Time-optimal control of infinite order hyperbolic systems with time delays

Casting, C. (1967). Sur les multi-applications measurables, Revue Francaise d'Informatique et de Recherche Operationelle 1: 91-126.10.1051/m2an/1967010100911Search in Google Scholar

Choquet, G. (1969). Lectures on Analysis, Vol. 2, W.A. Benjamin, New York, NY.Search in Google Scholar

Dubinskij, J. A. (1975). Sobolev spaces of infinite order and behavior of solution of some boundary value problems with unbounded increase of the order of the equation, Matiematiczeskii Sbornik 98: 163-184.Search in Google Scholar

Dubinskij, J. A. (1976). Non-trivality of Sobolev spaces of infinite order for a full euclidean space and a torus, Matiematiczeskii Sbornik 100: 436-446.Search in Google Scholar

Dubinskij, J. A. (1986). Sobolev Spaces of Infinite Order and Differential Equations, Teubner-Texte zur Mathematik, Vol. 87, Teubner-Verlag, Leipzig.Search in Google Scholar

Dunford, N. and Schwartz, J. (1958). Linear Operators, Vol. 1, John Wiley and Sons, New York, NY.Search in Google Scholar

El-Saify, H. A. and Bahaa, G. M. (2002). Optimal control for n x n hyperbolic systems involving operators of infinite order, Mathematica Slovaca 52: 409-422.Search in Google Scholar

Friedman, A. (1969). Partial Differential Equations, Holt, Reinhart and Winston, New York, NY.Search in Google Scholar

Knowles, G. (1978). Time optimal control of parabolic systems with boundary conditions involving time delays, Journal of Optimization Theory and Applications 25(4): 563-574.10.1007/BF00933521Search in Google Scholar

Kowalewski, A. (1993a). Boundary control of hyperbolic system with time lags, IMA Journal of Mathematical Control and Information 10: 261-272.10.1093/imamci/10.3.261Search in Google Scholar

Kowalewski, A. (1993b). Optimal control of hyperbolic system with time lags, Applied Mathematics and Computer Science 3(4): 687-697.Search in Google Scholar

Kowalewski, A. (1995). Optimal control of hyperbolic system with time-varying lags, IMA Journal of Mathematical Control and Information 12: 133-143.10.1093/imamci/12.2.133Search in Google Scholar

Kowalewski, A. (1998). Optimal control of a distributed hyperbolic system with multiple time-varying lags, International Journal of Control 71: 419-435.10.1080/002071798221759Search in Google Scholar

Kowalewski, A. (2000). Optimal control of distributed hyperbolic systems with deviating arguments, International Journal of Control 73: 1026-1041.10.1080/002071700411313Search in Google Scholar

Kowalewski, A. (2003). Time-optimal control problem of hyperbolic systems with deviating arguments, International Journal of Control 76: 557-565.10.1080/0020717031000079472Search in Google Scholar

Lions, J. (1971). Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, Berlin/Heidelberg.10.1007/978-3-642-65024-6Search in Google Scholar

Lions, J. and Magenes, E. (1972). Non-Homogeneous Boundary Value Problems and Applications, Vols. 1 and 2, Springer-Verlag, Berlin/Heidelberg.Search in Google Scholar

Olech, C. (1966). Extremal solutions of a control system, Journal of Differential Equations 2: 74-101.10.1016/0022-0396(66)90064-7Search in Google Scholar

Tanabe, H. (1965). On differentiability and analyticity of weighted elliptic boundary-value problems, Osaka Mathematical Journal 2: 163-190.Search in Google Scholar

Wang, P. K. C. (1975). Optimal control of parabolic systems with boundary conditions involving time delays, SIAM Journal of Control 13(2): 274-293.10.1137/0313016Search in Google Scholar