A review on analysis and synthesis of nonlinear stochastic systems with randomly occurring incomplete information

Copyright q 2012 Hongli Dong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In the context of systems and control, incomplete information refers to a dynamical system in which knowledge about the system states is limited due to the difficulties in modeling complexity in a quantitative way. The well-known types of incomplete information include parameter uncertainties and norm-bounded nonlinearities. Recently, in response to the development of network technologies, the phenomenon of randomly occurring incomplete information has become more and more prevalent. Such a phenomenon typically appears in a networked environment. Examples include, but are not limited to, randomly occurring uncertainties, randomly occurring nonlinearities, randomly occurring saturation, randomly missing measurements and randomly occurring quantization. Randomly occurring incomplete information, if not properly handled, would seriously deteriorate the performance of a control system. In this paper, we aim to survey some recent advances on the analysis and synthesis problems for nonlinear stochastic systems with randomly occurring incomplete information. The developments of the filtering, control and fault detection problems are systematically reviewed. Latest results on analysis and synthesis of nonlinear stochastic systems are discussed in great detail. In addition, various distributed filtering technologies over sensor networks are highlighted. Finally, some concluding remarks are given and some possible future research directions are pointed out. © 2012 Hongli Dong et al.This work was supported in part by the National Natural Science Foundation of China under Grants 61273156, 61134009, 61273201, 61021002, and 61004067, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, the National Science Foundation of the USA under Grant No. HRD-1137732, and the Alexander von Humboldt Foundation of German

Kullback-Leibler-Quadratic Optimal Control

This paper presents advances in Kullback-Leibler-Quadratic (KLQ) optimal control: a stochastic control framework for Markovian models. The motivation is distributed control of large networks. As in prior work, the objective function is composed of a state cost in the form of Kullback-Leibler divergence plus a quadratic control cost. With this choice of objective function, the optimal probability distribution of a population of agents over a finite time horizon is shown to be an exponential tilting of the nominal probability distribution. The same is true for the controlled transition matrices that induce the optimal probability distribution. However, one limitation of the previous work is that randomness can only be introduced via the control policy; all uncontrolled (natural) processes must be modeled as deterministic to render them immutable under an exponential tilting. In this work, only the controlled dynamics are subject to tilting, allowing for more general probabilistic models. Another advancement is a reduction in complexity based on lossy compression using transform techniques. This is motivated by the need to consider time horizons that are much longer than the inter-sampling times required for reliable control. Numerical experiments are performed in a power network setting. The results show that the KLQ method enables the aggregate power consumption of a collection of flexible loads to track a time-varying reference signal, while simultaneously ensuring each individual load satisfies its own quality of service constraints