arXiv subjects

Ross Drummond

Publications and source records attributed to Ross Drummond.

At least 19 recordsLinked to original sources

arXiv2026

When are selector control strategies optimal for constrained monotone systems?

This paper considers optimal control problems defined by a monotone dynamical system, a monotone cost, and monotone constraints. We identify families of such problems for which the optimal solution is bang-ride, i.e., that it always operates on the constraint boundaries and switches between a finite number of state-feedback controllers. This motivates the use of simpler policies, such as selector control, that can be designed without perfect models and full state measurements. The approach is successfully applied to several variations of the health-aware fast charging problem for lithium-ion batteries.

math.OC↗

arXiv2026

Lifting-Free Quadratic Sum-Of-Squares Programming

Quadratic Sum-Of-Squares (QSOS) optimization problems appear in system identification and machine learning, but standard Schur-complement and second-order cone liftings enlarge conic dimensions and create computational bottlenecks for interior-point methods. This paper introduces a lifting-free regularization that preserves the original conic structure by adding a norm penalty to SOS variables, yielding closed-form primal updates and an unconstrained, concave dual with Lipschitz-continuous gradient. Accelerated first-order methods efficiently maximize this dual, and convergence analysis shows non-asymptotic recovery of the solution. Numerical experiments on constrained regression problems show the proposed method can be 40\% faster than existing solvers such as SCS and handle larger problems than MOSEK, with memory scaling only in the number of equality constraints.

math.OC↗

arXiv2025

Reformulating Parallel-Connected Lithium-Ion Battery Pack Dynamics with Interconnection Resistances as Ordinary Differential Equations

This work presents analytical solutions for the current distribution in lithium-ion battery packs composed of cells connected in parallel, explicitly accounting for the presence of interconnection resistances. These solutions enable the reformulation of the differential-algebraic equations describing the pack dynamics into a set of ordinary differential equations, thereby simplifying simulation and analysis. Conditions under which uniform current sharing across all cells occurs are also derived. The proposed formulation is validated against experimental data and confirms its ability to capture the key behaviours induced by interconnection resistances. These results can support the improved design and control of parallel-connected battery packs.

eess.SY↗

arXiv2025

Singular Arcs in Optimal Control: Closed-loop Implementations without Workarounds

Singular arcs emerge in the solutions of Optimal Control Problems (OCPs) when the optimal inputs on some finite time intervals cannot be directly obtained via the optimality conditions. Solving OCPs with singular arcs often requires tailored treatments, suitable for offline trajectory optimization. This approach can become increasingly impractical for online closed-loop implementations, especially for large-scale engineering problems. Recent development of Integrated Residual Methods (IRM) have indicated their suitability for handling singular arcs; the convergence of error measures in IRM automatically suppresses singular arc-induced fluctuations and leads to non-fluctuating solutions more suitable for practical problems. Through several examples, we demonstrate the advantages of solving OCPs with singular arcs using {IRM} under an economic model predictive control framework. In particular, the following observations are made: (i) IRM does not require special treatment for singular arcs, (ii) it solves the OCPs reliably with singular arc fluctuation suppressed, and (iii) the closed-loop results closely match the analytic optimal solutions.

math.OC↗

arXiv2024

Graded lithium-ion battery pouch cells to homogenise current distributions and mitigate lithium plating

Spatial distributions in current, temperature, state-of-charge and degradation across the plane of large format lithium-ion battery pouch cells can significantly impact their performance, especially at high C-rates. In this paper, a method to smooth out these spatial distributions by grading the electrode microstructure in-the-plane is proposed. A mathematical model of a large format pouch cell is developed and validated against both temperature and voltage experimental data. An analytical solution for the optimal graded electrode that achieves a uniform current distribution across the pouch cell is then derived. The model predicts that the graded electrodes could significantly reduce the likelihood of lithium plating in large format pouch cells, with grading increasing the C-rate at which plating occurs from 2.4C to 4.3C. These results indicate the potential of designing spatially varying electrode architectures to homogenise the response of large format pouch cells and improve their high rate performance.

cond-mat.mtrl-sci↗

arXiv2024

Convex neural network synthesis for robustness in the 1-norm

With neural networks being used to control safety-critical systems, they increasingly have to be both accurate (in the sense of matching inputs to outputs) and robust. However, these two properties are often at odds with each other and a trade-off has to be navigated. To address this issue, this paper proposes a method to generate an approximation of a neural network which is certifiably more robust. Crucially, the method is fully convex and posed as a semi-definite programme. An application to robustifying model predictive control is used to demonstrate the results. The aim of this work is to introduce a method to navigate the neural network robustness/accuracy trade-off.

eess.SY↗

arXiv2024

Mapping back and forth between model predictive control and neural networks

Model predictive control (MPC) for linear systems with quadratic costs and linear constraints is shown to admit an exact representation as an implicit neural network. A method to "unravel" the implicit neural network of MPC into an explicit one is also introduced. As well as building links between model-based and data-driven control, these results emphasize the capability of implicit neural networks for representing solutions of optimisation problems, as such problems are themselves implicitly defined functions.

