In this paper we analyze the properties of the set of solutions of the generalized continuous algebraic Riccati equation from a geometric perspective. In particular, we study the relationship existing between the solutions of the generalized Riccati equation and the output-nulling subspaces of the underlying system. This analysis reveals the presence of a subspace that plays an important role in the solution of the related optimal control problem.
On the geometry of the continuous-time generalized algebraic Riccati equation arising in LQ optimal control
FERRANTE, AUGUSTO;
2015
Abstract
In this paper we analyze the properties of the set of solutions of the generalized continuous algebraic Riccati equation from a geometric perspective. In particular, we study the relationship existing between the solutions of the generalized Riccati equation and the output-nulling subspaces of the underlying system. This analysis reveals the presence of a subspace that plays an important role in the solution of the related optimal control problem.
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