Structure Preserving Uncertainty Modelling and Robustness Analysis for Spatially Distributed Dissipative Dynamical Systems

Hamiltonian Structure for Dispersive and Dissipative Dynamical Systems

We develop a Hamiltonian theory of a time dispersive and dissipative inhomogeneous medium, as described by a linear response equation respecting causality and power dissipation. The proposed Hamiltonian couples the given system to auxiliary fields, in the universal form of a so-called canonical heat bath. After integrating out the heat bath the original dissipative evolution is exactly reproduc...

Robustness Analysis for Systems with Ellipsoidal Uncertainty

This note derives an explicit expression for computing the robustness margin for affine systems whose real and complex coefficients are related by an ellipsoidal constraint. The expression, which is an application of a result by Chen, Fan, and Nett for rank-one generalized structured singular-value problems, extends and unifies previous results on robustness margin computation for systems with ...

Dissipative Dynamical Systems

Parameter and Predictive Uncertainty Analysis of a Spatially Distributed Watershed

12 Uncertainty quantification is currently receiving a surge in attention in hydrology as researchers 13 are trying to better understand characteristics of the watersheds being studied and as decision 14 makers are keen to better quantify accuracy and precision of model predictions. Informal and 15 formal Bayesian approaches have been documented for assessment of parameter and model 16 predicti...

Distributed Control of Spatially Invariant Systems in Multiple Dimensions: A Structure Preserving Computational Technique

We consider the problem of analysis and control of discretely distributed systems in multidimensional arrays or lattices. For spatially(shift) invariant systems distributed in one spatial dimension, we build an efficient arithmetic that preserves the rational Laurent operator structure, leading to fast iterative methods of solving Lyapunov and Riccati equations and block diagonalizations, and t...