Nested &egr;-decompositions and clustering of complex systems
Automatica (Journal of IFAC)
Sequential LQG optimization of hierarchically structured systems
Automatica (Journal of IFAC)
Nested epsilon decompositions of linear systems: weakly coupled and overlapping blocks
SIAM Journal on Matrix Analysis and Applications
A Block-Parallel Newton Method Via OverlappingEpsilon Decompositions
SIAM Journal on Matrix Analysis and Applications
Large-scale systems: modeling, control, and fuzzy logic
Large-scale systems: modeling, control, and fuzzy logic
A Canonical Form for the Inclusion Principle of Dynamic Systems
SIAM Journal on Control and Optimization
Technical Communique: Upper bounds for the solution of the discrete algebraic Lyapunov equation
Automatica (Journal of IFAC)
A new approach to control design with overlapping information structure constraints
Automatica (Journal of IFAC)
Pair-wise decomposition and coordinated control of complex systems
Information Sciences: an International Journal
Hi-index | 22.14 |
This paper is concerned with decentralized controller design for large-scale interconnected systems of pseudo-hierarchical structure. Given such a system, one can use existing techniques to design a decentralized controller for the reference hierarchical model, obtained by eliminating certain weak interconnections of the original system. Although this indirect controller design is appealing as far as the computational complexity is concerned, it does not necessarily result in satisfactory performance for the original pseudo-hierarchical system. An LQ cost function is defined in order to evaluate the performance discrepancy between the pseudo-hierarchical system and its reference hierarchical model under the designed decentralized controller. A discrete Lyapunov equation is then solved to compute this performance index. However, due to the large-scale nature of the system, this equation cannot be handled efficiently in many real-world systems. Thus, attaining an upper bound on this cost function can be more desirable than finding its exact value, in practice. For this purpose, a novel technique is proposed which only requires solving a simple LMI optimization problem with three variables. The problem is then reduced to a scalar optimization problem, for which an explicit solution is provided. It is also shown that when the original model is exactly hierarchical, then the upper bounds obtained from the LMI and scalar optimization problems will both be equal to zero.