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Model predictive control (MPC) controller is considered for temperature management in buildings but its performance heavily depends on hyperparameters. Consequently, MPC necessitates meticulous hyperparameter tuning to attain optimal performance under diverse contracts. However, conventional building controller design is an open-loop process without critical hyperparameter optimization, often leading to suboptimal performance due to unexpected environmental disturbances and modeling errors. Furthermore, these hyperparameters are not adapted to different pricing schemes and may lead to non-economic operations. To address these issues, we propose an efficient performance-oriented building MPC controller tuning method based on a cutting-edge efficient constrained Bayesian optimization algorithm, CONFIG, with global optimality guarantees. We demonstrate that this technique can be applied to efficiently deal with real-world DSM program selection problems under customized black-box constraints and objectives. In this study, a simple MPC controller, which offers the advantages of reduced commissioning costs, enhanced computational efficiency, was optimized to perform on a comparable level to a delicately designed and computationally expensive MPC controller. The results also indicate that with an optimized simple MPC, the monthly electricity cost of a household can be reduced by up to 26.90% compared with the cost when controlled by a basic rule-based controller under the same constraints. Then we compared 12 real electricity contracts in Belgium for a household family with customized black-box occupant comfort constraints. The results indicate a monthly electricity bill saving up to 20.18% when the most economic contract is compared with the worst one, which again illustrates the significance of choosing a proper electricity contract., Comment: 15 pages, 9 figures

Model Predictive Control (MPC) has demonstrated significant potential in improving energy efficiency in building climate control, outperforming traditional controllers commonly used in modern building management systems. Among MPC variants, data-driven predictive control (DPC) offers the advantage of modeling building dynamics directly from data, thereby substantially reducing commissioning efforts. However, inevitable model uncertainties and measurement noise can result in comfort violations, even with dedicated MPC setups. This work introduces a disturbance-adaptive DPC (DAD-DPC) framework designed to ensure asymptotic satisfaction of predefined violation bounds under sufficient conditions. The framework employs a fully data-driven pipeline based on Willems' Fundamental Lemma and conformal prediction for application in building climate control. The proposed DAD-DPC framework was validated using four building cases, leveraging a high-fidelity simulation platform, BOPTEST, and an actual building testbed, Polydome. For a 5% violation bound, the framework achieved energy consumption increases of 2.82%, 2.24%, 3.75%, and 5.09% while reducing comfort violations by 77.62%, 79.51%, 73.26%, and 39.76%, respectively, compared to other controller configurations. These results demonstrate the framework's ability to effectively balance energy consumption and comfort violations, offering a practical solution for building climate control applications.

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., Comment: Accepted to NeurIPS 2024 as a spotlight

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.

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.

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., Comment: Accepted for publication by European Control Conference 2024

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., Comment: Accepted to ICML 2024

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.

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.

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., Comment: First two authors contributed equally. Submitted to IEEE TCST

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.

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., Comment: Accepted at ECC 2024

This paper studies the problem of distributed multi-agent Bayesian optimization with both coupled black-box constraints and known affine constraints. A primal-dual distributed algorithm is proposed that achieves similar regret/violation bounds as those in the single-agent case for the black-box objective and constraint functions. Additionally, the algorithm guarantees an $\mathcal{O}(N\sqrt{T})$ bound on the cumulative violation for the known affine constraints, where $N$ is the number of agents. Hence, it is ensured that the average of the samples satisfies the affine constraints up to the error $\mathcal{O}({N}/{\sqrt{T}})$. Furthermore, we characterize certain conditions under which our algorithm can bound a stronger metric of cumulative violation and provide best-iterate convergence without affine constraint. The method is then applied to both sampled instances from Gaussian processes and a real-world optimal power allocation problem for wireless communication; the results show that our method simultaneously provides close-to-optimal performance and maintains minor violations on average, corroborating our theoretical analysis.

We study the problem of tuning the parameters of a room temperature controller to minimize its energy consumption, subject to the constraint that the daily cumulative thermal discomfort of the occupants is below a given threshold. We formulate it as an online constrained black-box optimization problem where, on each day, we observe some relevant environmental context and adaptively select the controller parameters. In this paper, we propose to use a data-driven Primal-Dual Contextual Bayesian Optimization (PDCBO) approach to solve this problem. In a simulation case study on a single room, we apply our algorithm to tune the parameters of a Proportional Integral (PI) heating controller and the pre-heating time. Our results show that PDCBO can save up to 4.7% energy consumption compared to other state-of-the-art Bayesian optimization-based methods while keeping the daily thermal discomfort below the given tolerable threshold on average. Additionally, PDCBO can automatically track time-varying tolerable thresholds while existing methods fail to do so. We then study an alternative constrained tuning problem where we aim to minimize the thermal discomfort with a given energy budget. With this formulation, PDCBO reduces the average discomfort by up to 63% compared to state-of-the-art safe optimization methods while keeping the average daily energy consumption below the required threshold.

