Title

A HIERARCHICAL, TEMPORAL DECOMPOSITION APPROACH TO LONG HORIZON OPTIMAL CONTROL PROBLEMS

Date of Completion

January 1986

Keywords

Engineering, System Science

Degree

Ph.D.

Abstract

This dissertation presents a new solution methodology for the Generalized Scheduling Problem (GSP) in operation scheduling of engineering systems. A complex operation scheduling problem is commonly divided into a hierarchy of scheduling activities based on time scales involved. The GSP seeks for better integration of individual scheduling activities. In this dissertation, the scheduling problem is formulated as a long horizon, large-scale dynamic optimization problem. By applying temporal decomposition, the problem is converted into a hierarchical, two-level optimization problem. Stackelberg game concepts are then used to define interrelationship of subproblems, and suggest proper coordination schemes. Specifically, a target coordination scheme is investigated.^ The idea of target coordination is to use initial and terminal states of low-level subproblems as coordination terms. These coordination terms are then optimized by a high level problem. Consequently, the high level problem is a parameter optimization problem, and low level subproblems are optimal control problems having a shorter time horizon. In addition, low level subproblems are completely decoupled and can be solved in parallel. It is shown that the two-level problem has the same global optimum as the original problem, and that the high-level problem is a convex programming problem under appropriate conditions.^ To realize the target coordination scheme, a parallel, two-level optimization algorithm is designed and tested for a class of unconstrained problems. It adopts a parallel Newton method at the high level and the Differential Dynamic Programming (DDP) at the low level. Two-level optimization design issues are addressed. The algorithm is extended to the constrained case, using Quadratic Programming at the high level and Constrained DDP techniques at the low level. The constrained algorithm is then applied to hydro generation scheduling problems. Testing results of both unconstrained and constrained cases show the potential of the temporal decomposition approach in tackling long-horizon problems under parallel processing environments. The temporal decomposition structure matches the current hierarchical scheduling practice, and serves as a basis for further study of GSP. ^