Nonlinear Multiagent and Chaotic Systems

Any system that describes real processes is non-linear; linear systems are merely approximations of real processes in nature and technology. It is not always possible to use this approximation because the influence of nonlinearities is too strong (many technical systems, e.g. aircraft, biological systems, e.g. models of organ function) or the linear approximation does not sufficiently capture all aspects of the behavior of such a system - the most prominent example being chaotic systems such as weather patterns.

In practice, it is often necessary to manage ensembles of many identical systems that interact with each other and pursue a common goal - examples include controlling groups of drones, columns of vehicles, and so on. Such systems are called multi-agent systems. In the Control Theory Department, we are mainly concerned with the synchronization of nonlinear multiagent systems. The design of control systems also takes into account the delay of the signals that pass through the communication network - this is quite a common requirement for practical applications. It has been shown that accurate synchronization cannot be achieved in the presence of these delays, but the error caused by these delays can be noticeably suppressed. Furthermore, we study the effect of communication channel failures on a controlled multi-agent system, which can, for example, ensure that the system is sufficiently resilient to cyberattacks. The simulation shows the synchronization of several "inverse pendulum-on-a-cart" systems, a popular benchmark problem.

A related problem is the synchronization of chaotic systems. This area also has a wide range of practical applications: it can help to understand the function of various biological systems, such as brain or heart function, and it can be used to design algorithms for encrypted communication useful for the rapidly developing field of Internet-of-things, for example. The research first began by studying synchronisation between two (or more) chaotic systems with interconnections described by an acyclic graph. This problem was solved at the Control Theory Department. Recently, the researchers in this department have also focused on the problem of synchronization of chaotic systems with a more general topology of interconnections between the systems.

Chaotic behavior of a hybrid inverse pendulum