Abstract

This dissertation deals with the structurally constrained control of interconnected systems. A near-optimal decentralized control law is proposed for finite dimensional linear time-invariant (LTI) systems, which under certain conditions leads to a quadratic performance index arbitrarily close to the LQR performance. A method is then proposed to implement any centralized controller in a decentralized fashion in order to reduce the communication requirements. The decentralized controller obtained performs identically to the original centralized controller if some a priori knowledge of the nominal model of the system and the expected values of the initial states are available. The immediate application of this decentralization scheme is in control of a formation of spacecraft in deep space, as it is an ongoing research in JPL. Design of a high-performance decentralized generalized sampled-data hold functions (GSHF) is also studied, which relies on linear matrix inequality (LMI) techniques. Moreover, the problem of simultaneous stabilization of a set of LTI systems using a periodic control law is investigated. It is to be noted that prior to this work there were only sufficient conditions for simultaneous stabilizability of more than four systems, although this problem has been investigated in the literature for several decades. This thesis provides the first necessary and sufficient condition for simultaneous stabilizability of any arbitrary number of systems. Stabilizability of an interconnected system with respect to LTI decentralized control law and also general (nonlinear and time-varying) control law is investigated in the literature, by introducing the notions of decentralized fixed mode (DFM) and quotient fixed mode (QFM). Since the existing methods aiming at identifying these fixed modes are ill-conditioned, two graph-theoretic approaches are proposed here to obtain the DFMs and QFMs of a system in a more efficient manner. In addition, it is asserted that the nonzero and distinct DFMs of a system can be eliminated by means of a proper sampled-data controller. On the other hand, decentralized overlapping control as a more advanced form of structurally constrained control systems is investigated thoroughly. An onto mapping between the decentralized control and the decentralized overlapping control is introduced, which makes the decentralized control design techniques applicable to the decentralized overlapping problem. A systematic method is proposed to check stabilizability of general proper (as opposed to strictly proper) structurally constrained controllers with respect to LTI and non-LTI systems. It is to be noted that the extension of the existing techniques to this general problem not only is non-trivial, but not feasible indeed. Besides, robust stability of the closed-loop system in the presence of polynomial uncertainties is also investigated and a necessary and sufficient condition in the form of sum-of-squares (SOS) is presented. It is to be noted that this problem has been investigated in the literature for the past ten years but prior to this work, only sufficient conditions existed for robust stability of this type of systems. The results presented in this treatise are applied to several benchmark examples, including formation flying of three UAVs, to demonstrate the efficacy of this work