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.

Most of the real-time implementations of the stabilizing optimal control actions suffer from the necessity to provide high computational effort. This paper presents a cutting-edge approach for real-time evaluation of linear-quadratic model predictive control (MPC) that employs a novel generalized stopping criterion, achieving asymptotic stability in the presence of input constraints. The proposed method evaluates a fixed number of iterations independent of the initial condition, eliminating the necessity for computationally expensive methods. We demonstrate the effectiveness of the introduced technique by its implementation of two widely-used first-order optimization methods: the projected gradient descent method (PGDM) and the alternating directions method of multipliers (ADMM). The numerical simulation confirmed a significantly reduced number of iterations, resulting in suboptimality rates of less than 2\,\%, while the effort reductions exceeded 80\,\%. These results nominate the proposed criterion for an efficient real-time implementation method of MPC controllers.

For linear systems, many data-driven control methods rely on the behavioral framework, using historical data of the system to predict the future trajectories. However, measurement noise introduces errors in predictions. When the noise is bounded, we propose a method for designing historical experiments that enable the computation of an upper bound on the prediction error. This approach allows us to formulate a minimax control problem where robust constraint satisfaction is enforced. We derive an upper bound on the suboptimality gap of the resulting control input sequence compared to optimal control utilizing accurate measurements. As demonstrated in numerical experiments, the solution derived by our method can achieve constraint satisfaction and a small suboptimality gap despite the measurement noise.

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.

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.

This paper presents a novel distributed approach for solving AC power flow (PF) problems. The optimization problem is reformulated into a distributed form using a communication structure corresponding to a hypergraph, by which complex relationships between subgrids can be expressed as hyperedges. Then, a hypergraph-based distributed sequential quadratic programming (HDQ) approach is proposed to handle the reformulated problems, and the hypergraph-based distributed sequential quadratic programming (HDSQP) is used as the inner algorithm to solve the corresponding QP subproblems, which are respectively condensed using Schur complements with respect to coupling variables defined by hyperedges. Furthermore, we rigorously establish the convergence guarantee of the proposed algorithm with a locally quadratic rate and the one-step convergence of the inner algorithm when using the Levenberg-Marquardt regularization. Our analysis also demonstrates that the computational complexity of the proposed algorithm is much lower than the state-of-art distributed algorithm. We implement the proposed algorithm in an open-source toolbox, i.e., rapidPF, and conduct numerical tests that validate the proof and demonstrate the great potential of the proposed distributed algorithm in terms of communication effort and computational speed.

We consider the problem of optimizing a grey-box objective function, i.e., nested function composed of both black-box and white-box functions. A general formulation for such grey-box problems is given, which covers the existing grey-box optimization formulations as special cases. We then design an optimism-driven algorithm to solve it. Under certain regularity assumptions, our algorithm achieves similar regret bound as that for the standard black-box Bayesian optimization algorithm, up to a constant multiplicative term depending on the Lipschitz constants of the functions considered. We further extend our method to the constrained case and discuss special cases. For the commonly used kernel functions, the regret bounds allow us to derive a convergence rate to the optimal solution. Experimental results show that our grey-box optimization method empirically improves the speed of finding the global optimal solution significantly, as compared to the standard black-box optimization algorithm.

