Application of 2D systems to investigation of a process of gas filtration

In the paper, a process of gas filtration described by the 2D system with controls is considered. Sufficient conditions for the existence of optimal process are proved.

[1]  A. Ioffe,et al.  Theory of extremal problems , 1979 .

[2]  Ettore Fornasini,et al.  Doubly-indexed dynamical systems: State-space models and structural properties , 1978, Mathematical systems theory.

[3]  S. Łojasiewicz,et al.  An introduction to the theory of real functions , 1988 .

[4]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[5]  Dariusz Idczak,et al.  On the existence of a solution for some distributed optimal control hyperbolic system , 2000 .

[6]  Lamberto Cesari,et al.  Optimization-Theory And Applications , 1983 .

[7]  Manda Butchi Suryanarayana,et al.  Necessary Conditions for Optimization Problems with Hyperbolic Partial Differential Equations , 1973 .

[8]  G. Marchesini,et al.  State-space realization theory of two-dimensional filters , 1976 .

[9]  Tadeusz Kaczorek,et al.  Reachability and controllability of 2D positive linear systems with state feedbacks , 1999 .

[10]  E. Blum,et al.  The Mathematical Theory of Optimal Processes. , 1963 .

[11]  Shengyuan Xu,et al.  Robust output feedback stabilization for two-dimensional continuous systems in roesser form , 2004, Appl. Math. Lett..

[12]  Stanislaw Walczak,et al.  Some properties of cones in normed spaces and their application to investigating extremal problems , 1984 .

[13]  Zhong-Ping Jiang,et al.  Robust Output Feedback Stabilization , 2011 .

[14]  T. Kaczorek.  Two-Dimensional Linear Systems , 1985 .

[15]  Conservative linear systems, unitary colligations and Lax–Phillips scattering: multidimensional generalizations , 2004 .

[16]  D. Owens,et al.  Control theory for a class of 2D continuous-discrete linear systems , 2004 .

[17]  Singular 2D Behaviors: Fornasini–Marchesini and Givone–Roesser Models , 2009 .

[18]  T. H. Hildebrandt.  Introduction to the theory of integration , 1963 .

[19]  Tadeusz Kaczorek.  Perfect observers for singular 2-D Fornasini-Marchesini models , 2001, IEEE Trans. Autom. Control..

[20]  V. S. Vladimirov,et al.  Equations of mathematical physics , 1972 .

[21]  K. Teo,et al.  Computing optimal control With a hyperbolic partial differential equation , 1998, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[22]  Lamberto Cesari,et al.  Optimization with partial differential equations in dieudonné-rashevsky form and conjugate problems , 1969 .

[23]  Krzysztof Galkowski,et al.  An LMI approach to the computation of lower bounds for stability margins of 2D discrete systems , 2006 .