A simplified method for solving the matrix Riccati equation†

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Abstract
A simplified method of solving the matrix Riccati equation is discussed and illustrated in the context of optimal control theory. The method utilizes a preliminary solution with no requirement on boundary condition or sign definiteness. Utilizing this preliminary solution the desired solution is obtained by solving a linear problem of the same dimension as the state vector. One advantage of the method is that the boundary conditions for the terminal control problem which force some state variables to zero at the terminal time are easily implemented.

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