STRUCTURAL DECOMPOSITION-BASED CONTROL SYNTHESIS FOR MULTIVARIABLE SYSTEMS USING OBLIQUE PROJECTION OPERATORS
Аннотация
This paper proposes a novel approach to control synthesis for multivariable systems with algebraic constraints using oblique projection operators and their structural decomposition. The method transforms a standard control law into a structured form by decomposing the control input into constraint-satisfying and null-space components. A generalized oblique projector is constructed using a dual matrix, ensuring flexibility in shaping system properties. Furthermore, a recursive decomposition algorithm is developed, allowing the global projector to be represented as a sum of local operators corresponding to subsystem structures. The proposed framework enables modular control design, decoupling of interactions, and efficient implementation for large-scale systems. Theoretical properties of the operators are established, and the applicability of the method to constrained control problems is demonstrated. Furthermore, a recursive algorithm is introduced to decompose the global projection operator into local components associated with the subsystems. This decomposition not only reduces computational complexity but also enables a modular implementation, making the approach suitable for large-scale industrial systems.