eess.SY↗

arXiv2024

Tuning the feedback controller gains is a simple way to improve autonomous driving performance

Typical autonomous driving systems are a combination of machine learning algorithms (often involving neural networks) and classical feedback controllers. Whilst significant progress has been made in recent years on the neural network side of these systems, only limited progress has been made on the feedback controller side. Often, the feedback control gains are simply passed from paper to paper with little re-tuning taking place, even though the changes to the neural networks can alter the vehicle's closed loop dynamics. The aim of this paper is to highlight the limitations of this approach; it is shown that re-tuning the feedback controller can be a simple way to improve autonomous driving performance. To demonstrate this, the PID gains of the longitudinal controller in the TCP autonomous vehicle algorithm are tuned. This causes the driving score in CARLA to increase from 73.21 to 77.38, with the results averaged over 16 driving scenarios. Moreover, it was observed that the performance benefits were most apparent during challenging driving scenarios, such as during rain or night time, as the tuned controller led to a more assertive driving style. These results demonstrate the value of developing both the neural network and feedback control policies of autonomous driving systems simultaneously, as this can be a simple and methodical way to improve autonomous driving system performance and robustness.

eess.SY↗

arXiv2023

Constrained optimal control of monotone systems with applications to battery fast-charging

Enabling fast charging for lithium ion batteries is critical to accelerating the green energy transition. As such, there has been significant interest in tailored fast-charging protocols computed from the solutions of constrained optimal control problems. Here, we derive necessity conditions for a fast charging protocol based upon monotone control systems theory.

math.OC↗

arXiv2023

Logarithmically Completely Monotonic Rational Functions

This paper studies the class of logarithmically completely monotonic (LCM) functions. These functions play an important role in characterising externally positive linear systems which find applications in important control problems such as non-overshooting reference tracking. Conditions are proposed to ensure a rational function is LCM, a result that enables the known space of linear continuous-time externally positive systems to be enlarged and an efficient and optimal pole-placement procedure for the monotonic tracking controller synthesis problem to be developed. The presented conditions are shown to be less conservative than existing approaches whilst being computationally tractable.

math.OC↗

arXiv2022

Bounding the difference between model predictive control and neural networks

There is a growing debate on whether the future of feedback control systems will be dominated by data-driven or model-driven approaches. Each of these two approaches has their own complimentary set of advantages and disadvantages, however, only limited attempts have, so far, been developed to bridge the gap between them. To address this issue, this paper introduces a method to bound the worst-case error between feedback control policies based upon model predictive control (MPC) and neural networks (NNs). This result is leveraged into an approach to automatically synthesize MPC policies minimising the worst-case error with respect to a NN. Numerical examples highlight the application of the bounds, with the goal of the paper being to encourage a more quantitative understanding of the relationship between data-driven and model-driven control.

eess.SY↗

arXiv2021

Reduced-Order Neural Network Synthesis with Robustness Guarantees

In the wake of the explosive growth in smartphones and cyberphysical systems, there has been an accelerating shift in how data is generated away from centralised data towards on-device generated data. In response, machine learning algorithms are being adapted to run locally on board, potentially hardware limited, devices to improve user privacy, reduce latency and be more energy efficient. However, our understanding of how these device orientated algorithms behave and should be trained is still fairly limited. To address this issue, a method to automatically synthesize reduced-order neural networks (having fewer neurons) approximating the input/output mapping of a larger one is introduced. The reduced-order neural network's weights and biases are generated from a convex semi-definite programme that minimises the worst-case approximation error with respect to the larger network. Worst-case bounds for this approximation error are obtained and the approach can be applied to a wide variety of neural networks architectures. What differentiates the proposed approach to existing methods for generating small neural networks, e.g. pruning, is the inclusion of the worst-case approximation error directly within the training cost function, which should add robustness. Numerical examples highlight the potential of the proposed approach. The overriding goal of this paper is to generalise recent results in the robustness analysis of neural networks to a robust synthesis problem for their weights and biases.

cs.LG↗

arXiv2021

Regional Stability Analysis of Transitional Fluid Flows

A method to bound the maximum energy perturbation for which regional stability of transitional fluid flow models can be guaranteed is introduced. The proposed method exploits the fact that the fluid model's nonlinearities are both lossless and locally bounded and uses the axes lengths of the ellipsoids for the trajectory set containment as variables in the stability conditions. Compared to existing approaches, the proposed method leads to an average increase in the maximum allowable energy perturbation of 29% for the Waleffe-KimHamilton (WKH) shear flow model and of 38% for the 9-state reduced model of Couette flow.

