Reduced-order solution to the finite-time optimal-control problems of linear weakly coupled systems

The optimal solution to the finite-time optimal-control problem of weakly coupled linear systems is found in terms of completely decoupled reduced-order differential equations for both closed-loop and open-loop control. This is achieved through the use of the decoupling transformation that block diagonalizes the Hamiltonian matrix of the weakly coupled linear-quadratic control problem. The convergence to the optimal solution is pretty rapid. The proposed technique is very well suited for parallel computations