arXiv subjects

Kaouther Moussa

Publications and source records attributed to Kaouther Moussa.

7 recordsLinked to original sources

arXiv2026

Linear Stochastic Systems with i.i.d. uncertainties: Exact Covariance Characterization, Stability Analysis and State-feedback Design

This paper studies linear discrete-time systems affected by independent and identically distributed (i.i.d.) multiplicative uncertainties and additive noise. It establishes the main links between covariance recursions, the spectral properties of associated Kronecker-based matrices, and mean-square stability, and exploits these links to derive tractable conditions for controller synthesis. We first derive a deterministic covariance recursion within the tube-based Stochastic Model Predictive Control (SMPC) framework using a Kronecker product based matrix augmentation. For linear stochastic systems with multiplicative uncertainty and without additive noise, we show that the full-space matrix representation arising from the covariance recursion has the same spectral radius as its symmetric-space counterpart. Combined with the existing symmetric-space characterization, this establishes that Schur stability of the full-space augmented matrix is equivalent to mean-square stability. For state-feedback design, we propose new sufficient Linear Matrix Inequality (LMI) conditions that are numerically more tractable owing to their reduced size compared with the conventional necessary and sufficient conditions. Numerical tests illustrate the usefulness of the covariance characterization for recursively estimating the covariance without relying on sampling-based methods. We also assess the computational burden of the proposed LMI conditions and their conservatism relative to the necessary and sufficient ones.

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arXiv2026

Covariance Stabilization for a class of Stochastic Discrete-time Linear Systems using the S-Variable Approach

This paper deals with the problem of covariance stabilization for a class of linear stochastic discrete-time systems in the Stochastic Model Predictive Control (SMPC) framework. The considered systems are affected by independent and identically distributed (i.i.d.) additive and parametric stochastic uncertainties (potentially unbounded), in addition to polytopic deterministic uncertainties bounding the mean of the state and input parameters. The design conditions presented in this paper are formulated as Linear Matrix Inequalities (LMIs), using the S-variable approach in order to reduce the potential conservatism. These conditions are derived using a deterministic exact characterization of the covariance dynamics, the latter involves bilinear terms in the control gain. A technique to linearize such dynamics is presented, it results in a descriptor representation allowing to derive sufficient conditions for the design of a covariance-stabilizing controller. The derived condition is first compared with a known necessary and sufficient stability condition for systems without deterministic uncertainties and additive stochastic noise. Although more conservative, the proposed condition is more numerically tractable, with an LMI size scaling as O(n^2) instead of O(n^3). Then, the same condition is used to design controllers that are robust to both deterministic and stochastic uncertainties. Several numerical examples are presented for comparison and illustration.

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arXiv2025

How is remifentanil dosed without dedicated indicator?

This study investigates the paradigm of intraoperative analgesic dosage using a data-driven approach based on retrospective clinical data. Remifentanil, an analgesic widely used during anesthesia, presents a dosing challenge due to the absence of an universally accepted indicator of analgesia. To examine how changes in patient state correlate with adjustments in remifentanil target concentration triggered by the practitioner, we analyzed data from two sources: VitalDB (Seoul, Korea) and PREDIMED (Grenoble, France). Results show that only features derived from arterial pressure are consistently associated with changes in remifentanil targets. This finding is robust across both datasets despite variations in specific thresholds. In particular, increases in remifentanil targets are associated with high or rising arterial pressure over short periods (1--2 minutes), whereas decreases are linked to low, stable, or declining arterial pressure over longer periods (5--7 minutes). By capturing anesthesiologists' dosing strategies we provide a foundation for the future development of closed-loop control algorithms. Beyond the specific example of remifentanil's change prediction, the proposed feature generation and associated sparse fitting approach can be applied to other domain where human decision can be viewed as sensors interpretation.

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arXiv2025

MPC for tracking for anesthesia dynamics

In this paper, an MPC for tracking formulation is proposed for the control of anesthesia dynamics. It seamlessly enables the optimization of the steady-states pair that is not unique due to the MISO nature of the model. Anesthesia dynamics is a multi-time scale system with two types of states characterized, respectively, by fast and slow dynamics. In anesthesia control, the output equation depends only on the fast dynamics. Therefore, the slow states can be treated as disturbances, and compensation terms can be introduced. Subsequently, the system can be reformulated as a nominal one allowing the design of an MPC for tracking strategy. The presented framework ensures recursive feasibility and asymptotic stability, through the design of appropriate terminal ingredients in the MPC for tracking framework. The controller performance is then assessed on a patient in a simulation environment.

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arXiv2025

Covariance Propagation and Stabilization for Tube-Based Stochastic MPC under Parametric and Additive Uncertainties

This work addresses an SMPC-oriented characterization of the error covariance dynamics for linear discrete-time systems subject to both additive and parametric stochastic uncertainties that are potentially unbounded. In contrast with the standard additive-noise case, the covariance dynamics are coupled with the nominal trajectory because the parametric uncertainty acts on the full state. Using this characterization, the problem of control design for error covariance dynamics is addressed, providing conditions that are conservative yet more tractable compared to standard necessary and sufficient ones for the same class of systems. Numerical results assess this covariance characterization by comparing it to the empirical covariance and illustrate the control design problem.

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arXiv2021

Toward simple "in silico" experiments for drugs administration in some cancer treatments

We present some "in silico" experiments to design combined chemo- and immunotherapy treatment schedules. We introduce a new framework by combining flatness-based control, which is a model-based setting, along with model-free control. The flatness property of the used mathematical model yields straightforward reference trajectories. They provide us with the nominal open-loop control inputs. Closing the loop via model-free control allows to deal with the uncertainties on the injected drug doses. Several numerical simulations illustrating different case studies are displayed. We show in particular that the considered health indicators are driven to the safe region, even for critical initial conditions. Furthermore, in some specific cases there is no need to inject chemotherapeutic agents.

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arXiv2020

Probabilistically Certified Region of Attraction of a Tumor Growth Model with Combined Chemo- and Immunotherapy

This paper deals with the estimation of regions of attraction (RoAs) under parametric uncertainties for a cancer growth model with combined therapies. We propose a framework of probabilistic certification, based on the randomized methods, in order to derive probabilistically certified RoAs of a cancer growth model. The model that we consider in this paper describes the interaction between tumor and immune system in presence of a combined chemo- and immunotherapy. Furthermore, we model the concentration of the chemotherapy agent in the body via a pharmacokinetic equation.

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