Optimisation of control network topology for distributed control of cyber-physical systems

Networked systems are ubiquitous in modern applications ranging from engineering to biology, physics and sociology. Although they can accomplish complex behaviours through local communication, control actions are fundamental to guarantee efficient operation. Centralised control scheme, wherever possible, may provide acceptable performance, but with high complexity, limiting convenient implementation, reliability and scalability. In order to overcome these limitations, one may effectively use distributed control schemes where control action is performed by local controllers interacting over a control network while the process is running through a physical network.

It has been shown that topology of network has a major role on emerging collective behaviours, such as synchronisation and consensus. This thesis aims to investigate the role of control network topology on the performance of dynamical systems. The thesis first studies how the control network topology impacts the dynamical performance of a large-scale Cyber-Physical System (CPS). The state-space model of a two-layer CPS composed of physical and control networks, is first derived. Then, a novel metric is introduced to quantify the relationship between topology of the control structure and dynamical performance of the CPS. This metric is applied to a power system as an application. Modern power systems are indeed a good example of CPS where a physical network transmits electricity to consumers while a control system is responsible for power quality. Based on stability analysis of the distributed generating power system, a new metric is introduced to rank control network topologies. The proposed metric is applied to compare different topologies in terms of their role in the stability. The findings show that small-world networks with smaller connection probability and scale-free networks with smaller values of average degree have better stabilising effects when selected as the control network. It is further shown that homogenous control networks are better candidates to control CPS than their heterogeneous counterparts.

In addition to the stability, the decay rate is also studied as a dynamical performance criterion of a CPS when the control network topology is a design parameter. Two optimisation problems aiming to design the topology of the control network are proposed and solved in this thesis. The first one aims to enhance the system decay rate in the case of fixed communication budget, i.e., specified number of links in the control network. This is a non-convex optimisation problem that is solved using evolutionary algorithms. The proposed evolutionary algorithm is enriched by an intelligent rewiring technique, which is derived using eigenvalue perturbation analysis. This modification helps avoiding local minima.

The second optimisation problem is formulated to design a control network with minimum number of links, whose decay rate is better than a given value. Although sparsity promoting optimal control is a non-convex problem and has been studied in previous research studies, there is no straightforward solution for the combination of the sparsity optimal problem with the decay rate optimisation problem. It is also a controversial problem with considerable complexity as a non-convex, non-smooth and non-Lipschitz problem. Thus, an equivalent convex optimisation problem is proposed and proved that the minimiser of this equivalent problem meets the constraint of the main problem. As the final step, a general framework is developed by which a trade-off between the decay rate of the system and the number of links in distributed control network is addressed. This problem is solved in order to achieve topologies resulting in a decay rate better than a pre-specified value. The algorithm is tested on some large-scale interconnected power systems.