A Homotopy Algorithm for Solving Algebraic Riccati Equations

A novel homotopy algorithm is presented which allows solution of a Riccati equation by effectively exploiting knowledge of the solution of a Riccati equation whose parameters are "close" to the parameters of the equation with unknown solution. This algorithm can thus be used to improve computational efficiency in a practical control design process that involves generating a series of control designs by varying a set of weights. The algorithm can also be extended to solve modified Riccati equations that have appeared as integral parts of the solutions to important problems in control theory and design.