arXiv subjects

Mirko Fiacchini

Publications and source records attributed to Mirko Fiacchini.

At least 19 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

Beyond Ellipsoids: Semi-Algebraic Tightening for Chance Constraints Under Actuator Saturation

Motivated by stochastic model predictive control applications, we present a semi-algebraic approach to constraint tightening for chance-constrained systems with unbounded additive disturbances and saturated inputs. The saturated error dynamics are handled via their exact piecewise-affine structure, which naturally accommodates asymmetric saturation bounds. A polynomial Lyapunov function satisfying a drift condition is then designed using sum-of-squares optimization, yielding finite-time probabilistic reachable sets and a probabilistic ultimate bound. The set geometry is explicitly optimized for constraint tightening, further reducing conservatism. A numerical example demonstrates the effectiveness of the design.

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arXiv2026

A Stochastic Tube-Based MPC Framework with Hard Input Constraints

This work presents a stochastic tube-based model predictive control framework that guarantees hard input constraint satisfaction for linear systems subject to unbounded additive disturbances. The approach relies on a structured design of probabilistic reachable sets that explicitly incorporates actuator saturation into the error dynamics and bounds the resulting nonlinearity within a convex embedding. The proposed controller retains the computational efficiency and structural advantages of stochastic tube-based approaches while ensuring state chance constraint satisfaction alongside hard input limits. Recursive feasibility and mean-square stability are established for our scheme, and a numerical example illustrates its effectiveness.

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arXiv2026

An Age-Structured Vaccination Strategy for Epidemic Containment: A Model Predictive Control Approach

This work presents a novel Model Predictive Control (MPC) approach to develop an optimal age-structured vaccination strategy for the containment of COVID-19 in Wallonia, Belgium. The proposed MPC framework is designed to minimize deaths, achieve early disease eradication, and adhere to operational constraints. By incorporating an age-structured Susceptible-Infected-Recovered-Deceased (SIRD) model with an additional term for vaccination, the MPC strategy dynamically adapts to the evolving epidemic state. A detailed proof of the asymptotic stability and recursive feasibility of the proposed MPC algorithm is provided. This ensures that the optimal cost at each step provides an upper bound on the minimal number obtainable of deaths at the end of the pandemic. Moreover, simulations demonstrate that the proposed MPC approach outperforms the decreasing age vaccination strategy adopted by the Belgian government during the first wave of vaccinations. The results highlight the potential of MPC-based vaccination strategies to reduce the total number of deaths, accelerate disease eradication, and optimize vaccine administration.

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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

Imitation Learning with Safety and L2 Stability Certificates for Boundary Control of Reaction-Diffusion PDEs

This paper proposes an imitation learning (IL) framework for synthesizing neural network (NN) controllers that achieve boundary stabilization of systems governed by reaction-diffusion partial differential equations (PDEs). The plant is assumed to be actuated through a Dirichlet boundary condition and subject to a Neumann condition on the unactuated side. The design is based on a finite-dimensional truncated model that captures the unstable dynamics of the original infinite-dimensional system, which is obtained via spectral decomposition. Convex stability and safety conditions are then derived for this truncated model by combining Lyapunov theory with local quadratic constraints (QC), which bound the nonlinear activation functions of the NN and guarantee robustness to model truncation, thus addressing the spillover problem. These conditions are integrated into the IL process to jointly minimize the imitation loss and maximize the volume of the certified region of attraction (ROA). The proposed framework is validated on an unstable reaction-diffusion PDE, demonstrating that the resulting NN controller efficiently reproduces the expert policy while ensuring formal stability guarantees.

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arXiv2025

Recursive feasibility for stochastic MPC and the rationale behind fixing flat tires

In this paper, we address the problem of designing stochastic model predictive control (SMPC) schemes for linear systems affected by unbounded disturbances. The contribution of the paper is rooted in a measured-state initialization strategy. First, due to the nonzero probability of violating chance-constraints in the case of unbounded noise, we introduce ellipsoidal-based probabilistic reachable sets and we include constraint relaxations to recover recursive feasibility conditioned to the measured state. Second, we prove that the solution of this novel SMPC scheme guarantees closed-loop chance constraints satisfaction under minimum relaxation. Last, we demonstrate that, in expectation, the need of relaxing the constraints vanishes over time, which leads the closed-loop trajectories steered towards the unconstrained LQR invariant region. This novel SMPC scheme is proven to satisfy the recursive feasibility conditioned to the state realization, and its superiority with respect to open-loop initialization schemes is shown through numerical examples.

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arXiv2025

Probabilistic Reachable Set Estimation for Saturated Systems with Unbounded Additive Disturbances

In this paper, we present an analytical approach for the synthesis of ellipsoidal probabilistic reachable sets of saturated systems subject to unbounded additive noise. Using convex optimization methods, we compute a contraction factor of the saturated error dynamics that allows us to tightly bound its evolution and therefore construct accurate reachable sets. The proposed approach is applicable to independent, zero mean disturbances with a known covariance. A numerical example illustrates the applicability and effectiveness of the proposed design.

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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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arXiv2024

Measured-state conditioned recursive feasibility for stochastic model predictive control

In this paper, we address the problem of designing stochastic model predictive control (MPC) schemes for linear systems affected by unbounded disturbances. The contribution of the paper is twofold. First, motivated by the difficulty of guaranteeing recursive feasibility in this framework, due to the nonzero probability of violating chance-constraints in the case of unbounded noise, we introduce the novel definition of measured-state conditioned recursive feasibility in expectation. Second, we construct a stochastic MPC scheme, based on the introduction of ellipsoidal probabilistic reachable sets, which implements a closed-loop initialization strategy, i.e., the current measured-state is employed for initializing the optimization problem. This new scheme is proven to satisfy the novel definition of recursive feasibility, and its superiority with respect to open-loop initialization schemes, arising from the fact that one never neglects the information brought by the current measurement, is shown through numerical examples.

