arXiv subjects

Colin N. Jones

Publications and source records attributed to Colin N. Jones.

At least 37 records · Page 2Linked to original sources

arXiv2025

Polynomial and Parallelizable Preconditioning for Block Tridiagonal Positive Definite Matrices

The efficient solution of moderately large-scale linear systems arising from the KKT conditions in optimal control problems (OCPs) is a critical challenge in robotics. With the stagnation of Moore's law, there is growing interest in leveraging GPU-accelerated iterative methods, and corresponding parallel preconditioners, to overcome these computational challenges. To improve the performance of such solvers, we introduce a parallel-friendly, parametrized multi-splitting polynomial preconditioner framework. We first construct and prove the optimal parametrization theoretically in terms of the least amount of distinct eigenvalues and the narrowest spectrum range. We then compare the theoretical time complexity of solving the linear system directly or iteratively. We finally show through numerical experiments how much the preconditioning improves the convergence of OCP linear systems solves.

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arXiv2025

Model Predictive Building Climate Control for Mitigating Heat Pump Noise Pollution (Extended Version)

Noise pollution from heat pumps (HPs) has been an emerging concern to their broader adoption, especially in densely populated areas. This paper explores a model predictive control (MPC) approach for building climate control, aimed at minimizing the noise nuisance generated by HPs. By exploiting a piecewise linear approximation of HP noise patterns and assuming linear building thermal dynamics, the proposed design can be generalized to handle various HP acoustic patterns with mixed-integer linear programming (MILP). Additionally, two computationally efficient options for defining the noise cost function in the proposed MPC design are discussed. Numerical experiments on a high-fidelity building simulator are performed to demonstrate the viability and effectiveness of the proposed design. Simulation results show that the proposed approach can effectively reduce the noise pollution caused by HPs with negligible energy cost increase.

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arXiv2025

Brunovsky Riccati Recursion for Linear Model Predictive Control

In almost all algorithms for Model Predictive Control (MPC), the most time-consuming step is to solve some form of Linear Quadratic (LQ) Optimal Control Problem (OCP) repeatedly. The commonly recognized best option for this is a Riccati recursion based solver, which has a time complexity of $\mathcal{O}(N(n_x^3 + n_x^2 n_u + n_x n_u^2 + n_u^3))$. In this paper, we propose a novel \textit{Brunovsky Riccati Recursion} algorithm to solve LQ OCPs for Linear Time Invariant (LTI) systems. The algorithm transforms the system into Brunovsky form, formulates a new LQ cost (and constraints, if any) in Brunovsky coordinates, performs the Riccati recursion there, and converts the solution back. Due to the sparsity (block-diagonality and zero-one pattern per block) of Brunovsky form and the data parallelism introduced in the cost, constraints, and solution transformations, the time complexity of the new method is greatly reduced to $\mathcal{O}(n_x^3 + N(n_x^2 n_u + n_x n_u^2 + n_u^3))$ if $N$ threads/cores are available for parallel computing.

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arXiv2025

Cooperative distributed model predictive control for embedded systems: Experiments with hovercraft formations

This paper presents experiments for embedded cooperative distributed model predictive control applied to a team of hovercraft floating on an air hockey table. The hovercraft collectively solve a centralized optimal control problem in each sampling step via a stabilizing decentralized real-time iteration scheme using the alternating direction method of multipliers. The efficient implementation does not require a central coordinator, executes onboard the hovercraft, and facilitates sampling intervals in the millisecond range. The formation control experiments showcase the flexibility of the approach on scenarios with point-to-point transitions, trajectory tracking, collision avoidance, and moving obstacles.

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arXiv2025

Constrained Efficient Global Optimization of Expensive Black-box Functions

We study the problem of constrained efficient global optimization, where both the objective and constraints are expensive black-box functions that can be learned with Gaussian processes. We propose CONFIG (CONstrained efFIcient Global Optimization), a simple and effective algorithm to solve it. Under certain regularity assumptions, we show that our algorithm enjoys the same cumulative regret bound as that in the unconstrained case and similar cumulative constraint violation upper bounds. For commonly used Matern and Squared Exponential kernels, our bounds are sublinear and allow us to derive a convergence rate to the optimal solution of the original constrained problem. In addition, our method naturally provides a scheme to declare infeasibility when the original black-box optimization problem is infeasible. Numerical experiments on sampled instances from the Gaussian process, artificial numerical problems, and a black-box building controller tuning problem all demonstrate the competitive performance of our algorithm. Compared to the other state-of-the-art methods, our algorithm significantly improves the theoretical guarantees, while achieving competitive empirical performance.