Data-enabled predictive control (DeePC) is a recently established form of Model Predictive Control (MPC), based on behavioral systems theory. While eliminating the need to explicitly identify a model, it requires an additional regularization with a corresponding weight to function well with noisy data. The tuning of this weight is non-trivial and has a significant impact on performance. In this paper, we compare three reformulations of DeePC that either eliminate the regularization, or simplify the tuning to a trivial point. A building simulation study shows a comparable performance for all three reformulations of DeePC. However, a conventional MPC with a black-box model slightly outperforms them, while solving much faster, and yielding smoother optimal trajectories. Two of the DeePC variants also show sensitivity to an unobserved biased input noise, which is not present in the conventional MPC., Comment: Submitted to CDC 2023

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., Comment: 22 pages, 8 figures

This paper studies the problem of online performance optimization of constrained closed-loop control systems, where both the objective and the constraints are unknown black-box functions affected by exogenous time-varying contextual disturbances. A primal-dual contextual Bayesian optimization algorithm is proposed that achieves sublinear cumulative regret with respect to the dynamic optimal solution under certain regularity conditions. Furthermore, the algorithm achieves zero time-average constraint violation, ensuring that the average value of the constraint function satisfies the desired constraint. The method is applied to both sampled instances from Gaussian processes and a continuous stirred tank reactor parameter tuning problem; simulation results show that the method simultaneously provides close-to-optimal performance and maintains constraint feasibility on average. This contrasts current state-of-the-art methods, which either suffer from large cumulative regret or severe constraint violations for the case studies presented.

This paper presents PIQP, a high-performance toolkit for solving generic sparse quadratic programs (QP). Combining an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM), the algorithm can handle ill-conditioned convex QP problems without the need for linear independence of the constraints. The open-source implementation is written in C++ with interfaces to C, Python, Matlab, and R leveraging the Eigen3 library. The method uses a pivoting-free factorization routine and allocation-free updates of the problem data, making the solver suitable for embedded applications. The solver is evaluated on the Maros-M\'esz\'aros problem set and optimal control problems, demonstrating state-of-the-art performance for both small and large-scale problems, outperforming commercial and open-source solvers.

(Extended Version) Data-driven control can facilitate the rapid development of controllers, offering an alternative to conventional approaches. In order to maintain consistency between any known underlying physical laws and a data-driven decision-making process, preprocessing of raw data is necessary to account for measurement noise and any inconsistencies it may introduce. In this paper, we present a physics-based filter to achieve this and demonstrate its effectiveness through practical applications, using real-world datasets collected in a building on the Ecole Polytechnique Federale de Lausanne (EPFL) campus. Two distinct use cases are explored: indoor temperature control and demand response bidding.

The potential of Model Predictive Control in buildings has been shown many times, being successfully used to achieve various goals, such as minimizing energy consumption or maximizing thermal comfort. However, mass deployment has thus far failed, in part because of the high engineering cost of obtaining and maintaining a sufficiently accurate model. This can be addressed by using adaptive data-driven approaches. The idea of using behavioral systems theory for this purpose has recently found traction in the academic community. In this study, we compare variations thereof with different amounts of data used, different regularization weights, and different methods of data selection. Autoregressive models with exogenous inputs (ARX) are used as a well-established reference. All methods are evaluated by performing iterative system identification on two long-term data sets from real occupied buildings, neither of which include artificial excitation for the purpose of system identification. We find that: (1) Sufficient prediction accuracy is achieved with all methods. (2) The ARX models perform slightly better, while having the additional advantages of fewer tuning parameters and faster computation. (3) Adaptive and non-adaptive schemes perform similarly. (4) The regularization weights of the behavioral systems theory methods show the expected trade-off characteristic with an optimal middle value. (5) Using the most recent data yields better performance than selecting data with similar weather as the day to be predicted. (6) More data improves the model performance.

We study the problem of performance optimization of closed-loop control systems with unmodeled dynamics. Bayesian optimization (BO) has been demonstrated to be effective for improving closed-loop performance by automatically tuning controller gains or reference setpoints in a model-free manner. However, BO methods have rarely been tested on dynamical systems with unmodeled constraints and time-varying ambient conditions. In this paper, we propose a violation-aware contextual BO algorithm (VACBO) that optimizes closed-loop performance while simultaneously learning constraint-feasible solutions under time-varying ambient conditions. Unlike classical constrained BO methods which allow unlimited constraint violations, or 'safe' BO algorithms that are conservative and try to operate with near-zero violations, we allow budgeted constraint violations to improve constraint learning and accelerate optimization. We demonstrate the effectiveness of our proposed VACBO method for energy minimization of industrial vapor compression systems under time-varying ambient temperature and humidity., Comment: arXiv admin note: substantial text overlap with arXiv:2110.07479

