pwc-archive/papers-with-abstracts huggingface dataset:
Nonlinear moving horizon estimation for robust state and parameter estimation - extended version
Authors: Julian D. Schiller, Matthias A. Müller
Date: 2023-12-20 00:00:00
Tasks: parameter estimation

We propose a moving horizon estimation scheme to estimate the states and the unknown constant parameters of general nonlinear uncertain discrete-time systems. The proposed framework and analysis explicitly do not involve the a priori verification of a particular excitation condition for the parameters. Instead, we use online information about the actual excitation of the parameters at any time during operation and ensure that the regularization term in the cost function is always automatically selected appropriately. This ensures that the state and parameter estimation error is bounded for all times, even if the parameters are never (or only rarely) excited during operation. Robust exponential stability of the state and parameter estimation error emerges under an additional uniform condition on the maximum duration of insufficient excitation. The theoretical results are illustrated by a numerical example.
Feasibility Conditions for Mobile LiFi
Authors: Shuai Ma, Haihong Sheng, Junchang Sun, Hang Li, Xiaodong Liu, Chen Qiu, Majid Safari, Naofal Al-Dhahir, Shiyin Li
Date: 2023-12-20 00:00:00

Light fidelity (LiFi) is a potential key technology for future 6G networks. However, its feasibility of supporting mobile communications has not been fundamentally discussed. In this paper, we investigate the time-varying channel characteristics of mobile LiFi based on measured mobile phone rotation and movement data. Specifically, we define LiFi channel coherence time to evaluate the correlation of the channel timing sequence. Then, we derive the expression of LiFi transmission rate based on the m-pulse-amplitude-modulation (M-PAM). The derived rate expression indicates that mobile LiFi communications is feasible by using at least two photodiodes (PDs) with different orientations. Further, we propose two channel estimation schemes, and propose a LiFi channel tracking scheme to improve the communication performance. Finally, our experimental results show that the channel coherence time is on the order of tens of milliseconds, which indicates a relatively stable channel. In addition, based on the measured data, better communication performance can be realized in the multiple-input multiple-output (MIMO) scenario with a rate of 36Mbit/s, compared to other scenarios. The results also show that the proposed channel estimation and tracking schemes are effective in designing mobile LiFi systems.
Joint Trading and Scheduling among Coupled Carbon-Electricity-Heat-Gas Industrial Clusters
Authors: Dafeng Zhu, Bo Yang, Yu Wu, Haoran Deng, ZhaoYang Dong, Kai Ma, Xinping Guan
Date: 2023-12-20 00:00:00
Tasks: energy trading, Management, Scheduling

This paper presents a carbon-energy coupling management framework for an industrial park, where the carbon flow model accompanying multi-energy flows is adopted to track and suppress carbon emissions on the user side. To deal with the quadratic constraint of gas flows, a bound tightening algorithm for constraints relaxation is adopted. The synergies among the carbon capture, energy storage, power-to-gas further consume renewable energy and reduce carbon emissions. Aiming at carbon emissions disparities and supply-demand imbalances, this paper proposes a carbon trading ladder reward and punishment mechanism and an energy trading and scheduling method based on Lyapunov optimization and matching game to maximize the long-term benefits of each industrial cluster without knowing the prior information of random variables. Case studies show that our proposed trading method can reduce overall costs and carbon emissions while relieving energy pressure, which is important for Environmental, Social and Governance (ESG).
Stochastic Control Barrier Functions with Bayesian Inference for Unknown Stochastic Differential Equations
Authors: Chuanzheng Wang, Yiming Meng, Jun Liu, Stephen Smith
Date: 2023-12-20 00:00:00
Tasks: Bayesian Inference

Control barrier functions are widely used to synthesize safety-critical controls. However, the presence of Gaussian-type noise in dynamical systems can generate unbounded signals and potentially result in severe consequences. Although research has been conducted in the field of safety-critical control for stochastic systems, in many real-world scenarios, we do not have precise knowledge about the stochastic dynamics. In this paper, we delve into the safety-critical control for stochastic systems where both the drift and diffusion components are unknown. We employ Bayesian inference as a data-driven approach to approximate the system. To be more specific, we utilize Bayesian linear regression along with the central limit theorem to estimate the drift term, and employ Bayesian inference to approximate the diffusion term. Through simulations, we verify our findings by applying them to a nonlinear dynamical model and an adaptive cruise control model.
Stochastic Control Barrier Functions for Economics
Authors: David van Wijk
Date: 2023-12-19 00:00:00
Tasks: Portfolio Optimization