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arXiv2024

Adaptive Data-Driven Prediction in a Building Control Hierarchy: A Case Study of Demand Response in Switzerland

By providing various services, such as Demand Response (DR), buildings can play a crucial role in the energy market due to their significant energy consumption. However, effectively commissioning buildings for such desired functionalities requires significant expert knowledge and design effort, considering the variations in building dynamics and intended use. In this study, we introduce an adaptive data-driven prediction scheme based on Willems' Fundamental Lemma within the building control hierarchy. This scheme offers a versatile, flexible, and user-friendly interface for diverse prediction and control objectives. We provide an easy-to-use tuning process and an adaptive update pipeline for the scheme, both validated through extensive prediction tests. We evaluate the proposed scheme by coordinating a building and an energy storage system to provide Secondary Frequency Control (SFC) in a Swiss DR program. Specifically, we integrate the scheme into a three-layer hierarchical SFC control framework, and each layer of this hierarchy is designed to achieve distinct operational goals. Apart from its flexibility, our approach significantly improves cost efficiency, resulting in a 28.74% reduction in operating costs compared to a conventional control scheme, as demonstrated by a 52-day experiment in an actual building. Our findings emphasize the potential of the proposed scheme to reduce the commissioning costs of advanced building control strategies and to facilitate the adoption of new techniques in building control.

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arXiv2024

Principled Bayesian Optimisation in Collaboration with Human Experts

Bayesian optimisation for real-world problems is often performed interactively with human experts, and integrating their domain knowledge is key to accelerate the optimisation process. We consider a setup where experts provide advice on the next query point through binary accept/reject recommendations (labels). Experts' labels are often costly, requiring efficient use of their efforts, and can at the same time be unreliable, requiring careful adjustment of the degree to which any expert is trusted. We introduce the first principled approach that provides two key guarantees. (1) Handover guarantee: similar to a no-regret property, we establish a sublinear bound on the cumulative number of experts' binary labels. Initially, multiple labels per query are needed, but the number of expert labels required asymptotically converges to zero, saving both expert effort and computation time. (2) No-harm guarantee with data-driven trust level adjustment: our adaptive trust level ensures that the convergence rate will not be worse than the one without using advice, even if the advice from experts is adversarial. Unlike existing methods that employ a user-defined function that hand-tunes the trust level adjustment, our approach enables data-driven adjustments. Real-world applications empirically demonstrate that our method not only outperforms existing baselines, but also maintains robustness despite varying labelling accuracy, in tasks of battery design with human experts.

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arXiv2024

SIMBa: System Identification Methods leveraging Backpropagation

This manuscript details and extends the SIMBa toolbox (System Identification Methods leveraging Backpropagation) presented in previous work, which uses well-established Machine Learning tools for discrete-time linear multi-step-ahead state-space System Identification (SI). SIMBa leverages linear-matrix-inequality-based free parametrizations of Schur matrices to guarantee the stability of the identified model by design. In this paper, backed up by novel free parametrizations of Schur matrices, we extend the toolbox to show how SIMBa can incorporate known sparsity patterns or true values of the state-space matrices to identify without jeopardizing stability. We extensively investigate SIMBa's behavior when identifying diverse systems with various properties from both simulated and real-world data. Overall, we find it consistently outperforms traditional stable subspace identification methods, and sometimes significantly, especially when enforcing desired model properties. These results hint at the potential of SIMBa to pave the way for generic structured nonlinear SI. The toolbox is open-sourced on https://github.com/Cemempamoi/simba.