Model-free Reinforcement Learning (RL) generally suffers from poor sample complexity, mostly due to the need to exhaustively explore the state-action space to find well-performing policies. On the other hand, we postulate that expert knowledge of the system often allows us to design simple rules we expect good policies to follow at all times. In this work, we hence propose a simple yet effective modification of continuous actor-critic frameworks to incorporate such rules and avoid regions of the state-action space that are known to be suboptimal, thereby significantly accelerating the convergence of RL agents. Concretely, we saturate the actions chosen by the agent if they do not comply with our intuition and, critically, modify the gradient update step of the policy to ensure the learning process is not affected by the saturation step. On a room temperature control case study, it allows agents to converge to well-performing policies up to 6-7x faster than classical agents without computational overhead and while retaining good final performance., Comment: Accepted to CDC 2023

In this paper, the CONFIG algorithm, a simple and provably efficient constrained global optimization algorithm, is applied to optimize the closed-loop control performance of an unknown system with unmodeled constraints. Existing Gaussian process based closed-loop optimization methods, either can only guarantee local convergence (e.g., SafeOPT), or have no known optimality guarantee (e.g., constrained expected improvement) at all, whereas the recently introduced CONFIG algorithm has been proven to enjoy a theoretical global optimality guarantee. In this study, we demonstrate the effectiveness of CONFIG algorithm in the applications. The algorithm is first applied to an artificial numerical benchmark problem to corroborate its effectiveness. It is then applied to a classical constrained steady-state optimization problem of a continuous stirred-tank reactor. Simulation results show that our CONFIG algorithm can achieve performance competitive with the popular CEI (Constrained Expected Improvement) algorithm, which has no known optimality guarantee. As such, the CONFIG algorithm offers a new tool, with both a provable global optimality guarantee and competitive empirical performance, to optimize the closed-loop control performance for a system with soft unmodeled constraints. Last, but not least, the open-source code is available as a python package to facilitate future applications.

Despite the immense success of neural networks in modeling system dynamics from data, they often remain physics-agnostic black boxes. In the particular case of physical systems, they might consequently make physically inconsistent predictions, which makes them unreliable in practice. In this paper, we leverage the framework of Irreversible port-Hamiltonian Systems (IPHS), which can describe most multi-physics systems, and rely on Neural Ordinary Differential Equations (NODEs) to learn their parameters from data. Since IPHS models are consistent with the first and second principles of thermodynamics by design, so are the proposed Physically Consistent NODEs (PC-NODEs). Furthermore, the NODE training procedure allows us to seamlessly incorporate prior knowledge of the system properties in the learned dynamics. We demonstrate the effectiveness of the proposed method by learning the thermodynamics of a building from the real-world measurements and the dynamics of a simulated gas-piston system. Thanks to the modularity and flexibility of the IPHS framework, PC-NODEs can be extended to learn physically consistent models of multi-physics distributed systems., Comment: First two authors contributed equally. Submitted to IFAC 2023

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., Comment: Accepted to ICML 2023; We revise the Theorem 5.1 on infeasibility declaration in the published version of PMLR

Cooperative control of connected and automated vehicles (CAVs) promises smoother traffic flow. In mixed traffic, where human-driven vehicles with unknown dynamics coexist, data-driven predictive control techniques allow for CAV safe and optimal control with measurable traffic data. However, the centralized control setting in most existing strategies limits their scalability for large-scale mixed traffic flow. To address this problem, this paper proposes a cooperative DeeP-LCC (Data-EnablEd Predictive Leading Cruise Control) formulation and its distributed implementation algorithm. In cooperative DeeP-LCC, the traffic system is naturally partitioned into multiple subsystems with one single CAV, which collects local trajectory data for subsystem behavior predictions based on the Willems' fundamental lemma. Meanwhile, the cross-subsystem interaction is formulated as a coupling constraint. Then, we employ the Alternating Direction Method of Multipliers (ADMM) to design the distributed DeeP-LCC algorithm. This algorithm achieves both computation and communication efficiency, as well as trajectory data privacy, through parallel calculation. Our simulations on different traffic scales verify the real-time wave-dampening potential of distributed DeeP-LCC, which can reduce fuel consumption by over 31.84% in a large-scale traffic system of 100 vehicles with only 5%-20% CAVs., Comment: 28 pages, 9 figures

Buildings are a promising source of flexibility for the application of demand response. In this work, we introduce a novel battery model formulation to capture the state evolution of a single building. Being fully data-driven, the battery model identification requires one dataset from a period of nominal controller operation, and one from a period with flexibility requests, without making any assumptions on the underlying controller structure. We consider parameter uncertainty in the model formulation and show how to use risk measures to encode risk preferences of the user in robust uncertainty sets. Finally, we demonstrate the uncertainty-aware prediction of flexibility envelopes for a building simulation model from the Python library Energym., Comment: 7 pages, 3 figures. Submitted to the 2023 American Control Conference (ACC)