Control barrier functions (CBFs) and safety-critical control have seen a rapid increase in popularity in recent years, predominantly applied to systems in aerospace, robotics and neural network controllers. Control barrier functions can provide a computationally efficient method to monitor arbitrary primary controllers and enforce state constraints to ensure overall system safety. One area that has yet to take advantage of the benefits offered by CBFs is the field of finance and economics. This manuscript re-introduces three applications of traditional control to economics, and develops and implements CBFs for such problems. We consider the problem of optimal advertising for the deterministic and stochastic case and Merton's portfolio optimization problem. Numerical simulations are used to demonstrate the effectiveness of using traditional control solutions in tandem with CBFs and stochastic CBFs to solve such problems in the presence of state constraints.
Optimal Power Flow Pursuit via Feedback-based Safe Gradient Flow
Authors: Antonin Colot, Yiting Chen, Bertrand Cornelusse, Jorge Cortes, Emiliano Dall'Anese
Date: 2023-12-19 00:00:00

This paper considers the problem of controlling inverter-interfaced distributed energy resources (DERs) in a distribution grid to solve an AC optimal power flow (OPF) problem in real time. The AC OPF includes voltage constraints, and seeks to minimize costs associated with the economic operation, power losses, or the power curtailment from renewables. We develop an online feedback optimization method to drive the DERs' power setpoints to solutions of an AC OPF problem based only on voltage measurements (and without requiring measurements of the power consumption of non-controllable assets). The proposed method - grounded on the theory of control barrier functions - is based on a continuous approximation of the projected gradient flow, appropriately modified to accommodate measurements from the power network. We provide results in terms of local exponential stability, and assess the robustness to errors in the measurements and in the system Jacobian matrix. We show that the proposed method ensures anytime satisfaction of the voltage constraints when no model and measurement errors are present; if these errors are present and are small, the voltage violation is practically negligible. We also discuss extensions of the framework to virtual power plant setups and to cases where constraints on power flows and currents must be enforced. Numerical experiments on a 93-bus distribution system and with realistic load and production profiles show a superior performance in terms of voltage regulation relative to existing methods.
Safety verification of Neural-Network-based controllers: a set invariance approach
Authors: Louis Jouret, Adnane Saoud, Sorin Olaru
Date: 2023-12-18 00:00:00

This paper presents a novel approach to ensure the safety of continuous-time linear dynamical systems controlled by a neural network (NN) based state-feedback. Our method capitalizes on the use of continuous piece-wise affine (PWA) activation functions (e.g. ReLU) which render the NN a PWA continuous function. By computing the affine regions of the latter and applying Nagumo's theorem, a subset of boundary points can effectively verify the invariance of a potentially non-convex set. Consequently, an algorithm that partitions the state space in affine regions is proposed. The scalability of our approach is thoroughly analyzed, and extensive tests are conducted to validate its effectiveness.
Learning flow functions of spiking systems
Authors: Miguel Aguiar, Amritam Das, Karl H. Johansson
Date: 2023-12-19 00:00:00

We propose a framework for surrogate modelling of spiking systems. These systems are often described by stiff differential equations with high-amplitude oscillations and multi-timescale dynamics, making surrogate models an attractive tool for system design and simulation. We parameterise the flow function of a spiking system using a recurrent neural network architecture, allowing for a direct continuous-time representation of the state trajectories. The spiking nature of the signals makes for a data-heavy and computationally hard training process; thus, we describe two methods to mitigate these difficulties. We demonstrate our framework on two conductance-based models of biological neurons, showing that we are able to train surrogate models which accurately replicate the spiking behaviour.
Stable Relay Learning Optimization Approach for Fast Power System Production Cost Minimization Simulation
Authors: Zishan Guo, Qinran Hu, Tao Qian, Xin Fang, Renjie Hu, Zaijun Wu
Date: 2023-12-19 00:00:00
Tasks: Imitation Learning, Reinforcement Learning (RL)

Production cost minimization (PCM) simulation is commonly employed for assessing the operational efficiency, economic viability, and reliability, providing valuable insights for power system planning and operations. However, solving a PCM problem is time-consuming, consisting of numerous binary variables for simulation horizon extending over months and years. This hinders rapid assessment of modern energy systems with diverse planning requirements. Existing methods for accelerating PCM tend to sacrifice accuracy for speed. In this paper, we propose a stable relay learning optimization (s-RLO) approach within the Branch and Bound (B&B) algorithm. The proposed approach offers rapid and stable performance, and ensures optimal solutions. The two-stage s-RLO involves an imitation learning (IL) phase for accurate policy initialization and a reinforcement learning (RL) phase for time-efficient fine-tuning. When implemented on the popular SCIP solver, s-RLO returns the optimal solution up to 2 times faster than the default relpscost rule and 1.4 times faster than IL, or exhibits a smaller gap at the predefined time limit. The proposed approach shows stable performance, reducing fluctuations by approximately 50% compared with IL. The efficacy of the proposed s-RLO approach is supported by numerical results.
Angle-Displacement Rigidity Theory with Application to Distributed Network Localization
Authors: Xu Fang, Xiaolei Li, Lihua Xie
Date: 2023-12-19 00:00:00
Tasks: Position

