Ph.D Student | Zaslavsky Ron |
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Subject | Sampled-Data H2 Estimation Problems Motivated by Tensegrity Structures |

Department | Department of Mechanical Engineering |

Supervisor | Professor Leonid Mirkin |

Full Thesis text |

Control and estimation in large-scale spatially distributed systems is an emerging topic in the control literature. Technological developments make it feasible to incorporate large arrays of sensors and actuators into various products. This opens new opportunities and poses new challenges for control theory. The main challenge is the need to handle a huge number of control channels, which is not (and, probably, will not be) feasible using existing (centralized) control strategies. Decentralized schemes could be a remedy, yet the development of numerically reliable analytical design methods with decentralized controller structure is still an open problem.

This thesis puts forward an alternative approach based on spatial clustering. The idea is first to aggregate, using a simple finite memory algorithm, sensed information from a group of closely located sensors into a single signal (spatial sampling). This results in a substantially smaller number of measurements entering the controller, which therefore can process this information in a centralized fashion and produce a number of control signals. Each of these signals is then post-processed, using again simple finite memory algorithms, and locally distributed by a group of closely located actuators (spatial hold functions). This kind of controller can be analyzed and designed by the tools from sampled-data control theory. The main technical challenge in the transition from temporal to spatial sampling is the need to handle relaxed causality (Spatial dynamics do not need to be causal.).

Several steps
toward the solution of the spatial clustering problem are presented, in two
parts. The first (Unstable-unit-cell tensegrity plate design), motivates the
problem by presenting an example of spatially distributed system requiring a
huge number of sensors and actuators to function properly. The second part
(Sampled-data estimation, with relaxed causality), presents the solution of the
estimation version of the spatial clustering problem. The feasibility of the
UUTP topology has been proven, and an algorithm for the design of UUTPs with
many members has been developed. Several sampled-data estimation problems with
relaxed causality constraints and generalized sampling devices have been
solved. We solved the H^{2} sampled-data fixed-interval and fixed-lag
estimation (smoothing) problems. Similar to the sampled-data Kalman filter case,
a discrete algebraic Riccati equation is solved**, **the non-causal
estimators are made of a cascade of discrete-time LTI filter and a stationary
generalized hold, and their pulse response is inherently consistent. Unlike the
Kalman filter, the estimators pulse response is continuous, and the hold
function depends on the sampler parameters.