physics.flu-dyn↗

arXiv2021

Cell-Level State of Charge Estimation for Battery Packs Under Minimal Sensing

This manuscript presents an algorithm for individual Lithium-ion (Li-ion) battery cell state of charge (SOC) estimation in a large-scale battery pack under minimal sensing, where only pack-level voltage and current are measured. For battery packs consisting of up to thousands of cells in electric vehicle or stationary energy storage applications, it is desirable to estimate individual cell SOCs without cell local measurements in order to reduce sensing costs. Mathematically, pure series connected cells yield dynamics given by ordinary differential equations under classical full voltage sensing. In contrast, parallel--series connected battery packs are evidently more challenging because the dynamics are governed by a nonlinear differential--algebraic equations (DAE) system. The majority of the conventional studies on SOC estimation for battery packs benefit from idealizing the pack as a lumped single cell which ultimately lose track of cell-level conditions and are blind to potential risks of cell-level over-charge and over-discharge. This work explicitly models a battery pack with high fidelity cell-by-cell resolution based on the interconnection of single cell models, and examines the observability of cell-level state with only pack-level measurements. A DAE-based state observer with linear output error injection is formulated, where the individual cell SOC and current can be reconstructed from minimal number of pack sensing. The mathematically guaranteed asymptotic convergence of differential and algebraic state estimates is established by considering local Lipschitz continuity property of system nonlinearities. Simulation results for Graphite/NMC cells illustrate convergence for cell SOCs, currents, and voltages.

eess.SY↗

arXiv2021

Robust error bounds for quantised and pruned neural networks

With the rise of smartphones and the internet-of-things, data is increasingly getting generated at the edge on local, personal devices. For privacy, latency and energy saving reasons, this shift is causing machine learning algorithms to move towards decentralisation with the data and algorithms stored, and even trained, locally on devices. The device hardware becomes the main bottleneck for model capability in this set-up, creating a need for slimmed down, more efficient neural networks. Neural network pruning and quantisation are two methods that have been developed for this, with both approaches demonstrating impressive results in reducing the computational cost without sacrificing significantly on model performance. However, the understanding behind these reduction methods remains underdeveloped. To address this issue, a semi-definite program is introduced to bound the worst-case error caused by pruning or quantising a neural network. The method can be applied to many neural network structures and nonlinear activation functions with the bounds holding robustly for all inputs in specified sets. It is hoped that the computed bounds will provide certainty to the performance of these algorithms when deployed on safety-critical systems.

cs.LG↗

arXiv2020

Structural Identifiability of a Pseudo-2D Li-ion Battery Electrochemical Model

Growing demand for fast charging and optimised battery designs is fuelling significant interest in electrochemical models of Li-ion batteries. However, estimating parameter values for these models remains a major challenge. In this paper, a structural identifiability analysis was applied to a pseudo-2D Li-ion electrochemical battery model that can be considered as a linearised and decoupled form of the benchmark Doyle-Fuller-Newman model. From an inspection of the impedance function, it was shown that this model is uniquely parametrised by 21 parameters, being combinations of the electrochemical parameters like the conductivities and diffusion coefficients. The well-posedness of the parameter estimation problem with these parameters was then established. This result could lead to more realistic predictions about the internal state of the battery by identifying the parameter set that can be uniquely identified from the data.

eess.SY↗

arXiv2020

Resolving Kirchhoff's laws for state-estimator design of Li-ion battery packs connected in parallel

A state-space model for Li-ion battery packs with parallel connected cells is introduced. The key feature of this model is an explicit solution to Kirchhoff's laws for parallel connected packs, which expresses the branch currents directly in terms of the model's states, applied current and cell resistances. This avoids the need to solve these equations numerically. To illustrate the potential of the proposed model for pack-level control and estimation, a state-estimator is introduced for the nonlinear parallel pack model. By exploiting the system structure seen in the solution to Kirchhoff's laws, algebraic conditions for the observer gains are obtained that guarantee convergence of the estimator's error. Error convergence is demonstrated through an argument based upon Aizerman's conjecture. It is hoped that the insight brought by this model formulation will allow the wealth of results developed for series connected packs to be applied to those with parallel connections.

eess.SY↗

arXiv2020

Impact of Disturbances on Mixed Traffic Control with Autonomous Vehicles

This paper investigates the impact of disturbances on controlling an autonomous vehicle to smooth mixed traffic flow in a ring road setup. By exploiting the ring structure of this system, it is shown that velocity perturbations impacting any vehicle on the ring enter an uncontrollable and marginally stable mode defined by the sum of relative vehicle spacings. These disturbances are then integrated up by the system and cannot be unwound via controlling the autonomous vehicle. In particular, if the velocity disturbances are zero-mean Gaussians, then the traffic flow on the ring will undergo a random walk with the variance growing indefinitely and independently of the control policy applied. In contrast, the impact of acceleration disturbances is benign as these disturbances do no enter the uncontrollable mode, meaning that they can be easily regulated using the autonomous vehicle. Our results support and complement the existing theoretic analysis and field experiments.

eess.SY↗