Boundary control of a hyperbolic system with time lags

This paper considers an optimal boundary control problem fora hyperbolic system in which constant time lags appear in thestate equation and in the boundary condition simultaneously.Making use of Lion's scheme, necessary and sufficient conditionsof optimality for the Neumann problem are derived.     

Time-optimal control of a parabolic system with time lags given in the integral form

In this paper the time-optimal control problem for a distributedparabolic system in which time lags appear in the integral formboth in the state equation and in the boundary condition ispresented. The particular properties of the optimal controlare discussed.     

Control of distributed time delay systems with Dirichlet boundary conditions

Various optimization problems associated with the optimal controlof distributed parameter systems with time lags appearing inthe boundary conditions have been studied recently by Wang (1975),Knowles (1978), Wong (1987), Kowalewski (1987a,b, 1988a,b,c,1990a,b,c,d, 1991, 1993a,b,c,d, 1995) and Kowalewski & Duda(1992). In this paper optimal boundary control problems fordistributed systems described by linear partial differentialequations of parabolic and hyperbolic type in which constanttime delays appear in the state equations are considered. Sufficientconditions for the existence of a unique solutions of such equationswith the Dirichlet boundary conditions are proved. The performancefunctional has the quadratic form. The time horizon T is fixed.Finally, we impose some constraints on the control. Making useof Lions' scheme (Lions 1971) necessary and sufficient conditionsof optimality for the Dirichlet problem with the quadratic performancefunctional and constrained control are derived. The flow chartof the algorithm, which can be used in the numerical solvingof certain optimization problems for distributed parameter systems,is also presented.     

Minimum time problem for a parabolic system with time-varying lags

In this paper the time-optimal control problem for a distributedparabolic system in which time-varying lags appear both in thestate equation and in the boundary condition is presented. Theparticular properties of the optimal control are discussed.     

Feedback Control of a Distributed Parabolic System with Boundary Condition Involving a Time-Varying Lag

In this paper, a feedback control problem for a distributed-parametersystem with boundary condition involving a time-varying lagis considered. Neccessary and sufficient conditions for optimalityare derived. The optimal control is obtained in feedback form.Estimates for the solutions of parabolic systems with specifiedforms of feedback control are established.     

Nuclear spin relaxation in solution of paramagnetic complexes with large transient zero-field splitting

A theory for paramagnetic relaxation enhancement (PRE) in systems with S> 1 at low magnetic field is developed for the case when the fluctuations of zero-field splitting (ZFS) in the molecular frame are larger than the averaged ZFS. The validity limits of the new theory are discussed, and its performance is evaluated by comparisons with the general slow-motion approach. The relevance of the new approach for the proton PRE in aqueous solution of Ni(II) is discussed.     

Laplace Transform and New Mathematical Theory of Viscoelasticity

In this paper generalized variational principles in thesense of the Laplace transform for viscoelastic problems arederived. Then mathematical theory of viscoelasticity ingeneralized Hardy spaces and in weighted anisotropic Sobolevspaces and spectral theory of corresponding non-selfadjointoperators is elaborated. Finally the Laplace transform--FEMfor numerical analysis of time-dependent problems of themathematical physics is proposed and analysed.     

Optimal control of a hyperbolic system with time-varying lags

In this paper, an optimal distributed control problem for ahyperbolic system in which time-varying lags appear in the stateequation and in the boundary condition simultaneously is considered.Making use of Lions' scheme, necessary and sufficient conditionsof optimality for the Neumann problem are derived.     

Optimal control of parabolic systems with time-varying lags

Various optimal control problems for linear parabolic systemswith time-varying lags are considered. Necessary and sufficientconditions of optimality are derived for the Neumann problem.The optimal control is obtained in the feedback form. Makinguse of the results of Schwart's, the representation of the optimalfeedback control is given.     

Optimal Control of Distributed Parabolic Systems Involving Time Lags

Various optimal control problems for linear parabolic systemswith constant time lags are considered. Necessary and sufficientconditions of optimality are derived for the Neumann problem.The optimal control is obtained in the feedback form. Makinguse of the results of Schwartz, the representation of the optimalfeedback control is given. A simple example of application isalso provided.