This paper investigates the localization problem of a network in 2-D and 3-D spaces given the positions of anchor nodes in a global frame and inter-node relative measurements in local coordinate frames. It is assumed that the local frames of different nodes have different unknown orientations. First, an angle-displacement rigidity theory is developed, which can be used to localize all the free nodes by the known positions of the anchor nodes and local relative measurements (local relative position, distance, local relative bearing, angle, or ratio-of-distance measurements). Then, necessary and sufficient conditions for network localizability are given. Finally, a distributed network localization protocol is proposed, which can globally estimate the locations of all the free nodes of a network if the network is infinitesimally angle-displacement rigid. The proposed method unifies local-relative-position-based, distance-based, local-relative-bearing-based, angle-based, and ratio-of-distance-based distributed network localization approaches. The novelty of this work is that the proposed method can be applied in both generic and non-generic configurations with an unknown global coordinate frame in both 2-D and 3-D spaces.
Distributed Semi-global Output Feedback Formation Maneuver Control of High-order Multi-agent Systems
Authors: Xu Fang, Lihua Xie
Date: 2023-12-19 00:00:00

This paper addresses the formation maneuver control problem of leader-follower multi-agent systems with high-order integrator dynamics. A distributed output feedback formation maneuver controller is proposed to achieve desired maneuvers so that the scale, orientation, translation, and shape of formation can be manipulated continuously, where the followers do not need to know or estimate the time-varying maneuver parameters only known to the leaders. Compared with existing relative-measurement-based formation maneuver control, the advantages of the proposed method are that it is output (relative output) feedback based and shows how to realize different types of formation shape. In addition, it can be applied to non-generic and non-convex nominal configurations and the leaders are allowed to be maneuvered. It is worth noting that the proposed method can also be extended to general linear multi-agent systems under some additional conditions. The theoretical results are demonstrated by a simulation example.
Dual parametric and state estimation for partial differential equations
Authors: Saviz Mowlavi, Mouhacine Benosman
Date: 2023-12-19 00:00:00
Tasks: State Estimation

Designing estimation algorithms for systems governed by partial differential equations (PDEs) such as fluid flows is challenging due to the high-dimensional and oftentimes nonlinear nature of the dynamics, as well as their dependence on unobserved physical parameters. In this paper, we propose two different lightweight and effective methodologies for real-time state estimation of PDEs in the presence of parametric uncertainties. Both approaches combine a Kalman filter with a data-driven polytopic linear reduced-order model obtained by dynamic mode decomposition (DMD). Using examples involving the nonlinear Burgers and Navier-Stokes equations, we demonstrate accurate estimation of both the state and the unknown physical parameter along system trajectories corresponding to various physical parameter values.
Singular Control of (Reflected) Brownian Motion: A Computational Method Suitable for Queueing Applications
Authors: Baris Ata, J. Michael Harrison, Nian Si
Date: 2023-12-19 00:00:00

Motivated by applications in queueing theory, we consider a class of singular stochastic control problems whose state space is the d-dimensional positive orthant. The original problem is approximated by a drift control problem, to which we apply a recently developed computational method that is feasible for dimensions up to d=30 or more. To show that nearly optimal solutions are obtainable using this method, we present computational results for a variety of examples, including queueing network examples that have appeared previously in the literature.
Learning disturbance models for offset-free reference tracking
Authors: Pablo Krupa, Mario Zanon, Alberto Bemporad
Date: 2023-12-18 00:00:00

This work presents a nonlinear MPC framework that guarantees asymptotic offset-free tracking of generic reference trajectories by learning a nonlinear disturbance model, which compensates for input disturbances and model-plant mismatch. Our approach generalizes the well-established method of using an observer to estimate a constant disturbance to allow tracking constant setpoints with zero steady-state error. In this paper, the disturbance model is generalized to a nonlinear static function of the plant's state and command input, learned online, so as to perfectly track time-varying reference trajectories under certain assumptions on the model and provided that future reference samples are available. We compare our approach with the classical constant disturbance model in numerical simulations, showing its superiority.
Data-driven Estimation of Under Frequency Load Shedding after Outages in Small Power Systems
Authors: Mohammad Rajabdorri, Lukas Sigrist, Enrique Lobato, Matthias C. M. Troffaes, Behzad Kazemtabrizi
Date: 2023-12-18 00:00:00
Tasks: Scheduling

