Optimal control of multiscale systems using reduced-order models

We study optimal control of diffusions with slow and fast variables and address a question raised by practitioners: is it possible to first eliminate the fast variables before solving the optimal control problem and then use the optimal control computed from the reduced-order model to control the original, high-dimensional system? The strategy "first reduce, then optimize"--rather than "first optimize, then reduce"--is motivated by the fact that solving optimal control problems for high-dimensional multiscale systems is numerically challenging and often computationally prohibitive. We state sufficient and necessary conditions, under which the "first reduce, then control" strategy can be employed and discuss when it should be avoided. We further give numerical examples that illustrate the "first reduce, then optmize" approach and discuss possible pitfalls

Research on optimal control, stabilization and computational algorithms for aerospace applications

The research carried out in the areas of optimal control and estimation theory and its applications under this grant is reviewed. A listing of the 257 publications that document the research results is presented

Estimation and control of non-linear and hybrid systems with applications to air-to-air guidance

Issued as Progress report, and Final report, Project no. E-21-67