Speciality:
01.01.09 (Discrete mathematics and mathematical cybernetics)
Website: https://researchers.anu.edu.au/researchers/vladimirov-i?term=Vladimirov Keywords: robust control,
stochastic systems,
entropy variational problems,
spatial discretizations,
dynamical systems,
lattice models of statistical mechanics,
transport in random media,
quantum mechanical systems,
quantum stochastic filtering and control
UDC: 519.21 MSC: 93E20, 93E10, 76S05, 82B20
Subject:
Development of the anisotropy-based theory of stochastic robust control, including the homotopy method for anisotropic controller design.
Study of forced oscillations in multivariable hysteresis systems, including the rate of convergence to limit periodic regimes.
Development of the method of frequency measurable quasiperiodic sets for probability theoretic study of spatially discretized dynamical systems.
Multivariate statistical methods for computing the moments of random matrices with application to Bayesian parameter estimation and prediction in diffusion and autoregressive processes.
Approximate computational methods for thermodynamic functions in lattice models of statistical mechanics of interacting particle systems and asymptotic methods for transport phenomena in random media.
Entropy variational problems and dissipation relationships for open stochastic systems under coloured noise of interaction with the environment.
Control/filtering problems for open quantum mechanical systems governed by quantum stochastic differential equations.
Main publications:
I.G. Vladimirov, and I.R. Petersen, “State distributions and minimum relative entropy noise sequences in uncertain stochastic systems: the discrete-time case”, SIAM Journal on Control and Optimization, 53:3 (2015), 1107–1153
I.G. Vladimirov, “The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields”, Discrete and Continuous Dynamical Systems Series B, 18:2 (2013), 575–600
I.G. Vladimirov, and A.Y. Klimenko, “Tracing diffusion in porous media with fractal properties”, SIAM: Multiscale Modeling and Simulation, 8:4 (2010), 1178–1211
I.G. Vladimirov, P. Diamond, and P. Kloeden, “Anisotropy-based robust performance analysis
of finite horizon linear discrete time varying systems”, Automation and Remote Control, 67:8 (2006), 1265–1282
I.G. Vladimirov, N.A. Kuznetsov, and P. Diamond, “Frequency measurability, algebras of quasiperiodic sets and spatial
discretizations of smooth dynamical systems”, Mathematics and Computers in Simulation, 52 (2000), 251–272
ISTINA
