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John Leth

Publications and source records attributed to John Leth.

At least 19 recordsLinked to original sources
arXiv2026

PAC-Bayesian Bounds for Learning Partially Observed Stochastic Linear Time-Invariant State-Space Systems with Inputs and Sub-Gaussian Noise

In this paper we derive a Probably Approximately Correct (PAC)-Bayesian error bound for partially observed linear time-invariant (LTI) stochastic dynamical systems in state-space form with inputs and sub-Gaussian noise. Such bounds are widespread in machine learning, and they are useful for characterizing the predictive power of models learned from finitely many data points. The bound derived in this paper relates the expectation of prediction errors with the prediction error generated by the model on the data used for learning. In addition, we show that it can also be used to derive bounds for the parameter estimation error. In turn, this allows us to provide finite-sample error bounds for the prediction error and parameter estimation error for a wide class of system identification algorithms. Furthermore, as LTI systems are a sub-class of recurrent neural networks (RNNs), these error bounds could be a first step towards PAC-Bayesian bounds for RNNs.

cs.LG↗
arXiv2025

A Robust Predictive Control Method for Pump Scheduling in Water Distribution Networks

Water utilities aim to reduce the high electrical costs of Water Distribution Networks (WDNs), primarily driven by pumping. However, pump scheduling is challenging due to model uncertainties and water demand forecast errors. This paper presents a Robust Model Predictive Control (RMPC) method for optimal and reliable pump scheduling, extending a previous efficient robust control method tailored to our model. A linear model with bounded additive disturbances is used to represent tank water level evolution, with uncertainty bounds derived from WDN simulation and demand data. At each time step, a pump scheduling policy, affine in past disturbances, is optimized to satisfy system constraints over a prediction horizon. The resulting policies are then applied in a receding horizon fashion. The optimization problem is formulated to require $\mathcal{O}(N^6)$ computations per iteration with an interior-point method, which is reduced to $\mathcal{O}(N^3)$ by reformulating it into a sparse form. When evaluated on a model representing the water distribution network of Randers, a medium-sized town in Denmark, the method surpasses nominal and constraint-tightening model predictive control (MPC) approaches in terms of meeting constraints and provides comparable economic outcomes.

eess.SY↗
arXiv2025

Optimal Sensor Scheduling and Selection for Continuous-Discrete Kalman Filtering with Auxiliary Dynamics

We study the Continuous-Discrete Kalman Filter (CD-KF) for State-Space Models (SSMs) where continuous-time dynamics are observed via multiple sensors with discrete, irregularly timed measurements. Our focus extends to scenarios in which the measurement process is coupled with the states of an auxiliary SSM. For instance, higher measurement rates may increase energy consumption or heat generation, while a sensor's accuracy can depend on its own spatial trajectory or that of the measured target. Each sensor thus carries distinct costs and constraints associated with its measurement rate and additional constraints and costs on the auxiliary state. We model measurement occurrences as independent Poisson processes with sensor-specific rates and derive an upper bound on the mean posterior covariance matrix of the CD-KF along the mean auxiliary state. The bound is continuously differentiable with respect to the measurement rates, which enables efficient gradient-based optimization. Exploiting this bound, we propose a finite-horizon optimal control framework to optimize measurement rates and auxiliary-state dynamics jointly. We further introduce a deterministic method for scheduling measurement times from the optimized rates. Empirical results in state-space filtering and dynamic temporal Gaussian process regression demonstrate that our approach achieves improved trade-offs between resource usage and estimation accuracy.

eess.SY↗
arXiv2025

Distributions and Direct Parametrization for Stable Stochastic State-Space Models

We present a direct parametrization for continuous-time stochastic state-space models that ensures external stability via the stochastic bounded-real lemma. Our formulation facilitates the construction of probabilistic priors that enforce almost-sure stability, which are suitable for sampling-based Bayesian inference methods. We validate our work with a simulation example and demonstrate its ability to yield stable predictions with uncertainty quantification.

stat.ME↗
arXiv2024

Optimizing Photovoltaic Panel Quantity for Water Distribution Networks

The paper introduces a procedure for determining an approximation of the optimal amount of photovoltaics (PVs) for powering water distribution networks (WDNs) through grid-connected PVs. The procedure aims to find the PV amount minimizing the total expected cost of the WDN over the lifespan of the PVs. The approach follows an iterative process, starting with an initial estimate of the PV quantity, and then calculating the total cost of WDN operation. To calculate the total cost of the WDN, we sample PV power profiles that represent the future production based on a probabilistic PV production model. Simulations are conducted assuming these sampled PV profiles power the WDN, and pump flow rates are determined using a control method designed for PV-powered WDNs. Following the simulations, the overall WDN cost is calculated. Since we lack access to derivative information, we employ the derivative-free Nelder-Mead method for iteratively adjusting the PV quantity to find an approximation of the optimal value. The procedure is applied for the WDN of Randers, a Danish town. By determining an approximation of the optimal quantity of PVs, we observe a 14.5\% decrease in WDN costs compared to the scenario without PV installations, assuming a 25 year lifespan for the PV panels.

