The reduced-order solution of the matrix differential Riccati equation of weakly coupled systems

An efficient numerical method for solving the matrix differential Riccati equation of weakly coupled systems is obtained in terms of the reduced-order problems. This is achieved via 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 rapid. The technique is well suited for the parallel computations. The proposed methods also reduce considerably the size of the required computations and introduce full parallelism in the problem under study.<>