9500908 Dunn Optimal control problems are often naturally formulated as specially structured mathematical programs in infinite-dimensional function spaces. In such cases, a study of algorithms for the limiting infinite-dimensional programs can predict the behavior of standard computational schemes that are actually implemented in approximating finite-dimensional spaces, and can also suggest new algorithms that have no counterparts in the standard methodology for finite-dimensional mathematical programs. In particular, recent studies have shown that standard nonlinear programming algorithms are best suited to optimal control problems with Hamiltonians that are uniformly convex in the control input vector, while other optimal control problems may require strong variation methods based on the inherently infinite-dimensional necessary condition of Pontryagin. The proposed investigation has the following immediate objectives: (i) to establish the convergence properties of Newtonian projection methods in Chebychev norm neighborhoods and root-mean-square neighborhoods of control functions that satisfy recently developed local optimality sufficient conditions for nonconvex nonquadratic constrained input regulator problems; (ii) to extend the analysis in (i) to hybrid algorithms that employ Newtonian projection and Lagrangian augmentation techniques for regulator problems with control variable and state variable constraints; (iii) to establish the convergence properties of strong variation methods in root-mean-square neighborhoods of control functions satisfying sharp local optimality sufficient conditions in the root-mean-square norm for optimal control problems with Hamiltonians that are not convex in the control input vector; (iv) to corroborate the predictions of the infinite dimensional convergence analyses in (i)--(iii) for approximate finite dimensional computations on fixed and nested grids. Optimal control problems arise in aircraft and spacecraft trajectory calcula tions, nuclear and chemical reactor control, structural and aerodynamic design, management of ecological systems, and many other applications. In the generic optimal control problem, a large number of control variables (forces, voltages, temperatures, etc.) are chosen at various points in time and space to bring some physical system into a desired state, and to accomplish this at the lowest possible cost (manuever duration, fuel or power consumption, etc.). Control and state variable values are also typically constrained by hardware or safety considerations, and state transitions are often governed by complicated systems of ordinary or partial differential equations. The associated optimization task is therefore demanding, and requires algorithms that effectively exploit control problem structure in the computation of their successive approximations, and also exhibit good global and local convergence characteristics for the problems in question. In broad terms, the goal of the proposed investigation is to understand which algorithm types are most effective for a given problem structure in the context of optimal control. ***
