Consensus, Control and Message Passing in Complex Control Systems

Abstract

Real-world merging systems are characterised by several challenges and high level of complexities, such as stochasticity, nonlinearities, high dimensionality, and systems with coupling. The aim of this thesis is to address these inconveniences in order to develop robust control algorithms for such real engineered emergent systems. The study in this thesis considered the development of the fully probabilistic (FP) framework that addresses the main challenge of controlling real-world stochastic and uncertain systems.The probabilistic framework characterises the dynamics of the system to be controlled in terms of probability distributions which is a desirable approach to handle the stochasticity of dynamical systems. Non-linearity of real-world systems on the other hand, hinders the derivation of analytic control solutions, yielding expensive numerical computations. To address this problem, a transformation method has been introduced to the developed FP control framework which facilitated the derivation of an analytic solution despite the nonlinearity of the system dynamics. This method transformed the nonlinear state function to another variant where the nonlinearities are preserved but have now been transformed to a nonlinear affine state function. The inclusion of this novelty allows for the control of more realistic systems which tend to be nonlinear. Further advancement includes the extension of the developed nonlinear FP control method to control large-scale complex nonlinear systems. This is achieved by decomposing the complex system into small subsystems and then decentrally controlling each individual subsystem by a local controller. Probabilistic message passing is thereafter used to coordinate between the subsystems constituting the complex system, thus achieving the overall objective of the controlled complex system. This decentralised control framework has further been advanced to consider several control objectives, including regulation, tracking and formation control where the subsystems that constitute the overall network rely on the probabilistic message passing approach to interact with each other.