A new approach is presented for solving long-horizon, constrained optimal control problems by using the mixed coordination method. The method was originally developed for unconstrained optimal control problems, with key ideas including time decomposition, mixed coordination and parallel processing. In extending the method to constrained problems, constraints on state and control variables are relaxed by using the multiplier method. For a given set of Lagrange multipliers, the problem is unconstrained and is solved by using the mixed coordination method. The Lagrange multipliers are then updated in a simple and efficient way. Three problems, including one with nonlinear system dynamics and constraints, and a hydroelectric scheduling problem with ten reservoirs, are tested. Results shows that the new approach is numerically stable, and significant speedups are obtained in a simulated parallel-processing environment. The method can be easily extended to handle unpredicted changes during the online operation phase of a system. >
['Jianxin Tang', 'Peter B. Luh']
The mixed coordination method and its application to the hydroelectric scheduling problems