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 spatio-temporal chaos. A version close to linear quadratic design gives an initial insight into possible behaviours of such networks.

KEYWORDS:

• Cooperative control
• optimal control
• complex systems
• stochastic systems

Acknowledgments

The authors would like to thank the anonymous reviewers and the Associate Editor for their invaluable remarks and suggestions.

Notes

1. Theorem 3.1 below indicates how to get this recursion. The general case with noisy measurements of the state is in Kárný and Guy (2006).

Additional information

Funding

The research was partially supported by GAČR 13-13502S.

Notes on contributors

Randa Herzallah

Randa Herzallah received her B.Sc. in Industrial Engineering and M.Sc. in Industrial Engineering/Manufacturing and Design at Jordan University, Jordan, and later her Ph.D. from Aston University, Birmingham, UK. She previously held the positions of Associate Professor at Al-AHliyya Amman University and Professor at Al-Balqa Applied University. She is currently a Lecturer in the Faculty of Engineering and Applied Science at Aston University, Birmingham, UK. Her general research focus is on the general topic of ‘Systems Modelling, Design and Control' . Her current research interests are nonlinear control theory, probabilistic and stochastic control, intelligent control, pinning control, adaptive control, distributed control, and optimal control.

Miroslav Kárný

Miroslav Kárnýis with Department of Adaptive Systems, Institute of Information and Automation, the Czech Academy of Science since 1973, since graduating at Faculty of Nuclear and Physical Engineering, the Czech Technical University, Prague. There, he defended his Ph.D. in 1977 and obtained degree Dr.Sc. in 1990. His contributions to theory of adaptive systems encounter: (1) model-structure estimation (2) forgetting (3) estimation and control with dynamic mixtures (4) fully probabilistic design (FPD) of decision strategies (5) use of FPD for knowledge and preference elicitation as well as cooperation of probabilistic controllers. He was involved in applications covering: (1) adaptive control of technological processes (2) probabilistic support of operator of complex systems (3) support of electronic democracy (4) trading with futures (5) estimation problems in physics, nuclear medicine, transportation and others. He is co-author of about 400 publications, he supervised 13 Ph.D. students to the successful completion and was principal investigator about 20 grant research projects. Theory of distributed probabilistic dynamic decision making of both human and non-human participants is his dominant current research interest.