Optimal Control Of Distributed Parameter Systems With Two Independent Variables

Optimal Control of Distributed Parameter Systems with Two Independent Variables

Optimum Control of Distributed Parameter Systems with Two Independent Variables

The modern methods of the Calculus of Variations are used to find the primary necessary conditions for optimal control. A general problem is formulated which involves: (1) state and control variables defined in a region R with the state variables described by partial differential equations, (2) conditions on the boundary of R which are, typically, the boundary conditions for the interior partial differential equations, and (3) algebraic equations which must hold at the corner points of the boundary of R.A standard format is developed in which a large number of problems may be stated. Once a problem is stated in this standard format the formulae obtained in the dissertation gives a complete system of partial differential equations together with boundary conditions which when solved will yield the optimal control sought. The method is equally applicable to elliptic, parabolic, and hyperbolic partial differential equations. Example problems demonstrate: (1) control within the interior of a region, (2) control using state variables on the boundary, (3) control by varying the shape of the boundary, (4) control with variables defined only on the boundary, and (5) control using quasi-control variables. A final example demonstrates the agreement of the general method developed in the dissertation with a specific method developed by A.I. Egorov. (Author).

A Survey of Optimal Control of Distributed-parameter Systems

The report is a survey of theoretical and computational methods in the field of optimal control of distributed parameter systems. This includes systems described by integral equations and partial differential equations. The various studies which have been done are grouped according to the method employed. A number of applications and potential applications of these methods are discussed, and certain deficiencies in the current state of knowledge are noted. Difficulties and opportunities in practical applications are discussed, and suggestions are offered for directions of research to render the results more readily usable. A list of references is included numbering more than 250 items: papers, report, and books.