Research Activity

Analysis and Control of sampled-data and discrete-time systems

Analysis and control of nonlinear systems have been representing a core paradigm in our community with a huge and exhaustive focus towards continuous-time dynamics. As a matter of fact, most plants evolve continuously over time so motivating this interest especially when focusing on analysis of the structural properties. Though, as far as control and sensing are concerned, the designed control laws are implemented through digital devices and sensors acquire only partial information on the system behavior. In both cases, those equipments act over discrete-time instants in a synchronous or synchronous way so making the necessity of a suitable control design unavoidable. Those classes of systems are generally referred to as sampled-data systems in the sense that they combine discrete and continuous-time evolutions. Roughly speaking, measures of the output are available only at sporadic discrete-time instants while the control is piecewise constant over a fixed time interval (the sampling period). In this context, several pioneering works have been developed since the early 80s although a sustained gap still remains to be bridged with respect to the actual state of the art on continuous-time systems.

For this purpose, different approaches have been proposed throughout the decades based on several frameworks. As an example, a large number of researchers has included sampled-data systems into the class of time-delay systems so using the corresponding tools for solving some of the arising problems. As an alternative, based on the hybrid nature of the overall system, several design approaches have been presented based on the theory concerning hybrid systems. Though, both the aforementioned approaches are generally ad hoc and are hard to extend to more general problems and do not allow to completely study even basic structural properties of the system (such as accessibility, controllability).

For these reasons, the study we propose is based on the so-called sampled-data equivalent model that describes the evolutions of the system at the sampling instants. Although several properties are lost by this equivalent model, this inherits some useful properties that allow to carry out an interesting and powerful body of tools for addressing both analysis and design. In doing so, the knowledge of a suitable framework for dealing with discrete-time systems is necessary.

Moreover, other than sampling, the plant is affected by measurements and/or input delays that are not negligible in most practical situations. In that case, the design can be pursued by suitably exploiting the sampling process and its relation with the time delays acting over.

Analysis and control of nonlinear multi-agent systems

Networked systems are nowadays well-considered a bridging paradigm among several disciplines spanning, among many others, from physics to engineering, psychology to medicine, biology to computer science.

As typical in control theory, we refer to a network (or multi-agent) system as composed of several dynamical units (agents) interconnected through a communication graph} each node of the communication graph uniquely corresponds to one dynamical unit whereas edges model the corresponding exchange of information among agents. As a consequence, even for simple agents and with no issue in the network interconnection (e.g., time-delays), the network behavior is described by a complex dynamical system.

In this sense, we investigate the effect of the network-based interconnection over the behavior of each dynamical system. Then, the design of local/decentralized controllers is addressed so to shape a suitable network behavior (i.e., dynamical consensus) induced by the notion of almost equitable partitions.

The classes of dynamics under investigations embed the case of heterogeneous agents in different scenarios including sampling, time delays or hybrid/switching communication exchange.