Distributed Control of Interconnected Systems in the Behavioural Framework

Abstract

The rapid development of technology has made the design, monitoring and data storage of large-scale, complex interconnected systems possible. These efficient and economical interconnected systems come with a price: the complex dynamics due to convoluted interconnections make the effective control of such a system incredibly difficult. The behaviour of the subsystems in a network is vastly different than that when it is not, and the inherent uncertainties due to modelling errors may be amplified as a result of the strong interactions. Furthermore, the ability to collect and process large amount of data leads to the paradigm shift from model-centric description to data-centric description or hybrid model/data description of a system. These challenges necessitate the need for a unified foundation for the control of complex systems that is able to admit descriptions of systems not only limited to the conventional differential/difference models.

Motivated by these challenges, this thesis aims to develop such a framework for the distributed control of an interconnected system using the behavioural systems theory. As a theory that focuses on analysing the dynamics of the external variables and places the trajectories admissible within the system as the central role of describing a dynamical system, it is perfect for the construction of a platform that unifies various classes of systems and is effective in the analysis of interconnections. The framework is eventually set up as a completely representation-free structure, allowing for free choice of representations for the systems according to the specific needs. Algorithms for several representation structures are also provided.

For the case where the subsystems are represented as linear time-invariant differential systems while the global requirements are specified as H-infinity type conditions, the control design follows a two-step algorithm. Firstly, the behaviours of the subsystems, the (to-be-designed) controllers as well as the global requirements are all represented as dissipative dynamical systems with quadratic supply rates, from which the (to-be-determined) controller supply rates can be found. Secondly, parametrisations of the supply rates are carried out to search for linear time-invariant representations for the controllers. Algorithms for subsystems with various types of parametric uncertainties are given to add robustness to the controllers. The resulting framework deals with interconnections, uncertainties in the subsystems and disturbance attenuation simultaneously.

For the general framework, neither the subsystems nor the controllers have prescribed representations. The behaviours of the subsystems are denoted by their respective sets of trajectories and interconnections are interpreted entirely as variable sharing instead of signal flows. Furthermore, the network of an interconnected system is also defined as a dynamical system with its own behaviour, leading to a generic, scalable and flexible representation of the interconnected behaviour. From this structure, necessary and sufficient conditions for the existence of the controller behaviours can be given and all distributed controller behaviours can be constructed explicitly. This framework unites various representations and descriptions of the features of dynamical systems as behaviours, thereby allowing for the formation of a hybrid platform for the analysis and distributed control generically and systematically.