Patrizio Colaneri

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.

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.

This paper is entirely devoted to the study of optimal linear periodic filters for discrete-time LTI systems. A new performance index inspired by the well-known H2 norm of LTI systems, is proposed to take into account time-varying disturbance characteristics in both deterministic and stochastic frameworks. For that class of design problems, the optimality conditions show that the periodic filter in the observer-form outperforms the classical LTI filter. They are expressed through LMIs being solved by the machinery available in the literature. For completeness, the design problem is reformulated and solved in the realm of periodic filtering. Academic examples, simulated with the Monte Carlo method, illustrate the theoretical results.

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 tackles the optimal partial output feedback control problem for discrete-time time-invariant systems with quadratic cost. It is shown via the theory of periodic systems and using simple examples, that the classical linear time-invariant $\mathcal {H}_{2}$ optimal full-order output feedback controller can be outperformed by a linear periodic full-order output feedback controller. In our opinion, this fact is not available till now in the literature. A new design procedure for the optimal controller is proposed via LMI. The optimal closed-loop cost is evaluated as a function of the period $h$. Illustrative examples are solved, solutions are compared and consequences are discussed.

Cascading failures, such as bankruptcies and defaults, pose a serious threat for the resilience of the global financial system. Indeed, because of the complex investment and cross-holding relations within the system, failures can occur as a result of the propagation of a financial collapse from one organization to another. While this problem has been studied in depth from a static angle, namely, when the system is at an equilibrium, we take a different perspective and study the corresponding dynamical system. The contribution of this paper is threefold. First, we carry out a systematic analysis of the regions of attraction and invariance of the system orthants, defined by the positive and negative values of the organizations' equity. Second, we investigate periodic solutions and show through a counterexample that there could exist periodic solutions of period greater than 2. Finally, we study the problem of finding the smallest cash injection that would bring the system to the maximal invariant region of the positive orthant.

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.

This article establishes a systematic methodology to improve the utilization efficiency of probabilistic information for the stability analysis and stabilizing control of discrete-time semi-Markov jump linear systems (SMJLSs). The transition and sojourn information is incompletely known, and the coupling between the known (or unknown) transition and unknown (or known) sojourn information renders the known probabilistic information difficult to be fully leveraged, which can lead to conservative results in system analysis and synthesis. To approximate the unknown transition and sojourn information, a polyhedral approach is developed, which facilitates the incorporation of the known probabilistic information coupled with unknown information. Accordingly, novel vertex-based Lyapunov functions are proposed to establish stability conditions. New criteria are established for the stability analysis and control of SMJLSs by incorporating all the jointly known transition and sojourn information, all the known probabilistic information, and both the known and the approximation of unknown probabilistic information, respectively. The effectiveness and superiority of the theoretical results are illustrated by a numerical example and a simulated continuous stirred tank reactor process.