Suboptimal shape control for quasi-static distributed-parameter systems

We propose an on-line control approach which will adjust the steady-state shape of a large antenna arbitrarily close to any achievable desired profile. The method makes use of distributed-parameter system theory and allows refocusing using a limited number of control actuators and sensors.The controller gains are calculated by approximating the solution to an infinite-dimensional optimal quasi-static control problem. The controller gain calculation is computationally simpler than that proposed in a companion paper. The Galerkin (finite element) approximation method is used for model reduction. We prove that both gain and state convergence can be achieved by using the proposed approximation scheme.This work was partially supported by the Air Force Office of Scientific Research, Grant No. AFOSR 83-0124, and by the National Aeronautics and Space Administration, Grant No. NAG-1-515.     

Benders's method revisited

The master problem in Benders's partitioning method is an integer program with a very large number of constraints, each of which is usually generated by solving the integer program with the constraints generated earlier. Computational experience shows that the subset B of those constraints of the master problem that are satisfied with equality at the linear programming optimum often play a crucial role in determining the integer optimum, in the sense that only a few of the remaining inequalities are needed. We characterize this subset B of inequalities. If an optimal basic solution to the linear program is nondegenerate in the continuous variables and has p integer-constrained basic variables, then the corresponding set B contains at most 2^p inequalities, none of which is implied by the others. We give an efficient procedure for generating an appropriate subset of the inequalities in B, which leads to a considerably improved version of Benders's method.     

A note on duality in disjunctive programming

We state a duality theorem for disjunctive programming, which generalizes to this class of problems the corresponding result for linear programming.This work was supported by the National Science Foundation under Grant No. MPS73-08534 A02 and by the US Office of Naval Research under Contract No. N00014-75-C-0621-NR047-048.     

Stability of distributed parameter systems with finite-dimensional controller-compensators using singular perturbations

Using a singular perturbation formulation of the linear time-invariant distributed parameter system, we develop a method to design finite-dimensional feedback compensators of any fixed order which will stabilize the infinite-dimensional distributed parameter system. The synthesis conditions are given entirely in terms of a finite-dimensional reduced-order model; the stability results depend on an infinite-dimensional version of the Klimushchev-Krasovskii lemma presented here.