The Controllability of Parabolic Systems with Delay and Distributed Parameters on the Graph

The optimal boundary control problem for a differential system with delay and distributed parameters on the graph is considered. As a state-space systems and the space of boundary control and observation, the classes of integrable functions is used. The conditions of the unique solvability of the problem of optimal control are obtained. And finally, the existence conditions of a unique control action and the controllability system are obtained.

[1]  J. Lions,et al.  Contrôle optimal de systèmes gouvernés par des équations aux dérivées partielles , 1968 .

[2]  Tatiana M. Ledeneva,et al.  Intelligent modeling systems: Design principles , 2013, Autom. Remote. Control..

[3]  Vyacheslav V. Provotorov.  Boundary control of a parabolic system with distributed parameters on a graph in the class of summable functions , 2015, Autom. Remote. Control..

[4]  A. S. Volkova,et al.  On the solvability of boundary-value problems for parabolic and hyperbolic equations on geometrical graphs , 2014, Autom. Remote. Control..

[5]  A. S. Volkova,et al.  Generalized solutions and generalized eigenfunctions of boundary-value problems on a geometric graph , 2014 .

[6]  V. Provotorov.  Boundary control of a parabolic system with delay and distributed parameters on the graph , 2015, 2015 International Conference "Stability and Control Processes" in Memory of V.I. Zubov (SCP).

[7]  A. Zhabko,et al.  On the asymptotic stability of equilibria of nonlinear mechanical systems with delay , 2013 .

[8]  A. Yu. Aleksandrov,et al.  Delay-Independent Stability Conditions for Some Classes of Nonlinear Systems , 2014, IEEE Transactions on Automatic Control.

[9]  Semen L. Podvalny,et al.  A multi-alternative approach to control in open systems: Origins, current state, and future prospects , 2015, Automation and Remote Control.

[10]  Semen L. Podvalny,et al.  Evolutionary principles for construction of intellectual systems of multi-alternative control , 2015, Automation and Remote Control.

[11]  Semen L. Podvalny,et al.  Models of multi-alternative control and decision-making in complex systems , 2014, Autom. Remote. Control..

[12]  S. Podvalny,et al.  The questions of controllability of parabolic systems with distributed parameters on the graph , 2015, 2015 International Conference "Stability and Control Processes" in Memory of V.I. Zubov (SCP).