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Articles 1 - 3 of 3
Full-Text Articles in Dynamical Systems
Optimal Control Of Stochastic Systems: A Numerical Study Of The Stochastic Linear Quadratic Regulator Framework, Gülşen Orucova Büyüköz, Yaprak Güldoğan Dericioğlu, Tuğçem Partal
Optimal Control Of Stochastic Systems: A Numerical Study Of The Stochastic Linear Quadratic Regulator Framework, Gülşen Orucova Büyüköz, Yaprak Güldoğan Dericioğlu, Tuğçem Partal
Mathematical Modelling and Numerical Simulation with Applications
Optimal control of stochastic linear systems is fundamental in control theory, with applications in robotics, finance, and engineering. The Stochastic Linear Quadratic Regulator (SLQR) derives optimal feedback laws via the Riccati equation but requires numerical discretization of the resulting stochastic dynamics. Despite extensive studies on numerical methods for stochastic differential equations, their performance within the SLQR framework remains insufficiently explored. This study compares two predictor–corrector schemes of different orders: the Order 1.0 Predictor-Corrector (PC) method and the Order 2.0 Weak PC method. A one-dimensional linear quadratic problem with a closed-form solution enables precise error evaluation against the analytical trajectory. Convergence …
Ideals, Big Varieties, And Dynamic Networks, Ian H. Dinwoodie
Ideals, Big Varieties, And Dynamic Networks, Ian H. Dinwoodie
Mathematics and Statistics Faculty Publications and Presentations
The advantage of using algebraic geometry over enumeration for describing sets related to attractors in large dynamic networks from biology is advocated. Examples illustrate the gains.
Exact Tests For Singular Network Data, Ian H. Dinwoodie, Kruti Pandya
Exact Tests For Singular Network Data, Ian H. Dinwoodie, Kruti Pandya
Mathematics and Statistics Faculty Publications and Presentations
We propose methodology for exact statistical tests of hypotheses for models of network dynamics. The methodology formulates Markovian exponential families, then uses sequential importance sampling to compute expectations within basins of attraction and within level sets of a sufficient statistic for an over-dispersion model. Comparisons of hypotheses can be done conditional on basins of attraction. Examples are presented.