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arXiv2023

Automated Multi-Drugs Administration During Total Intravenous Anesthesia Using Multi-Model Predictive Control

In this paper, a multi-model predictive control approach is used to automate the co-administration of propofol and remifentanil from bispectral index measurement during general anesthesia. To handle the parameter uncertainties in the non-linear output function, multiple Extended Kalman Filters are used to estimate the state of the system in parallel. The best model is chosen using a model-matching criterion and used in a non-linear MPC to compute the next drug rates. The method is compared with a conventional non-linear MPC approach and a PID from the literature. The robustness of the controller is evaluated using Monte-Carlo simulations on a wide population introducing uncertainties in the models. Both simulation setup and controller codes are accessible in open source for further use. Our preliminary results show the potential interest in using a multi-model method to handle parameter uncertainties.

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arXiv2023

Output Regulation of Stochastic Sampled-Data Systems with Post-processing Internal Model

This paper deals with the output regulation problem (ORP) of a linear time-invariant (LTI) system in the presence of sporadically sampled measurement streams with the inter-sampling intervals following a stochastic process. Under such sporadically available measurement streams, a regulator consisting of a hybrid observer, continuous-time post-processing internal model, and stabilizer are proposed, which resets with the arrival of new measurements. The resulting system exhibits a deterministic behavior except for the jumps that occur at random sampling times and therefore the overall closed-loop system can be categorized as a piecewise deterministic Markov process (PDMP). In existing works on ORPs with aperiodic sampling, the requirement of boundedness on inter-sampling intervals precludes extending the solution to the random sampling intervals with possibly unbounded support. Using the Lyapunov-like theorem for the stability analysis of stochastic systems, we offer sufficient conditions to ensure that the overall closed-loop system is mean exponentially stable (MES) and the objectives of the ORP are achieved under stochastic sampling of measurement streams. The resulting LMI conditions lead to a numerically tractable design of the hybrid regulator. Finally, with the help of an illustrative example, the effectiveness of the theoretical results are verified.

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arXiv2020

The Ockham's razor applied to COVID-19 model fitting French data

This paper presents a data-based simple model for fitting the available data of the Covid-19 pandemic evolution in France. The time series concerning the 13 regions of mainland France have been considered for fitting and validating the model. An extremely simple, two-dimensional model with only two parameters demonstrated to be able to reproduce the time series concerning the number of daily demises caused by Covid-19, the hospitalizations, intensive care and emergency accesses, the daily number of positive test and other indicators, for the different French regions. These results might contribute to stimulate a debate on the suitability of much more complex models for reproducing and forecasting the pandemic evolution since, although relevant from a mechanistic point of view, they could lead to nonidentifiability issues.

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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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arXiv2020

Probabilistic reachable and invariant sets for linear systems with correlated disturbance

In this paper a constructive method to determine and compute probabilistic reachable and invariant sets for linear discrete-time systems, excited by a stochastic disturbance, is presented. The samples of the disturbance signal are not assumed to be uncorrelated, only a bound on the correlation matrices is supposed to be known. The concept of correlation bound is introduced and employed to determine probabilistic reachable sets and probabilistic invariant sets. Constructive methods for their computation, based on convex optimization, are given.

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arXiv2018

Computing control invariant sets in high dimension is easy

In this paper we consider the problem of computing control invariant sets for linear controlled high-dimensional systems with constraints on the input and on the states. Set inclusions conditions for control invariance are presented that involve the N-step sets and are posed in form of linear programming problems. Such conditions allow to overcome the complexity limitation inherent to the set addition and vertices enumeration and can be applied also to high dimensional systems. The efficiency and scalability of the method are illustrated by computing approximations of the maximal control invariant set, based on the 10-step operator, for a system whose state and input dimensions are 30 and 15, respectively.

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arXiv2018

LMI-Based Reset Unknown Input Observer for State Estimation of Linear Uncertain Systems

This paper proposes a novel kind of Unknown Input Observer (UIO) called Reset Unknown Input Observer (R-UIO) for state estimation of linear systems in the presence of disturbance using Linear Matrix Inequality (LMI) techniques. In R-UIO, the states of the observer are reset to the after-reset value based on an appropriate reset law in order to decrease the $L_2$ norm and settling time of estimation error. It is shown that the application of the reset theory to the UIOs in the LTI framework can significantly improve the transient response of the observer. Moreover, the devised approach can be applied to both SISO and MIMO systems. Furthermore, the stability and convergence analysis of the devised R-UIO is addressed. Finally, the efficiency of the proposed method is demonstrated by simulation results.

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arXiv2017

Computing control invariant sets is easy

In this paper we consider the problem of computing control invariant sets for linear controlled systems with constraints on the input and on the states. We focus in particular on the complexity of the computation of the N-step operator, given by the Minkowski addition of sets, that is the basis of many of the iterative procedures for obtaining control invariant sets. Set inclusions conditions for control invariance are presented that involve the N-step sets and are posed in form of linear programming problems. Such conditions are employed in algorithms based on LP problems that allow to overcome the complexity limitation inherent to the set addition and can be applied also to high dimensional systems. The efficiency and scalability of the method are illustrated by computing in less than two seconds an approximation of the maximal control invariant set, based on the 15-step operator, for a system whose state and input dimensions are 20 and 10 respectively.

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