Development of hierarchical optimal control algorithms for interconnected nonlinear dynamical systems
The main concern of this thesis is to develop and advance the knowledge of new hierarchical algorithms for optimal control of interconnected nonlinear systems. To achieve this, four basic hierarchical structures are developed by taking into account the manner in which real process measurements taken from interaction inputs are incorporated and utilized in the model-based optimal control problem. The structures are iterative in nature, and are derived using the dynamic integrated system optimization and parameter estimation (DISOPE) technique to take into account model-reality differences that may have been deliberately introduced to facilitate the solution of the complex nonlinear problem or due to uncertainty in the model used for computation. Three of the four basic hierarchical structures are used as a basis for developing hierarchical optimal control algorithms using a linear quadratic model formulation. Two approaches are used in the coordination problem of the algorithms, price coordination approach and the direct coordination approach. The algorithms are then implemented using two techniques, the single loop and the double loop techniques. All the algorithms are implemented in software and a simulation study is carried out using two examples to investigate their effectiveness and convergence properties. The optimality of the solution provided by the structures and the algorithms described in this research work are established. In addition, convergence analysis is carried out to provide sufficient convergence conditions of the double loop algorithms. Suggestions for future research as a continuation of the work presented in this thesis are also made.