Gian Paolo Incremona

The emergence of antimicrobial resistance (AMR) is a global health threat that can be mitigated through the careful planning of multi-drug therapies. We analyse a model that captures the interplay between the host immune system and susceptible and resistant bacterial populations, accounting for the use of antibiotics and for treatment-induced mutations and horizontal transfer phenomena that favour the growth of resistant populations. We extend the model to consider multiple antibiotics and all the ensuing possible combinations of resistance. We formulate an optimal control problem aimed at minimising the overall bacterial population size as well as the use of antibiotics, and we rigorously prove that an optimal solution exists, which can be thus computed numerically. For the considered optimal control problem, we analyse necessary conditions for optimality based on the Pontryagin minimum principle, as well as singular controls. We also discuss an alternative approach for treatment design through a model predictive control (MPC) scheme. Our computational experiments, which illustrate both the direct solution to the optimal control problem and the MPC approach, with realistic parameters from the biological literature and initial conditions chosen according to several different scenarios, validate our theoretical results and demonstrate the flexibility of the framework, which adapts the therapy to the presence and numerosity of resistant populations, so that the optimal treatment strongly depends on both the cost functional weights and the initial conditions for the system dynamics.

We present an anti-windup technique, independent of the controller structure, targeted at optimizing the transients that the controlled variable and the control input undergo when the latter exits saturation, which is an aspect where the available techniques offer hardly any control. We formulate the problem as a constrained quadratic optimization one, and obtain for it an analytic solution. This solution provides a value to which we reset the controller state on exiting saturation. The resulting implementation is computationally lightweight, hence readily applicable to industrial controllers. The reported simulation and experimental results evidence its ease of use, together with the yielded advantages.

This paper introduces a data-based integral sliding mode control scheme for robustification of model-reference controllers, accommodating generic multivariable linear systems with unknown dynamics and affected by matched disturbances. Specifically, an integral sliding mode control (ISMC) law is recast into a data-based framework relying on an integral sliding variable depending only on the reference model, without the need of modeling the plant. The main strength of the proposed approach is the enforcement of the desired reference model in closed-loop under sliding mode conditions, despite the lack of knowledge of the model dynamics and the presence of the matched disturbances. Moreover, the conditions required to guarantee an integral sliding mode generation and the closed-loop stability are formally analyzed in the paper, remarking the generality of the proposed data-driven integral sliding mode control (DD-ISMC) with respect to the related model-based counterpart. Finally, the main practices for the data-based design of the proposed control scheme are deeply discussed in the paper, and the proposed method is tested in simulation on a benchmark example, and experimentally on a real laboratory setup. Simulation and experimental evidence fully corroborates the theoretical analysis, thus motivating further research in this direction.

This article addresses the problem of stabilization of switched affine systems under dwell-time constraint, giving guarantees on the bound of the quadratic cost associated with the proposed state switching control law. Specifically, two switching rules are presented relying on the solution of differential Lyapunov equalities and Lyapunov–Metzler inequalities, from which the stability conditions are expressed. The first one allows to regulate the state of linear switched systems to zero, whereas the second one is designed for switched affine systems, proving practical stability of the origin. In both cases, the determination of a guaranteed cost associated with each control strategy is shown. In the cases of linear and affine systems, the existence of the solution for the Lyapunov–Metzler condition is discussed, and guidelines for the selection of a solution ensuring suitable performance of the system evolution are provided. The theoretical results are finally assessed by means of three examples.

The paper studies a general regulator problem with an internal model in a subset of measurement channels. It proposes a procedure to reduce the stabilization problem for an augmented system (the plant plus internal model) to an equivalent one based on a process without the internal model and having the complexity of the plant. A key idea is to introduce stable compensation of internal model (CIM) elements to the controller, which are, in a sense, dual to the dead-time compensators used in the control of delay systems. Closed-form state-space expressions for such CIM elements and the resulting equivalent plant are derived for both finite-dimensional and repetitive internal models. The complexity of the design of stabilizers is then substantially lower than in approaches based on system augmentation.

This paper offers a data-driven approach for designing adaptive suboptimal second-order sliding mode (ASSOSM) controllers for single-input nonlinear systems, characterized by perturbed strict-feedback structures with unknown dynamics. The proposed approach is recursive, in which the system dynamics are first decomposed into two parts, referred to as the upper and lower dynamics. The control design task is then divided into two stages, that is, designing a virtual controller for the upper dynamics, followed by synthesizing the actual controller for the full-order system. To this end, we start by collecting noisy data from the system through a finite-time experiment, referred to as a single trajectory. We then formulate a data-dependent condition as a semidefinite program, whose feasibility enables the design of a virtual controller that ensures global asymptotic stability of the origin for the upper dynamics. Building upon this virtual controller, we subsequently propose a data-driven sliding variable that facilitates the design of an ASSOSM controller for the unknown full-order system. This controller guarantees semi-global asymptotic stability of the origin in the presence of disturbances. Specifically, for any prescribed bounded set--no matter how large--the controller's design parameters can be chosen to ensure asymptotic stability of the origin. The effectiveness of the proposed method is demonstrated through three case studies, reflecting different aspects of the approach.

Large-scale interconnected networks, composed of multiple low-dimensional subsystems, serve as a crucial framework for modeling a wide range of real-world applications. Despite offering computational scalability, the inherent interdependence among subsystems poses significant challenges to the effective control of such networks. This complexity is further exacerbated in the presence of external perturbations and when the dynamics of individual subsystems, and accordingly the overall network, are unknown-scenarios frequently encountered in modern practical applications. In this paper, we develop a compositional data-driven approach to ensure the global asymptotic stability (GAS) of large-scale nonlinear networks with unknown mathematical models, subjected to external perturbations. To achieve this, we first gather two sets of data from each unknown nominal subsystem without perturbation, which we refer to as two input-state trajectories. The collected data from each subsystem is then utilized to design an input-to-state stable (ISS) Lyapunov function and its corresponding controller for each nominal subsystem, rendering them ISS. To cancel the effect of external perturbations on the dynamic of each subsystem, and accordingly the whole network, we then design a local integral sliding mode (ISM) controller for each subsystem using the collected data. Under a small-gain compositional condition, we employ data-driven ISS Lyapunov functions designed for subsystems and construct a control Lyapunov function for the network, rendering the assurance of GAS property over the nominal network. We then extend this compositional result to network perturbed models, demonstrating that the synthesized ISM controllers ensure the GAS property even in the presence of perturbations.

This paper addresses the problem of stabilization of switched affine systems under dwell-time constraint, giving guarantees on the bound of the quadratic cost associated with the proposed state switching control law. Specifically, two switching rules are presented relying on the solution of differential Lyapunov inequalities and Lyapunov-Metzler inequalities, from which the stability conditions are expressed. The first one allows to regulate the state of linear switched systems to zero, whereas the second one is designed for switched affine systems proving practical stability of the origin. In both cases, the determination of a guaranteed cost associated with each control strategy is shown. In the cases of linear and affine systems, the existence of the solution for the Lyapunov-Metzler condition is discussed and guidelines for the selection of a solution ensuring suitable performance of the system evolution are provided. The theoretical results are finally assessed by means of three examples.