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

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

Stochastic recruitment strategies for controlling artificial muscles

Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (p. 171-176).This thesis presents a new architecture for controlling active material actuators inspired by biological motor recruitment. An active material is broken down into many small fibers and grouped together to form one large actuator. Each of these fibers is held in a binary state, either relaxed or contracted, using a small local controller which responds to a broadcast input signal from a central controller. The output force and displacement of the actuator is a function of the number of contracted fibers at any point in time. This architecture enables the creation of large-scale, controllable actuators from highly non-linear active materials. The key innovation enabling the central controller to coordinate the behavior of very many small identical units is to randomize the behavior of each unit. This thesis explains how a collection of active material motor units responding in a random, uncorrelated fashion to broadcast commands will exhibit a predictable response that can be stabilized with feedback control and observed using a Kalman filter. Various control strategies will be presented and discussed, including open-loop plant behavior, linear feedback, optimal control, and model-based look-ahead control. Performance metrics such as accuracy and convergence time will be analyzed using dynamic programming and other control techniques. Parallels will also be discussed between this control problem and similar control problems in the field of swarm robotics.(cont.) The stochastic, recruitment-like actuator architecture is demonstrated in shape memory alloy actuators, each composed of 60 individual elements, having a displacement of over 20 mm and a peak force of over 100 N. Control of displacement, isometric force and stiffness are demonstrated using the observer-controller framework. Two actuators are used in an antagonistic fashion to control the stiffness and position of a 1-DOF arm joint.by Lael Ulam Odhner.Sc.D