Finding and Breaking Lie Symmetries: Implications for Structural Identifiability and Observability in Biological Modelling

A dynamic model is structurally identifiable (respectively, observable) if it is theoretically possible to infer its unknown parameters (respectively, states) by observing its output over time. The two properties, structural identifiability and observability, are completely determined by the model equations. Their analysis is of interest for modellers because it informs about the possibility of gaining insight into a model’s unmeasured variables. Here we cast the problem of analysing structural identifiability and observability as that of finding Lie symmetries. We build on previous results that showed that structural unidentifiability amounts to the existence of Lie symmetries. We consider nonlinear models described by ordinary differential equations and restrict ourselves to rational functions. We revisit a method for finding symmetries by transforming rational expressions into linear systems. We extend the method by enabling it to provide symmetry-breaking transformations, which allows for a semi-automatic model reformulation that renders a non-observable model observable. We provide a MATLAB implementation of the methodology as part of the STRIKE-GOLDD toolbox for observability and identifiability analysis. We illustrate the use of the methodology in the context of biological modelling by applying it to a set of problems taken from the literature.

Sparsity-Based Robust Bistatic MIMO Radar Imaging in the Presence of Array Errors

A sparse recovery method for robust transmit-receive angle imaging in a bistatic MIMO radar is proposed to deal with the effect of array gain-phase errors. The impact of multiplicative array gain-phase errors is changed to be additive through model reformulation, and transmit-receive angle imaging is formulated to a sparse total least square signal problem. Then, an iterative algorithm is proposed to solve the optimization problem. Compared with existing methods, the proposed method can achieve a significant performance gain in the case that the number of snapshots is small. Simulation results verify the effectiveness of the proposed method.

A Computationally Efficient Approach for Optimizing Lithium-Ion Battery Charging

This paper presents a framework for optimizing lithium-ion battery charging, subject to side reaction constraints. Such health-conscious control can improve battery performance significantly, while avoiding damage phenomena, such as lithium plating. Battery trajectory optimization problems are computationally challenging because the problems are often nonlinear, nonconvex, and high-order. We address this challenge by exploiting: (i) time-scale separation, (ii) orthogonal projection-based model reformulation, (iii) the differential flatness of solid-phase diffusion dynamics, and (iv) pseudospectral trajectory optimization. The above tools exist individually in the literature. For example, the literature examines battery model reformulation and the pseudospectral optimization of battery charging. However, this paper is the first to combine these four tools into a unified framework for battery management and also the first work to exploit differential flatness in battery trajectory optimization. A simulation study reveals that the proposed framework can be five times more computationally efficient than pseudospectral optimization alone.