A matrix approach to graph maximum stable set and coloring problems with application to multi-agent systems

This paper studies the synchronization of interconnected k-valued logical networks, as well as that of interconnected higher order k-valued logical networks, based on their algebraic representations. For interconnected k-valued logical networks, one necessary and sufficient criterion of synchronization is established via the definition of synchronization and another equivalent condition is given by combining synchronization with fixed points and cycles. Furthermore, with some special properties of semi-tensor product, the third necessary and sufficient condition for synchronization of interconnected k-valued logical networks is raised in terms of transition matrices. Then, the limit set method can be used to analyze the synchronization of interconnected higher order k-valued logical networks. Finally, three examples, including the Boolean model for interconnected biochemical oscillators in the cell cycle, are presented to illustrate effectiveness of the results.

Synchronization of Interconnected Multi‐valued Logical Networks

A general structure of specific optimal control

Specific optimal control of an aluminum casting furnace

Piecewise suboptimal control laws for differential games

Two suboptimal control policies employing integral state feedback suitable for nonlinear systems and nonquadratic performance functionals have been proposed. Necessary conditions are obtained using the variational approach to select optimally the time-invariant parameters for a general control structure of which the two suboptimal policies proposed are particular cases. A numerical example is worked out and the results compared and discussed.

T. Natarajan

Papers

On proportional plus proportional-integral suboptimal control