| With the development of large-scale computing and sensing capabilities, many technological challenges involve the control of large scale systems which are spatially interconnected. This dissertation comprises five chapters wherein control problems involving such systems are posed and solved. The emphasis is on the tractable computation of control laws. First, a technique is given for the distributed control of large scale, discrete-time, spatially invariant systems (Chapter 1). It is pointed out in Chapter 2 that certain systems with finite boundaries can be made spatially invariant by an appropriate control design at the boundaries, which makes the computationally tractable results on the control of spatially invariant systems applicable. Chapter 3 focuses on the analysis of spatially invariant systems and derives a sufficient condition for stability and performance which is also shown to be necessary when the class of systems is relaxed in a natural manner. The analysis is then extended to heterogeneous large scale systems with delays between subsystems. The important notion of robustness with respect to small time delays between spatially separated subsystems of a large scale system is introduced. The control strategy in Chapter 4 solves the problem of ensuring stability and performance of large-scale heterogeneous systems in the face of small communication delays. Chapter 5 deals with the synthesis of antenna arrays that can be mounted on small unmanned aerial vehicles to improve communications between clusters of these vehicles and a base station. Conic optimization theory is used to relax this non-convex problem and allows a computationally tractable solution which is proved to be close to optimality. The last chapter is experimental in nature and demonstrates a strategy of flying aircraft in formation wherein substantial fuel savings can be realized. This idea is shown to be feasible by means of an experimental demonstration on a formation of wings in a wind tunnel. |