Efficient global optimization is a widely used method for optimizing expensive black-box functions such as tuning hyperparameter, and designing new material, etc. Despite its popularity, less attention has been paid to analyzing the inherent hardness of the problem although, given its extensive use, it is important to understand the fundamental limits of efficient global optimization algorithms. In this paper, we study the worst-case complexity of the efficient global optimization problem and, in contrast to existing kernel-specific results, we derive a unified lower bound for the complexity of efficient global optimization in terms of the metric entropy of a ball in its corresponding reproducing kernel Hilbert space~(RKHS). Specifically, we show that if there exists a deterministic algorithm that achieves suboptimality gap smaller than $\epsilon$ for any function $f\in S$ in $T$ function evaluations, it is necessary that $T$ is at least $\Omega\left(\frac{\log\mathcal{N}(S(\mathcal{X}), 4\epsilon,\|\cdot\|_\infty)}{\log(\frac{R}{\epsilon})}\right)$, where $\mathcal{N}(\cdot,\cdot,\cdot)$ is the covering number, $S$ is the ball centered at $0$ with radius $R$ in the RKHS and $S(\mathcal{X})$ is the restriction of $S$ over the feasible set $\mathcal{X}$. Moreover, we show that this lower bound nearly matches the upper bound attained by non-adaptive search algorithms for the commonly used squared exponential kernel and the Mat\'ern kernel with a large smoothness parameter $\nu$, up to a replacement of $d/2$ by $d$ and a logarithmic term $\log\frac{R}{\epsilon}$. That is to say, our lower bound is nearly optimal for these kernels.

We propose a framework for the stability verification of Mixed-Integer Linear Programming (MILP) representable control policies. This framework compares a fixed candidate policy, which admits an efficient parameterization and can be evaluated at a low computational cost, against a fixed baseline policy, which is known to be stable but expensive to evaluate. We provide sufficient conditions for the closed-loop stability of the candidate policy in terms of the worst-case approximation error with respect to the baseline policy, and we show that these conditions can be checked by solving a Mixed-Integer Quadratic Program (MIQP). Additionally, we demonstrate that an outer and inner approximation of the stability region of the candidate policy can be computed by solving an MILP. The proposed framework is sufficiently general to accommodate a broad range of candidate policies including ReLU Neural Networks (NNs), optimal solution maps of parametric quadratic programs, and Model Predictive Control (MPC) policies. We also present an open-source toolbox in Python based on the proposed framework, which allows for the easy verification of custom NN architectures and MPC formulations. We showcase the flexibility and reliability of our framework in the context of a DC-DC power converter case study and investigate its computational complexity.

Nonlinear model predictive control has been widely adopted to manipulate bilinear systems with dynamics that include products of the inputs and the states. These systems are ubiquitous in chemical processes, mechanical systems, and quantum physics, to name a few. Running a bilinear MPC controller in real time requires solving a non-convex optimization problem within a limited sampling time. This paper proposes a novel parallel proximal-point Lagrangian based bilinear MPC solver via an interlacing horizon-splitting scheme. The resulting algorithm converts the non-convex MPC control problem into a set of parallelizable small-scale multi-parametric quadratic programs (mpQPs) and an equality-constrained linear-quadratic regulator problem. As a result, the solutions of mpQPs can be pre-computed offline to enable efficient online computation. The proposed algorithm is validated on a simulation of an HVAC system control. It is deployed on a TI LaunchPad XL F28379D microcontroller to execute speed control on a field-controlled DC motor, where the MPC updates at 10 ms and solves the problem in 1.764 ms on average and at most 2.088 ms.

Smart home appliances can time-shift and curtail their power demand to assist demand side management or allow operation with limited power, as in an off-grid application. This paper proposes a scheduling process to start appliances with time-varying deterministic load profiles. Self-triggered model predictive control is used to limit the household net power demand below a given threshold. Meanwhile, deterministic load profiles are more difficult to schedule compared to variable charging or thermal loads because system failure will occur once power demand is not satisfied. The proposed scheme formulates the decision of the load shifting time as a continuous optimization problem, and an inhomogeneous time grid system is introduced to handle the optimization of different appliances and their consensus at this resolution. The efficacy of the proposed scheme is studied by numerical comparison with a mixed-integer MPC controller and by a case study of three home appliances and an interruptible washing machine.

