Linear-Quadratic Problems and the Riccati Equation

Abstract

Linear-Quadratic (LQ) control problems have been investigated intensively since the fundamental and seminal paper of R.E. Kalman in 1960 ([KA]). In that paper, it was shown that the Riccati Equation plays an important role for the LQ-Problem. It is the purpose of the present paper to give an overview of the results relating the Riccati Equation with the LQ-Problem. LQ problems are also treated using the Hamiltonian matrix instead of the Riccati Equation. This will not be discussed in this paper. Neither will we deal with the use of Riccati equations outside of the LQ-problem context, e.g. in differential games and the H∞-optimization problem.KeywordsRiccati EquationImaginary AxisSingular CaseDissipation InequalityStatic State FeedbackThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.