Some Optimal-Control Problems in Distributed-Parameter Systems

摘要

The dissertation concerns itself with the extension of some of the results known for the optimal control of lumped-parameter systems to distributed systems. The analytical design of the optimal regulator is worked out in detail for linear time-invariant distributed systems. The necessary conditions of optimality are derived using calculus of variations, and the boundary effects are studied in some generality. Two methods are suggested to solve the boundary value problems arising from the regulator problem for linear time-invariant systems. As a further application of the principles involved in the analytical design, the optimal control of a fluid interface is discussed. Next, optimal control of distributed systems with constraints on the control functions is studied. Functions analogous to the Hamiltonian of lumped-parameter systems are defined on the distributed field and on its boundary. Their relations on the boundary are also obtained. A necessary condition for optimality is enunciated as a maximum principle. A non-rigorous proof of this principle is presented. The situations when the maximum principle gives both necessary and sufficient conditions for optimality, are indicated. (Author)