This manuscript offers the perspective of experimentalists on a number of modern data-driven techniques: model predictive control relying on Gaussian processes, adaptive data-driven control based on behavioral theory, and deep reinforcement learning. These techniques are compared in terms of data requirements, ease of use, computational burden, and robustness in the context of real-world applications. Our remarks and observations stem from a number of experimental investigations carried out in the field of building control in diverse environments, from lecture halls and apartment spaces to a hospital surgery center. The final goal is to support others in identifying what technique is best suited to tackle their own problems.

Federated learning (FL) is a promising learning paradigm that can tackle the increasingly prominent isolated data islands problem while keeping users' data locally with privacy and security guarantees. However, FL could result in task-oriented data traffic flows over wireless networks with limited radio resources. To design communication-efficient FL, most of the existing studies employ the first-order federated optimization approach that has a slow convergence rate. This however results in excessive communication rounds for local model updates between the edge devices and edge server. To address this issue, in this paper, we instead propose a novel over-the-air second-order federated optimization algorithm to simultaneously reduce the communication rounds and enable low-latency global model aggregation. This is achieved by exploiting the waveform superposition property of a multi-access channel to implement the distributed second-order optimization algorithm over wireless networks. The convergence behavior of the proposed algorithm is further characterized, which reveals a linear-quadratic convergence rate with an accumulative error term in each iteration. We thus propose a system optimization approach to minimize the accumulated error gap by joint device selection and beamforming design. Numerical results demonstrate the system and communication efficiency compared with the state-of-the-art approaches., Comment: 30 pages, 9 figures

Replacing poorly performing existing controllers with smarter solutions will decrease the energy intensity of the building sector. Recently, controllers based on Deep Reinforcement Learning (DRL) have been shown to be more effective than conventional baselines. However, since the optimal solution is usually unknown, it is still unclear if DRL agents are attaining near-optimal performance in general or if there is still a large gap to bridge. In this paper, we investigate the performance of DRL agents compared to the theoretically optimal solution. To that end, we leverage Physically Consistent Neural Networks (PCNNs) as simulation environments, for which optimal control inputs are easy to compute. Furthermore, PCNNs solely rely on data to be trained, avoiding the difficult physics-based modeling phase, while retaining physical consistency. Our results hint that DRL agents not only clearly outperform conventional rule-based controllers, they furthermore attain near-optimal performance., Comment: Submitted to IEEE ICCA 2022 - 6 pages, 5 figures

This paper addresses a data-driven input reconstruction problem based on Willems' Fundamental Lemma in which unknown input estimators (UIEs) are constructed directly from historical I/O data. Given only output measurements, the inputs are estimated by the UIE, which is shown to asymptotically converge to the true input without knowing the initial conditions. Both open-loop and closed-loop UIEs are developed based on Lyapunov conditions and the Luenberger-observer-type feedback, whose convergence properties are studied. An experimental study is presented demonstrating the efficacy of the closed-loop UIE for estimating the occupancy of a building on the EPFL campus via measured carbon dioxide levels.

The increasing application of voltage source converter (VSC) high voltage direct current (VSC-HVDC) technology in power grids has raised the importance of incorporating DC grids and converters into the existing transmission network. This poses significant challenges in dealing with the resulting optimal power flow (OPF) problem. In this paper, a recently proposed nonconvex distributed optimization algorithm -- Augmented Lagrangian based Alternating Direction Inexact Newton method (ALADIN), is tailored to solve the nonconvex AC/DC OPF problem for emerging voltage source converter (VSC) based multiterminal high voltage direct current (VSC-MTDC) meshed AC/DC hybrid systems. The proposed scheme decomposes this AC/DC hybrid OPF problem and handles it in a fully distributed way. Compared to the existing state-of-art Alternating Direction Method of Multipliers(ADMM), which is in general, not applicable for nonconvex problems, ALADIN has a theoretical convergence guarantee. Applying these two approaches to (VSC-MTDC) coupled with an IEEE benchmark AC power system illustrates that the tailored ALADIN outperforms ADMM in convergence speed and numerical robustness.