This paper presents a data-driven methodology for estimating Under Frequency Load Shedding (UFLS) in small power systems. UFLS plays a vital role in maintaining system stability by shedding load when the frequency drops below a specified threshold following loss of generation. Using a dynamic System Frequency Response (SFR) model we generate different values of UFLS (i.e., labels) predicated on a set of carefully selected operating conditions (i.e., features). Machine Learning (ML) algorithms are then applied to learn the relationship between chosen features and the UFLS labels. A novel regression tree and the Tobit model are suggested for this purpose and we show how the resulting non-linear model can be directly incorporated into a Mixed Integer Linear Programming (MILP) problem. The trained model can be used to estimate UFLS in security-constrained operational planning problems, improving frequency response, optimizing reserve allocation, and reducing costs. The methodology is applied to the La Palma island power system, demonstrating its accuracy and effectiveness. The results confirm that the amount of UFLS can be estimated with the Mean Absolute Error (MAE) as small as 0.213 MW for the whole process, with a model that is representable as a MILP for use in scheduling problems such as unit commitment among others.
Data-Driven Continuous-Time Framework for Frequency-Constrained Unit Commitment
Authors: Mohammad Rajabdorri, Enrique Lobato, Lukas Sigrist, Jamshid Aghaei
Date: 2023-12-18 00:00:00

The conventional approach to solving the unit commitment problem involves discrete intervals at an hourly scale, particularly when integrating frequency dynamics to formulate a frequency-constrained unit commitment. To overcome this limitation, a novel continuous-time frequency-constrained unit commitment framework is proposed in this paper. In this approach, Bernstein polynomials represent continuous variables in the unit commitment problem and enable the calculation of frequency response-related metrics such as the rate of change of frequency, quasi-steady-state frequency, and frequency nadir. Notably, startup and shut-down trajectories are meticulously considered, transforming the formulation into a fully continuous-time model and simplifying constraints related to variable continuity. To address the complexities associated with integrating the obtained non-linear frequency nadir constraint into a mixed-integer linear problem, an alternative data-driven frequency nadir constraint is proposed, which accurately constrains frequency nadir deviations throughout the time interval. To validate the proposed model, it is applied to the real-life network of the Spanish Island of La Palma. The results demonstrate the effectiveness of the proposed formulation, indicating that the model is solved timely while mitigating the impact of intra-hour real-time power fluctuations on system frequency.
State-action control barrier functions: Imposing safety on learning-based control with low online computational costs
Authors: Kanghui He, Shengling Shi, Ton van den Boom, Bart De Schutter
Date: 2023-12-18 00:00:00
Tasks: CPU, valid

Learning-based control with safety guarantees usually requires real-time safety certification and modifications of possibly unsafe learning-based policies. The control barrier function (CBF) method uses a safety filter containing a constrained optimization problem to produce safe policies. However, finding a valid CBF for a general nonlinear system requires a complex function parameterization, which in general, makes the policy optimization problem difficult to solve in real time. For nonlinear systems with nonlinear state constraints, this paper proposes the novel concept of state-action CBFs, which not only characterize the safety at each state but also evaluate the control inputs taken at each state. State-action CBFs, in contrast to CBFs, enable a flexible parameterization, resulting in a safety filter that involves a convex quadratic optimization problem. This, in turn, significantly alleviates the online computational burden. To synthesize state-action CBFs, we propose a learning-based approach exploiting Hamilton-Jacobi reachability. The effect of learning errors on the effectiveness of state-action CBFs is addressed by constraint tightening and introducing a new concept called contractive CBFs. These contributions ensure formal safety guarantees for learned CBFs and control policies, enhancing the applicability of learning-based control in real-time scenarios. Simulation results on an inverted pendulum with elastic walls validate the proposed CBFs in terms of constraint satisfaction and CPU time.
Robust Optimal Control With Binary Adjustable Uncertainties
Authors: Yun Li, Neil Yorke-Smith, Tamas Keviczky
Date: 2023-12-18 00:00:00

Robust Optimal Control (ROC) with adjustable uncertainties has proven to be effective in addressing critical challenges within modern energy networks, especially the reserve and provision problem. However, prior research on ROC with adjustable uncertainties has predominantly focused on the scenario of uncertainties modeled as continuous variables. In this paper, we explore ROC with binary adjustable uncertainties, where the uncertainties are modeled by binary decision variables, marking the first investigation of its kind. To tackle this new challenge, firstly we introduce a metric designed to quantitatively measure the extent of binary adjustable uncertainties. Then, to balance computational tractability and adaptability, we restrict control policies to be affine functions with respect to uncertainties, and propose a general design framework for ROC with binary adjustable uncertainties. To address the inherent computational demands of the original ROC problem, especially in large-scale applications, we employ strong duality (SD) and big-M-based reformulations to create a scalable and computationally efficient Mixed-Integer Linear Programming (MILP) formulation. Numerical simulations are conducted to showcase the performance of our proposed approach, demonstrating its applicability and effectiveness in handling binary adjustable uncertainties within the context of modern energy networks.