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arXiv2024

Risk-aware Scheduling and Dispatch of Flexibility Events in Buildings

Residential and commercial buildings, equipped with systems such as heat pumps (HPs), hot water tanks, or stationary energy storage, have a large potential to offer their consumption flexibility as grid services. In this work, we leverage this flexibility to react to consumption requests related to maximizing self-consumption and reducing peak loads. We employ a data-driven virtual storage modeling approach for flexibility prediction in the form of flexibility envelopes for individual buildings. The risk-awareness of this prediction is inherited by the proposed scheduling algorithm. A Mixed-integer Linear Program (MILP) is formulated to schedule the activation of a pool of buildings in order to best respond to an external aggregated consumption request. This aggregated request is then dispatched to the active individual buildings, based on the previously determined schedule. The effectiveness of the approach is demonstrated by coordinating up to 500 simulated buildings using the Energym Python library and observing about 1.5 times peak power reduction in comparison with a baseline approach while maintaining comfort more robustly. We demonstrate the scalability of the approach by solving problems with 2000 buildings in about 21 seconds, with solving times being approximately linear in the number of considered assets.

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arXiv2024

Principled Preferential Bayesian Optimization

We study the problem of preferential Bayesian optimization (BO), where we aim to optimize a black-box function with only preference feedback over a pair of candidate solutions. Inspired by the likelihood ratio idea, we construct a confidence set of the black-box function using only the preference feedback. An optimistic algorithm with an efficient computational method is then developed to solve the problem, which enjoys an information-theoretic bound on the total cumulative regret, a first-of-its-kind for preferential BO. This bound further allows us to design a scheme to report an estimated best solution, with a guaranteed convergence rate. Experimental results on sampled instances from Gaussian processes, standard test functions, and a thermal comfort optimization problem all show that our method stably achieves better or competitive performance as compared to the existing state-of-the-art heuristics, which, however, do not have theoretical guarantees on regret bounds or convergence.

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arXiv2024

On identifying the non-linear dynamics of a hovercraft using an end-to-end deep learning approach

We present the identification of the non-linear dynamics of a novel hovercraft design, employing end-to-end deep learning techniques. Our experimental setup consists of a hovercraft propelled by racing drone propellers mounted on a lightweight foam base, allowing it to float and be controlled freely on an air hockey table. We learn parametrized physics-inspired non-linear models directly from data trajectories, leveraging gradient-based optimization techniques prevalent in machine learning research. The chosen model structure allows us to control the position of the hovercraft precisely on the air hockey table. We then analyze the prediction performance and demonstrate the closed-loop control performance on the real system.

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arXiv2024

Using Flexibility Envelopes for the Demand-Side Hierarchical Optimization of District Heating Networks

The demand-side control of district heating networks is notoriously challenging due to the large number of connected users and the high number of states to be considered. To overcome these challenges, this paper presents a hierarchical optimization scheme using the flexibility in heating demand provided by the users to improve the performance of the network. This hierarchical scheme relies on a low level controller to calculate the costs for a subsystem over a given set of potential pressure drops for that subsystem. The high level controller then uses these calculated costs to determine the optimal set of pressure drops for every subgraph of the partitioned network. The proposed hierarchical optimization scheme is demonstrated on a representative 20 user district heating network, resulting in a 67\% reduction in bypass mass flow while ensuring all network users stay within 2 \degree C of their desired nominal temperatures.

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arXiv2024

SOStab: a Matlab Toolbox for Transient Stability Analysis

This paper presents a new Matlab toolbox, aimed at facilitating the use of polynomial optimization for stability analysis of nonlinear systems. In the past decade several decisive contributions made it possible to recast this type of problems as convex optimization ones that are tractable in modest dimensions. However, available software requires their user to be fluent in Sum-of-Squares programming, preventing them from being more widely explored by practitioners. To address this issue, SOStab entirely automates the writing and solving of optimization problems, and directly outputs relevant data for the user, while requiring minimal input. In particular, no specific knowledge of optimization is needed for implementation. The toolbox allows a user to obtain outer and inner approximates of the \ac{roa} of the operating point of different grid connected devices such as synchronous machines and power converters.

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arXiv2024

Stable Linear Subspace Identification: A Machine Learning Approach

Machine Learning (ML) and linear System Identification (SI) have been historically developed independently. In this paper, we leverage well-established ML tools - especially the automatic differentiation framework - to introduce SIMBa, a family of discrete linear multi-step-ahead state-space SI methods using backpropagation. SIMBa relies on a novel Linear-Matrix-Inequality-based free parametrization of Schur matrices to ensure the stability of the identified model. We show how SIMBa generally outperforms traditional linear state-space SI methods, and sometimes significantly, although at the price of a higher computational burden. This performance gap is particularly remarkable compared to other SI methods with stability guarantees, where the gain is frequently above 25% in our investigations, hinting at SIMBa's ability to simultaneously achieve state-of-the-art fitting performance and enforce stability. Interestingly, these observations hold for a wide variety of input-output systems and on both simulated and real-world data, showcasing the flexibility of the proposed approach. We postulate that this new SI paradigm presents a great extension potential to identify structured nonlinear models from data, and we hence open-source SIMBa on https://github.com/Cemempamoi/simba.

