Topics in the Study of Interconnected Systems.
Abstract
This report deals with the stability, stabilization and optimization of systems which can be meaningfully viewed as an interconnection of smaller subsystems. We consider systems whose properties can be determined by examining the corresponding properties of the subsystems and their interconnections rather than the system as a whole. The relevance of such systems to any theory of large scale systems is evident. We present some formulations of the weak interconnection concept in Section 2 in the context of stability studies of economic models. It is shown how the modelling of an economy requires the consideration of systems formed by suitably bounded interconnections of stable subsystems. Lyapunov's second method is employed to unify numerous results as well as to provide interesting extensions. The problem of decentralized stabilization is reduced to an infinite duration linear quadratic game, a complete solution of which is given in Section 5. As expected, Riccati-type equations play an important role in such problems. This role is clarified in Section 5. Section 3 deals with the comparison of the solutions of optimal control problems for interconnected systems. The theory of dynamic programming and the Hamilton Jacobi Bellman equation is the main tool used. In addition, the same theory is applied to an extensive study of optimization algorithms, the main result being the extension of the applicability of the well-known Kleinman algorithm for the Riccati equation to cover the ones encountered in Sections 4 and 5.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1976
- Accession Number
- ADA031565
Entities
People
- Evangelos F. Mageirou
Organizations
- Harvard University