Stochastic modeling and control of neural and small length scale dynamical systems.

摘要

Recent advancements in experimental and computational techniques have created tremendous opportunities in the study of fundamental questions of science and engineering by taking the approach of stochastic modeling and control of dynamical systems. Examples include but are not limited to neural coding and emergence of behaviors in biological networks. Integrating optimal control strategies with stochastic dynamical models has ignited the development of new technologies in many emerging applications. In this direction, particular examples are brain-machine interfaces (BMIs), and systems to manipulate submicroscopic objects. The focus of this dissertation is to advance these technologies by developing optimal control strategies under various feedback scenarios and system uncertainties.;Brain-machine interfaces (BMIs) establish direct communications between living brain tissue and external devices such as an artificial arm. By sensing and interpreting neuronal activity to actuate an external device, BMI-based neuroprostheses hold great promise in rehabilitating motor disabled subjects such as amputees. However, lack of the incorporation of sensory feedback, such as proprioception and tactile information, from the artificial arm back to the brain has greatly limited the widespread clinical deployment of these neuroprosthetic systems in rehabilitation. In the first part of the dissertation, we develop a systematic control-theoretic approach for a system-level rigorous analysis of BMIs under various feedback scenarios. The approach involves quantitative and qualitative analysis of single neuron and network models to the design of missing sensory feedback pathways in BMIs using optimal feedback control theory. As a part of our results, we show that the recovery of the natural performance of motor tasks in BMIs can be achieved by designing artificial sensory feedbacks in the proposed optimal control framework.;The second part of the dissertation deals with developing stochastic optimal control strategies using limited feedback information for applications in neural and small length scale dynamical systems. The stochastic nature of these systems coupled with the limited feedback information has greatly restricted the direct applicability of existing control strategies in stabilizing these systems. Moreover, it has recently been recognized that the development of advanced control algorithms is essential to facilitate applications in these systems. We propose a novel broadcast stochastic optimal control strategy in a receding horizon framework to overcome existing limitations of traditional control designs. We apply this strategy to stabilize multi-agent systems and Brownian ensembles. As a part of our results, we show the optimal trapping of an ensemble of particles driven by Brownian motion in a minimum trapping region using the proposed framework.