Freund and Jarre, we explore methods
for reducing the Newto...
Weyl group multiple Dirichlet series constructed from quadratic characters
Dirichlet coefficient function equation of variable properties
2014/12/25
We construct multiple Dirichlet series in several complex variables whose coefficients involve quadratic residue symbols. The series are shown to have an analytic continuation and satisfy a certain gr...
On the p-parts of quadratic Weyl group multiple Dirichlet series
Reduce the root dirichlet level dirichlet series
2014/12/24
Let Φ be a reduced root system of rank r. A Weyl group multiple Dirichlet series for Φ is a Dirichlet series in r complex variables s1,…, sr , initially converging for (si) sufficiently large, which h...
Estimating the quadratic covariation of an asynchronously observed semimartingale with jumps
asynchronous observations co-jumps statistics of semimartingales quadratic covariation
2013/6/14
We consider estimation of the quadratic (co)variation of a semimartingale from discrete observations which are irregularly spaced under high-frequency asymptotics. In the univariate setting, results b...
Estimating the quadratic covariation matrix from noisy observations: local method of moments and efficiency
adaptive estimation asymptotic equivalence asynchronous ob-servations integrated covolatility matrix quadratic covariation semiparametric eciency,microstructure noise spectral estimation
2013/4/28
An efficient estimator is constructed for the quadratic covariation or integrated covolatility matrix of a multivariate continuous martingale based on noisy and non-synchronous observations under high...
Efficient Reinforcement Learning for High Dimensional Linear Quadratic Systems
Efficient Reinforcement Learning High Dimensional Linear Quadratic Systems
2013/4/28
We study the problem of adaptive control of a high dimensional linear quadratic (LQ) system. Previous work established the asymptotic convergence to an optimal controller for various adaptive control ...
Statistical estimation of quadratic Rényi entropy for a stationary m-dependent sequence
Entropy estimation quadratic R′enyi entropy stationarym-dependent sequence inter-point distances U-statistics
2013/4/27
The R\'enyi entropy is a generalization of the Shannon entropy and is widely used in mathematical statistics and applied sciences for quantifying the uncertainty in a probability distribution. We cons...
Minimax testing of a composite null hypothesis defined via a quadratic functional in the model of regression
Nonparametric hypotheses testing sharp asymptotics separation rates minimax approach high-dimensional regression.
2012/9/17
We consider the problem of testing a particular type of composite null hypothesis under a nonparametric multivariate regression model. For a given quadraticfunctional Q, the null hypothesis states tha...
Riesz measures and Wishart laws associated to quadratic maps
convex cones homogeneous cones Riesz measures Wishart laws
2011/7/19
We introduce a natural definition of Riesz measures and Wishart laws associated to an $\Omega$-positive (virtual) quadratic map, where $\Omega \subset \real^n$ is a regular open convex cone.
An estimator for the quadratic covariation of asynchronously observed Itô processes with noise: Asymptotic distribution theory
Density estimation Kullback–Leibler divergence
2011/7/6
The article is devoted to the nonparametric estimation of the quadratic covariation of non-synchronously observed It\^o processes in an additive microstructure noise model.