arXiv subjects

Erik Weyer

Publications and source records attributed to Erik Weyer.

11 recordsLinked to original sources

arXiv2026

Analysis of Stability and Performance of Economic Model Predictive Control with State-Independent Costs

This paper studies economic model predictive Control (EMPC) schemes, where the stage cost depends only on control inputs. Such problems arise in applications like water distribution networks and differ from standard EMPC since multiple steady states can correspond to the unique optimal steady input. We show that, under a strict dissipativity assumption related to the set of optimal steady states, the closed-loop trajectories converge asymptotically to this set, ensuring convergence of the economic cost to the optimal steady state cost. To enhance Lyapunov stability, we propose a modified stage cost that preserves the optimal input while guaranteeing asymptotic stability of a specific equilibrium with a slight performance loss. The approach is further extended to EMPC of a class of linear systems with periodic costs and disturbances by lifting it to a multi-step EMPC problem for periodic operations. A case study with a water distribution network demonstrates the effectiveness of the proposed methods in achieving both asymptotic convergence and stability.

math.OC↗

arXiv2025

Context-Aware Stochastic Modeling of Consumer Energy Resource Aggregators in Electricity Markets

Aggregators of consumer energy resources (CERs) like rooftop solar and battery energy storage (BES) face challenges due to their inherent uncertainties. A sensible approach is to use stochastic optimization to handle such uncertainties, which can lead to infeasible problems or loss in revenues if not chosen appropriately. This paper presents three efficient two-stage stochastic optimization methods: risk-neutral, robust, and chance-constrained, to address the impact of CER uncertainties for aggregators who participate in energy and regulation services markets in the Australian National Electricity Market. Furthermore, these methods utilize the flexibility of BES, considering precise state-of-charge dynamics and complementarity constraints, aiming for scalable performance while managing uncertainty. The problems are formed as two-stage stochastic mixed-integer linear programs, with relaxations adopted for large scenario sets. The solution approach employs scenario-based methodologies and affine recourse policies to obtain tractable reformulations. These methods are evaluated across use cases reflecting diverse operational and market settings, uncertainty characteristics, and decision-making preferences, demonstrating their ability to mitigate uncertainty, enhance profitability, and provide context-aware guidance for aggregators in choosing the most appropriate stochastic optimization method.

eess.SY↗

arXiv2025

A Scenario-Based Approach for Stochastic Economic Model Predictive Control with an Expected Shortfall Constraint

This paper presents a novel approach to stochastic economic model predictive control (SEMPC) that minimizes average economic cost while satisfying an empirical expected shortfall (EES) constraint to manage risk. A new scenario-based problem formulation ensuring controlled risk with high confidence while minimizing the average cost is introduced. The probabilistic guarantees is dependent on the number of support elements over the entire input domain, which is difficult to find for high-dimensional systems. A heuristic algorithm is proposed to find the number of support elements. Finally, an efficient method is presented to reduce the computational complexity of the SEMPC problem with an EES constraint. The approach is validated on a water distribution network, showing its effectiveness in balancing performance and risk.

eess.SY↗

arXiv2024

Stochastic Co-design of Storage and Control for Water Distribution Systems

Water distribution systems (WDSs) are typically designed with a conservative estimate of the ability of a control system to utilize the available infrastructure. The controller is designed and tuned after a WDS has been laid out, a methodology that may introduce unnecessary conservativeness in both system design and control, adversely impacting operational efficiency and increasing economic costs. To address these limitations, we introduce a method to simultaneously design infrastructure and develop control parameters, the co-design problem, with the aim of improving the overall efficiency of the system. Nevertheless, the co-design of a WDS is a challenging task given the presence of stochastic variables (e.g. water demands and electricity prices). In this paper, we propose a tractable stochastic co-design method to design the best tank size and optimal control parameters for WDS, where the expected operating costs are established based on Markov chain theory. We also give a theoretical result showing that the average long-run operating cost converges to the expected operating cost with probability~1. Furthermore, this method is not only applicable to greenfield projects for the co-design of WDSs but can also be utilized to improve the operations of existing WDSs in brownfield projects. The effectiveness and applicability of the co-design method are validated through three illustrative examples and a real-world case study in South Australia.

eess.SY↗

arXiv2024

Signed-Perturbed Sums Estimation of ARX Systems: Exact Coverage and Strong Consistency (Extended Version)

Sign-Perturbed Sums (SPS) is a system identification method that constructs confidence regions for the unknown system parameters. In this paper, we study SPS for ARX systems, and establish that the confidence regions are guaranteed to include the true model parameter with exact, user-chosen, probability under mild statistical assumptions, a property that holds true for any finite number of observed input-output data. Furthermore, we prove the strong consistency of the method, that is, as the number of data points increases, the confidence region gets smaller and smaller and will asymptotically almost surely exclude any parameter value different from the true one. In addition, we also show that, asymptotically, the SPS region is included in an ellipsoid which is marginally larger than the confidence ellipsoid obtained from the asymptotic theory of system identification. The results are theoretically proven and illustrated in a simulation example.

eess.SY↗

arXiv2022

Improved Pump Setpoint Selection Using a Calibrated Hydraulic Model of a High-Pressure Irrigation System

