Towards probabilistic synchronisation of local controllers

Abstract

The traditional use of global and centralised control methods, fails for large, complex, noisy and highly connected systems, which typify many real world industrial and commercial systems. This paper provides an efficient bottom up design of distributed control in which many simple components communicate and cooperate to achieve a joint system goal. Each component acts individually so as to maximise personal utility whilst obtaining probabilistic information on the global system merely through local message-passing. This leads to an implied scalable and collective control strategy for complex dynamical systems, without the problems of global centralised control. Robustness is addressed by employing a fully probabilistic design, which can cope with inherent uncertainties, can be implemented adaptively and opens a systematic rich way to information sharing. This paper opens the foreseen direction and inspects the proposed design on a linearised version of coupled map lattice with spatiotemporal chaos. A version close to linear quadratic design gives an initial insight into possible behaviours of such networks.

DOBC Based Fully Probability Design for Stochastic System With the Multiplicative Noise

“…where ε k−1 as defined in Equation (24) is the disturbance estimation error. Since the prior disturbance estimationτ − k−1 is applied to the system in Equation 25, the covariance of ε k−1 is the prior covariance P − k−1 as defined in Equation (18). This means that ε k−1 is subjected to the following distribution,…”

“…It was initially proposed by Karny [17], and then further developed and applied in much literature. For example, a novel distributed FPD approach is presented in [18] for large, complex, noisy and highly connected systems. In [19], a generalised fully probabilistic controller design was studied for stochastic linear Gaussian systems where the uncertainty introduced by the model discrepancy is estimated as a function of the system inputs.…”

Probabilistic Message Passing for Decentralized Control of Stochastic Complex Systems

“…Proof: The proof of this proposition can be obtained by evaluating Equation (4) using the corresponding pdfs specified in Equations (5), (7), and (8) . Its detailed derivation can be found in [22]. As can be seen from Equation (10), only the two blocks defined in Equations (12) and (13) of the full Riccati matrix S t;i need to be solved.…”

“…A fundamental property often overlooked conventionally VOLUME 4, 2016 is that the control process of a subsystem of these typical networks-of-networks needs to consider constraints imposed from the external environment and neighboring subsystems. This has been addressed in our recent work [22], [23] where we postulated a decentralized architecture that incorporates higher interaction across the network through decoupling the effect of a subsystem into the subsystem's own state and external inputs from neighboring subsystem states estimated via probabilistic message passing. However, the decentralized architecture in [22], [23] has focused on the problem of determining optimal control inputs that make the complex system behave in a pre-specified way and have only developed incipient message passing technique that pass the parameters from one subsystem to another.…”

Fully Probabilistic Design for Stochastic Discrete System with Multiplicative Noise

“…A novel generalised fully probabilistic controller design was proposed in [15] for stochastic linear Gaussian systems where the dynamics of the system is unknown and where the uncertainty introduced by the model discrepancy is estimated as a function of the system inputs. In [19], the FPD is combine with distributed control for large, complex, noisy and highly connected systems. In [20], a probabilistic control method for adaptive synchronisation is proposed.…”