Adam Kowalewski

Optimal control of a distributed hyperbolic system with multiple time-varying lags

In this paper an optimal distributed control problem for a hyperbolic system in which different multiple time-varying lags appear both in the state equation and in the boundary condition is considered. Making use of Lions scheme, necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functional and constrained control are derived. A simple example of application is also presented

Boundary control of distributed parabolic system with boundary condition involving a time-varying lag

An optimal boundary control problem for a distributed-parameter system with a boundary condition involving a time-varying lag is solved. The time horizon is fixed. Making use of the Lions scheme, necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functional and constrained control are derived.

Optimization of parabolic systems with deviating arguments

Various optimal control problems for linear parabolic systems with deviating arguments given in the integral form are considered. Necessary and sufficient conditions of optimality are derived for the Neumann problem. The optimal control is obtained in feedback form. Making use of theresults of Schwartz, the representation of the optimal feed back control is given. A simple example of application is also provided.

Optimal control of distributed hyperbolic systems with deviating arguments

In this paper optimal control problems for hyperbolic systems in which deviating arguments appear in the integral form both in the state equations and in the boundary conditions are considered. Making use of Lions scheme, necessary and sufficient conditions of optimality for the Neumann problem are derived. A simple example of application is also provided.

Time-optimal control of hyperbolic systems with deviating arguments

In this paper the time-optimal control problem for distributed hyperbolic systems in which time delays appear in the integral form both in the state equations and in the boundary conditions is considered. The particular properties of the optimal control are discussed.

Optimal control of time delay parabolic systems

Various optimal control problems for linear parabolic systems with multiple constant time delays are considered. Necessary and sufficient conditions of optimality are derived for the Neumann problem. The optimal control is obtained in the feedback formMaking use of the results of Schwartzs, the representation of the optimal feedback control is given. A simple example of application is also provided

Optimal control of distributed parabolic systems with multiple time delays given in the integral form

Various optimal control problems for linear parabolic systems with multiple time delays given in the integral form are considered. Necessary and sufficient conditions of optimality are derived for the Neumann problem. The optimal control is obtained in the feedback form. Making use of the results of Schwartz, the representation of the optimal feedback control is given. A simple example of application is also provided.

Minimum time problem for distributed hyperbolic systems with time lags

Various optimization problems associated with the optimal control of distributed parameter systems with time lags appearing in the boundary conditions have been studied recently by Wang (1975); Knowles (1978); Wong (1987) and Kowalewski (1993a,b, 1995, 1998, 1999, 2000). In this paper, we consider the minimum time problem for linear hyperbolic systems in which constant time lags appear both in the state equations and in the Neumann boundary conditions. The optimal control is characterized by the adjoint equation. Using this characterization particular properties of the optimal control are proved. Moreover, a certain case of nonlinear control without convexity is considered.

Optimization Problems of Parabolic-Hyperbolic Systems with Time Delays 1 1The research presented here was carried out within the research programme AGH University of Science and Technology, No. 10.10.120.31.

Abstract Optimal boundary control problems for linear parabolic-hyperbolic systems with time delays given in the integral form are considered. Sufficient conditions for the existence of a unique solution for such parabolic-hyperbolic systems are proved. Necessary and sufficient conditions of optimality are derived for the Neumann problem. The problem of determining of the optimal control is discussed.