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Adaptive and optimal synchronization control of networked positive real infinite dimensional systems with virtual leader
Author(s) -
Demetriou Michael A.
Publication year - 2018
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.2920
Subject(s) - synchronization (alternating current) , control theory (sociology) , lyapunov function , computer science , parameterized complexity , partial differential equation , controller (irrigation) , adaptive control , metric (unit) , domain (mathematical analysis) , component (thermodynamics) , boundary (topology) , mathematics , control (management) , nonlinear system , engineering , computer network , mathematical analysis , channel (broadcasting) , operations management , physics , algorithm , quantum mechanics , artificial intelligence , agronomy , biology , thermodynamics
Summary This paper considers the design of synchronization controllers for a class of networked infinite dimensional positive real systems, which include partial differential equations with boundary or in‐domain actuation and sensing. The proposed distributed controllers have one component addressing a tracking objective based on static output feedback and another component addressing a synchronization objective. One method of selecting the synchronization gains is to consider the aggregate form of the networked systems and minimize an associated energy function of the resulting closed‐loop system parameterized by the synchronization gains. Thus, the optimal synchronization gains are found as the ones that minimize the trace of the solution to a parameterized operator Lyapunov equation. The adaptation of the synchronization gains constitutes an alternative method for their selection and uses a Lyapunov redesign approach to derive the update laws, which depend on local decentralized strategies. An extension dealing with restricted virtual leader information necessitating modifications to the proposed control laws is also considered and presented. Numerical studies for selecting the synchronization gains via an optimization of an associated performance metric as well as via time‐variation through adaptation are presented for one‐dimensional diffusion partial differential equations.