Maria Elena Valcher

Data-driven approaches have recently emerged in the analysis of Boolean control networks (BCNs), with the aim of addressing fundamental control problems, such as state-feedback stabilization, safe control, and output regulation, without requiring an explicit model, provided that a sufficiently informative dataset is available. This paper develops a data-based framework for the finite-horizon and infinite-horizon optimal control problems in BCNs. For the finite-horizon problem, the conditions for solvability are relatively mild. In contrast, solving the infinite-horizon problem from data imposes stricter requirements on both the generating BCN and the collected dataset. Our analysis builds on the concept of data informativity, which ensures that any proposed solution is feasible for all BCNs consistent with the data. While the resulting controllers may not be optimal for every such BCN, they represent the best performance attainable given the available information. The degree of sub-optimality is characterized in detail, and the effectiveness of the proposed (both finite- and infinite-horizon) methods is illustrated through an example based on a biological system of practical relevance.

In this paper, the problem of tracking a given reference output trajectory is investigated for the class of Boolean control networks, by resorting to their algebraic representation. First, the case of a finite-length reference trajectory is addressed, and the analysis and algorithm first proposed in [17] are extended to be able to deal with arbitrary initial conditions and to identify all possible solutions. The approach developed for the finite-length case is then adjusted to cope with periodic reference output trajectories. The results of the paper are illustrated through an example.

This article addresses the distributed state estimation problem for a discrete-time linear and time-invariant (LTI) state-space model, whose state equation is affected by disturbances. A connected sensor network, in which each sensor has access only to part of the control inputs and provides its own output signal (that represents a partial indirect measurement of the state), is deployed to reconstruct the state of a system. Such sensors exchange information with the goal of achieving consensus and providing an asymptotically correct estimate of the global system state. Necessary and sufficient conditions for the existence of distributed unknown input observers (DUIOs) with augmented states that achieve both goals are derived. Moreover, an algorithmic procedure to design the matrices of the proposed DUIO is presented. The problem solution leverages the theory of decentralized output feedback control, thus making it possible to exploit the algorithms available for the solution of that problem.

Networks of agents with logical states, namely Boolean networks, arise in various application domains including biology, computer networks, and social networks. The representation and control of Boolean networks have attracted much attention in recent years. In a parallel line of research, Koopman developed an operator view of nonlinear dynamical systems, which shows that, by making use of observable functions, every nonlinear dynamics can be represented as a (possibly infinite dimensional) linear system. In this article, we present a Koopman theory for Boolean networks. We introduce algebraic operations for logical functions over semirings of binary numbers, defining a semimodule of Boolean functions. The classical Koopman operator and Koopman theory are then established for Boolean networks, where the key ingredient to a linear representation is shown to be Koopman invariance. Next, we establish a necessary and sufficient condition for shaping the closed-loop dynamics via feedback into any desired form for Boolean control networks under the Koopman representation, and we develop a feedback control synthesis algorithm to solve this feedback shaping problem. Finally, feedback shaping is applied to a real-world gene regulatory network, and it is demonstrated that the dynamics of such a network may be arbitrarily manipulated by means of feedback control.

In this paper we investigate a data-driven approach to the design of an unknown-input observer (UIO). Specifically, we provide necessary and sufficient conditions for the existence of an unknown-input observer for a discrete-time linear time-invariant (LTI) system, designed based only on some available data, obtained on a finite time window. We also prove that, under weak assumptions on the collected data, the solvability conditions derived by means of the data-driven approach are in fact equivalent to those obtained through the model-based one. In other words, the data-driven conditions do not impose further constraints with respect to the classic model-based ones, expressed in terms of the original system matrices.

The purpose of this paper is to propose a novel perspective, based on Willems' "behavior theory", on the design of an unknown-input observer for a given linear time-invariant discrete-time state-space model, with unknown disturbances affecting both the state and the output equations. The problem is first addressed assuming that the original system model is known, and later assuming that the model is unknown but historical data satisfying a certain assumption are available. In both cases, fundamental concepts in behavior theory, as the projection of a behavior, the inclusion of a behavior in another one, and the use of kernel and image representations, provide quite powerful tools to determine necessary and sufficient conditions for the existence of an unknown-input observer (UIO), as well as algorithms to design one of them, if it exists.