This paper presents a case study of the operational management of the Robinvale high-pressure piped irrigation water delivery system (RVHPS) in Australia. Based on datasets available, improved pump setpoint selection using a calibrated hydraulic model is investigated. The first step was to implement pre-processing of measured flow and pressure data to identify errors in the data and possible faulty sensors. An EPANET hydraulic simulation model was updated with calibrated pipe roughness height values by using the processed pressure and flow data. Then, new pump setpoints were selected using the calibrated model given the actual measured demands such that the pressures in the network were minimized subject to required customer service standards. Based on a two-day simulation, it was estimated that 4.7% savings in pumping energy cost as well as 4.7% reduction in greenhouse gas emissions can be achieved by applying the new pump setpoints.

eess.SY↗

arXiv2022

Granger Causality from Quantized Measurements

An approach is proposed for inferring Granger causality between jointly stationary, Gaussian signals from quantized data. First, a necessary and sufficient rank criterion for the equality of two conditional Gaussian distributions is proved. Assuming a partial finite-order Markov property, a characterization of Granger causality in terms of the rank of a matrix involving the covariances is presented. We call this the causality matrix. The smallest singular value of the causality matrix gives a lower bound on the distance between the two conditional Gaussian distributions appearing in the definition of Granger causality and yields a new measure of causality. Then, conditions are derived under which Granger causality between jointly Gaussian processes can be reliably inferred from the second order moments of quantized measurements. A necessary and sufficient condition is proposed for Granger causality inference under binary quantization. Furthermore, sufficient conditions are introduced to infer Granger causality between jointly Gaussian signals through measurements quantized via non-uniform, uniform or high resolution quantizers. Apart from the assumed partial Markov order and joint Gaussianity, this approach does not require the parameters of a system model to be identified. No assumptions are made on the identifiability of the jointly Gaussian random processes through the quantized observations. The effectiveness of the proposed method is illustrated by simulation results.

eess.SY↗

arXiv2021

Minimizing Pumping Energy Cost in Real-time Operations of Water Distribution Systems using Economic Model Predictive Control

Optimizing pump operations is a challenging task for real-time management of water distribution systems (WDSs). With suitable pump scheduling, pumping costs can be significantly reduced. In this research, a novel economic model predictive control (EMPC) framework for real-time management of WDSs is proposed. Optimal pump operations are selected based on predicted system behavior over a receding time horizon with the aim to minimize the total pumping energy cost. Time-varying electricity tariffs are considered while all the required water demands are satisfied. The novelty of this framework is to choose the number of pumps to operate in each pump station as decision variables in order to optimize the total pumping energy costs. By using integer programming, the proposed EMPC is applied to a benchmark case study, the Richmond Pruned network. The simulation with an EPANET hydraulic simulator is implemented. Moreover, a comparison of the results obtained using the proposed EMPC with those obtained using trigger-level control demonstrates significant economic benefits of the proposed EMPC.

eess.SY↗

arXiv2018

Identification of FIR Systems with Binary Input and Output Observations

This paper considers the identification of FIR systems, where information about the inputs and outputs of the system undergoes quantization into binary values before transmission to the estimator. In the case where the thresholds of the input and output quantizers can be adapted, but the quantizers have no computation and storage capabilities, we propose identification schemes which are strongly consistent for Gaussian distributed inputs and noises. This is based on exploiting the correlations between the quantized input and output observations to derive nonlinear equations that the true system parameters must satisfy, and then estimating the parameters by solving these equations using stochastic approximation techniques. If, in addition, the input and output quantizers have computational and storage capabilities, strongly consistent identification schemes are proposed which can handle arbitrary input and noise distributions. In this case, some conditional expectation terms are computed at the quantizers, which can then be estimated based on binary data transmitted by the quantizers, subsequently allowing the parameters to be identified by solving a set of linear equations. The algorithms and their properties are illustrated in simulation examples.

eess.SY↗

arXiv2018

Sign-Perturbed Sums: A New System Identification Approach for Constructing Exact Non-Asymptotic Confidence Regions in Linear Regression Models

We propose a new system identification method, called Sign-Perturbed Sums (SPS), for constructing non-asymptotic confidence regions under mild statistical assumptions. SPS is introduced for linear regression models, including but not limited to FIR systems, and we show that the SPS confidence regions have exact confidence probabilities, i.e., they contain the true parameter with a user-chosen exact probability for any finite data set. Moreover, we also prove that the SPS regions are star convex with the Least-Squares (LS) estimate as a star center. The main assumptions of SPS are that the noise terms are independent and symmetrically distributed about zero, but they can be nonstationary, and their distributions need not be known. The paper also proposes a computationally efficient ellipsoidal outer approximation algorithm for SPS. Finally, SPS is demonstrated through a number of simulation experiments.

eess.SP↗

arXiv2015

Sign-Perturbed Sums (SPS) with Instrumental Variables for the Identification of ARX Systems - Extended Version

We propose a generalization of the recently developed system identification method called Sign-Perturbed Sums (SPS). The proposed construction is based on the instrumental variables estimate and, unlike the original SPS, it can construct non-asymptotic confidence regions for linear regression models where the regressors contain past values of the output. Hence, it is applicable to ARX systems, as well as systems with feedback. We show that this approach provides regions with exact confidence under weak assumptions, i.e., the true parameter is included in the regions with a (user-chosen) exact probability for any finite sample. The paper also proves the strong consistency of the method and proposes a computationally efficient generalization of the previously proposed ellipsoidal outer-approximation. Finally, the new method is demonstrated through numerical experiments, using both real-world and simulated data.

stat.ME↗