Federated learning (FL), as an emerging edge artificial intelligence paradigm, enables many edge devices to collaboratively train a global model without sharing their private data. To enhance the training efficiency of FL, various algorithms have been proposed, ranging from first-order to second-order methods. However, these algorithms cannot be applied in scenarios where the gradient information is not available, e.g., federated black-box attack and federated hyperparameter tuning. To address this issue, in this paper we propose a derivative-free federated zeroth-order optimization (FedZO) algorithm featured by performing multiple local updates based on stochastic gradient estimators in each communication round and enabling partial device participation. Under non-convex settings, we derive the convergence performance of the FedZO algorithm on non-independent and identically distributed data and characterize the impact of the numbers of local iterates and participating edge devices on the convergence. To enable communication-efficient FedZO over wireless networks, we further propose an over-the-air computation (AirComp) assisted FedZO algorithm. With an appropriate transceiver design, we show that the convergence of AirComp-assisted FedZO can still be preserved under certain signal-to-noise ratio conditions. Simulation results demonstrate the effectiveness of the FedZO algorithm and validate the theoretical observations., Comment: This work was accepted to Transaction on Signal Processing

Herein we report a multi-zone, heating, ventilation and air-conditioning (HVAC) control case study of an industrial plant responsible for cooling a hospital surgery center. The adopted approach to guaranteeing thermal comfort and reducing electrical energy consumption is based on a statistical non-parametric, non-linear regression technique named Gaussian processes. Our study aimed at assessing the suitability of the aforementioned technique to learning the building dynamics and yielding models for our model predictive control (MPC) scheme. Experimental results gathered while the building was under regular use showcase the final controller performance while subject to a number of measured and unmeasured disturbances. Finally, we provide readers with practical details and recommendations on how to manage the computational complexity of the on-line optimization problem and obtain high-quality solutions from solvers., Comment: 11 pages, 8 figures

Due to their high energy intensity, buildings play a major role in the current worldwide energy transition. Building models are ubiquitous since they are needed at each stage of the life of buildings, i.e. for design, retrofitting, and control operations. Classical white-box models, based on physical equations, are bound to follow the laws of physics but the specific design of their underlying structure might hinder their expressiveness and hence their accuracy. On the other hand, black-box models are better suited to capture nonlinear building dynamics and thus can often achieve better accuracy, but they require a lot of data and might not follow the laws of physics, a problem that is particularly common for neural network (NN) models. To counter this known generalization issue, physics-informed NNs have recently been introduced, where researchers introduce prior knowledge in the structure of NNs to ground them in known underlying physical laws and avoid classical NN generalization issues. In this work, we present a novel physics-informed NN architecture, dubbed Physically Consistent NN (PCNN), which only requires past operational data and no engineering overhead, including prior knowledge in a linear module running in parallel to a classical NN. We formally prove that such networks are physically consistent - by design and even on unseen data - with respect to different control inputs and temperatures outside and in neighboring zones. We demonstrate their performance on a case study, where the PCNN attains an accuracy up to 40% better than a classical physics-based resistance-capacitance model on 3-day long prediction horizons. Furthermore, despite their constrained structure, PCNNs attain similar performance to classical NNs on the validation data, overfitting the training data less and retaining high expressiveness to tackle the generalization issue., Comment: Preprint submitted to Applied Energy. 13 pages in the main text + 5 in appendix, 11 figures

The wide adoption of wireless devices in the Internet of Things requires controllers that are able to operate with limited resources, such as battery life. Operating these devices robustly in an uncertain environment, while managing available resources, increases the difficultly of controller design. This paper proposes a robust self-triggered model predictive control approach to optimize a control objective while managing resource consumption. In particular, a novel zero-order-hold aperiodic discrete-time feedback control law is developed to ensure robust constraint satisfaction for continuous-time linear systems., Comment: Accepted to L-CSS and ACC 2022

We study the problem of performance optimization of closed-loop control systems with unmodeled dynamics. Bayesian optimization (BO) has been demonstrated effective for improving closed-loop performance by automatically tuning controller gains or reference setpoints in a model-free manner. However, BO methods have rarely been tested on dynamical systems with unmodeled constraints. In this paper, we propose a violation-aware BO algorithm (VABO) that optimizes closed-loop performance while simultaneously learning constraint-feasible solutions. Unlike classical constrained BO methods which allow an unlimited constraint violations, or safe BO algorithms that are conservative and try to operate with near-zero violations, we allow budgeted constraint violations to improve constraint learning and accelerate optimization. We demonstrate the effectiveness of our proposed VABO method for energy minimization of industrial vapor compression systems.