eess.SY↗
arXiv2023

PAC-Bayes Generalisation Bounds for Dynamical Systems Including Stable RNNs

In this paper, we derive a PAC-Bayes bound on the generalisation gap, in a supervised time-series setting for a special class of discrete-time non-linear dynamical systems. This class includes stable recurrent neural networks (RNN), and the motivation for this work was its application to RNNs. In order to achieve the results, we impose some stability constraints, on the allowed models. Here, stability is understood in the sense of dynamical systems. For RNNs, these stability conditions can be expressed in terms of conditions on the weights. We assume the processes involved are essentially bounded and the loss functions are Lipschitz. The proposed bound on the generalisation gap depends on the mixing coefficient of the data distribution, and the essential supremum of the data. Furthermore, the bound converges to zero as the dataset size increases. In this paper, we 1) formalize the learning problem, 2) derive a PAC-Bayesian error bound for such systems, 3) discuss various consequences of this error bound, and 4) show an illustrative example, with discussions on computing the proposed bound. Unlike other available bounds the derived bound holds for non i.i.d. data (time-series) and it does not grow with the number of steps of the RNN.

cs.LG↗
arXiv2023

Scenario Based Cost Optimization of Water Distribution Networks Powered by Grid-Connected Photovoltaic Systems

The paper presents a predictive control method for the water distribution networks (WDNs) powered by photovoltaics (PVs) and the electrical grid. This builds on the controller introduced in a previous study and is designed to reduce the economic costs associated with operating the WDN. To account for the uncertainty of the system, the problem is solved in a scenario optimization framework, where multiple scenarios are sampled from the uncertain variables related to PV power production. To accomplish this, a day-ahead PV power prediction method with a stochastic model is employed. The method is tested on a high-fidelity model of a WDN of a Danish town and the results demonstrate a substantial reduction in electrical costs through the integration of PVs, with PVs supplying $66.95\%$ of the required energy. The study also compares the effectiveness of the stochastic optimization method with a deterministic optimization approach.

eess.SY↗
arXiv2023

PAC-Bayesian bounds for learning LTI-ss systems with input from empirical loss

In this paper we derive a Probably Approxilmately Correct(PAC)-Bayesian error bound for linear time-invariant (LTI) stochastic dynamical systems with inputs. Such bounds are widespread in machine learning, and they are useful for characterizing the predictive power of models learned from finitely many data points. In particular, with the bound derived in this paper relates future average prediction errors with the prediction error generated by the model on the data used for learning. In turn, this allows us to provide finite-sample error bounds for a wide class of learning/system identification algorithms. Furthermore, as LTI systems are a sub-class of recurrent neural networks (RNNs), these error bounds could be a first step towards PAC-Bayesian bounds for RNNs.

stat.ML↗
arXiv2023

Economic Predictive Control with Periodic Horizon for Water Distribution Networks

This paper deals with the control of pumps in large-scale water distribution networks with the aim of minimizing economic costs while satisfying operational constraints. Finding a control algorithm in combination with a model that can be applied in real-time is a challenging problem due to the nonlinearities presented by the pipes and the network sizes. We propose a predictive control algorithm with a periodic horizon. The method provides a way for the economic operation of large water networks with a small linear model. Economic Predictive control with a periodic horizon and a terminal state constraint is constructed to keep the state trajectories close to an optimal periodic trajectory. Barrier terms are also included in the cost function to prevent constraint violations. The proposed method is tested on the EPANET implementation of the water network of a medium size Danish town (Randers) and shown to perform as intended under varying conditions.

eess.SY↗
arXiv2022

PAC-Bayesian-Like Error Bound for a Class of Linear Time-Invariant Stochastic State-Space Models

In this paper we derive a PAC-Bayesian-Like error bound for a class of stochastic dynamical systems with inputs, namely, for linear time-invariant stochastic state-space models (stochastic LTI systems for short). This class of systems is widely used in control engineering and econometrics, in particular, they represent a special case of recurrent neural networks. In this paper we 1) formalize the learning problem for stochastic LTI systems with inputs, 2) derive a PAC-Bayesian-Like error bound for such systems, 3) discuss various consequences of this error bound.