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arXiv2024

Efficient Recursive Data-enabled Predictive Control (Extended Version)

In the field of model predictive control, Data-enabled Predictive Control (DeePC) offers direct predictive control, bypassing traditional modeling. However, challenges emerge with increased computational demand due to recursive data updates. This paper introduces a novel recursive updating algorithm for DeePC. It emphasizes the use of Singular Value Decomposition (SVD) for efficient low-dimensional transformations of DeePC in its general form, as well as a fast SVD update scheme. Importantly, our proposed algorithm is highly flexible due to its reliance on the general form of DeePC, which is demonstrated to encompass various data-driven methods that utilize Pseudoinverse and Hankel matrices. This is exemplified through a comparison to Subspace Predictive Control, where the algorithm achieves asymptotically consistent prediction for stochastic linear time-invariant systems. Our proposed methodologies' efficacy is validated through simulation studies.

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arXiv2024

Ensuring Data Privacy in AC Optimal Power Flow with a Distributed Co-Simulation Framework

During the energy transition, the significance of collaborative management among institutions is rising, confronting challenges posed by data privacy concerns. Prevailing research on distributed approaches, as an alternative to centralized management, often lacks numerical convergence guarantees or is limited to single-machine numerical simulation. To address this, we present a distributed approach for solving AC Optimal Power Flow (OPF) problems within a geographically distributed environment. This involves integrating the energy system Co-Simulation (eCoSim) module in the eASiMOV framework with the convergence-guaranteed distributed optimization algorithm, i.e., the Augmented Lagrangian based Alternating Direction Inexact Newton method (ALADIN). Comprehensive evaluations across multiple system scenarios reveal a marginal performance slowdown compared to the centralized approach and the distributed approach executed on single machines -- a justified trade-off for enhanced data privacy. This investigation serves as empirical validation of the successful execution of distributed AC OPF within a geographically distributed environment, highlighting potential directions for future research.

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arXiv2024

Real-Time Coordination of Integrated Transmission and Distribution Systems: Flexibility Modeling and Distributed NMPC Scheduling

This paper proposes a real-time distributed operational architecture to efficiently coordinate intergrated transmission and distribution systems (ITD). At the distribution system level, the distribution system operator (DSO) computes the aggregated flexibility of all controllable devices by power-energy envelopes and provides them to the transmission system operators. At the transmission system level, a distributed nonlinear MPC approach is proposed to coordinate the economic dispatch of multiple TSOs, considering the aggregated flexibility of all distribution systems. The subproblems of the proposed approach are associated with different TSOs and individual time periods. In addition, the aggregated flexibility of controllable devices in distribution networks is encapsulated, re-calculated, and communicated through the power-energy envelopes, facilitating a reduction in computational complexity and eliminating redundant information exchanges between TSOs and DSOs, thereby enhancing privacy and security. The framework's effectiveness and applicability in real-world scenarios are validated through simulated operational scenarios on a summer day in Germany, highlighting its robustness in the face of significant prediction mismatches due to severe weather conditions.

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arXiv2024

Advancing Distributed AC Optimal Power Flow for Integrated Transmission-Distribution Systems

This paper introduces a distributed operational solution for coordinating integrated transmission-distribution (ITD) systems regarding data privacy. To tackle the nonconvex challenges of AC optimal power flow (OPF) problems, our research proposes an enhanced version of the Augmented Lagrangian based Alternating Direction Inexact Newton method (ALADIN). This proposed framework incorporates a second-order correction strategy and convexification, thereby enhancing numerical robustness and computational efficiency. The theoretical studies demonstrate that the proposed distributed algorithm operates the ITD systems with a local quadratic convergence guarantee. Extensive simulations on various ITD configurations highlight the superior performance of our distributed approach in terms of convergence speed, computational efficiency, scalability, and adaptability.

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