arXiv subjects

Mohamad Al Ahdab

Publications and source records attributed to Mohamad Al Ahdab.

6 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

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↗

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↗

arXiv2023

Momentum-Based Learning of Nash Equilibria for LISA Pointing Acquisition

This paper addresses the pointing acquisition phase of the Laser Interferometer Space Antenna (LISA) mission as a guidance problem. It is formulated in a cooperative game setup, which solution is a sequence of corrections that can be used as a tracking reference to align all the spacecraft' laser beams simultaneously within the tolerances required for gravitational wave detection. We propose a model-free learning algorithm based on residual-feedback and momentum, for accelerated convergence to stable solutions, i.e. Nash Equilibria. Each spacecraft has 4 degrees of freedom, and the only measured output considered are laser misalignments with the local interferometer sensors. Simulation results demonstrate that the proposed strategy manages to achieve absolute misalignment errors $<1μ$rad in a timely manner.

eess.SY↗

arXiv2023

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↗

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↗