stat.ML↗
arXiv2022

An Online Stochastic Optimization Approach for Insulin Intensification in Type 2 Diabetes with Attention to Pseudo-Hypoglycemia

In this paper, we present a model free approach to calculate long-acting insulin doses for Type 2 Diabetic (T2D) subjects in order to bring their blood glucose (BG) concentration to be within a safe range. The proposed strategy tunes the parameters of a proposed control law by using a zeroth-order online stochastic optimization approach for a defined cost function. The strategy uses gradient estimates obtained by a Recursive Least Square (RLS) scheme in an adaptive moment estimation based approach named AdaBelief. Additionally, we show how the proposed strategy with a feedback rating measurement can accommodate for a phenomena known as relative hypoglycemia or pseudo-hypoglycemia (PHG) in which subjects experience hypoglycemia symptoms depending on how quick their BG concentration is lowered. The performance of the insulin calculation strategy is demonstrated and compared with current insulin calculation strategies using simulations with three different models.

eess.SY↗
arXiv2021

PAC-Bayesian theory for stochastic LTI systems

In this paper we derive a PAC-Bayesian error bound for autonomous stochastic LTI state-space models. The motivation for deriving such error bounds is that they will allow deriving similar error bounds for more general dynamical systems, including recurrent neural networks. In turn, PACBayesian error bounds are known to be useful for analyzing machine learning algorithms and for deriving new ones.

stat.ML↗
arXiv2020

Markovian Performance Model for Token Bucket Filter with Fixed and Varying Packet Sizes

We consider a token bucket mechanism serving a heterogeneous flow with a focus on backlog, delay and packet loss properties. Previous models have considered the case for fixed size packets, i.e. "one token per packet" with and M/D/1 view on queuing behavior. We partition the heterogeneous flow into several packet size classes with individual Poisson arrival intensities. The accompanying queuing model is a "full state" model, i.e. buffer content is not reduced to a single quantity but encompasses the detailed content in terms of packet size classes. This yields a high model cardinality for which upper bounds are provided. Analytical results include class specific backlog, delay and loss statistics and are accompanied by results from discrete event simulation.

cs.NI↗
arXiv2020

Glucose-insulin mathematical model for the combined effect of medications and life style of Type 2 diabetic patients

The goal of this paper is to propose a new mathematical model for the combined effect of different treatments and lifestyles on the glucose-insulin dynamics of Type 2 diabetes (T2D) patients. The model gives the possibility to take into consideration physical activity, stress, meals, and medications while evaluating or designing treatment plans for T2D patients. The model is proposed by combining and modifying some of the available models in the literature. Simulations were performed for the modifications to show how the model confirm with literature on T2D patients. Additionally, a discussion is provided to demonstrate the ability of the model to be used in the assessment of treatment plans and in the design for robust insulin dose guidance algorithms. An open source code for the model is additionally provided.

eess.SY↗
arXiv2020

Model reduction of linear hybrid systems

The paper proposes a model reduction algorithm for linear hybrid systems, i.e., hybrid systems with externally induced discrete events, with linear continuous subsystems, and linear reset maps. The model reduction algorithm is based on balanced truncation. Moreover, the paper also proves an analytical error bound for the difference between the input-output behaviors of the original and the reduced order model. This error bound is formulated in terms of singular values of the Gramians used for model reduction.

math.DS↗
arXiv2016

Moment matching for bilinear systems with nice selections

The paper develops a method for model reduction of bilinear control systems. It leans upon the observation that the input-output map of a bilinear system has a particularly simple Fliess series expansion. Subsequently, a model reduction algorithm is formulated such that the coefficients of Fliess series expansion for the original and reduced systems match up to certain predefined sets - nice selections. Algorithms for computing matrix representations of unobservability and reachability spaces complying with a nice selection are provided. Subsequently, they are used for calculating a partial realization of a given input-output map.

math.OC↗
arXiv2015

Moment Matching Based Model Reduction for LPV State-Space Models

We present a novel algorithm for reducing the state dimension, i.e. order, of linear parameter varying (LPV) discrete-time state-space (SS) models with affine dependence on the scheduling variable. The input-output behavior of the reduced order model approximates that of the original model. In fact, for input and scheduling sequences of a certain length, the input-output behaviors of the reduced and original model coincide. The proposed method can also be interpreted as a reachability and observability reduction (minimization) procedure for LPV-SS representations with affine dependence.

eess.SY↗