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1995•Transactions of the Society of Instrument and Control EngineersOpen access

Optimal Regulator for Continuous-Time Descriptor System Using Generalized Riccati Equation

Tohru Katayama, K. Minamino

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Abstract

This paper considers an LQ regulator problem for a continuous-time descriptor system Ex =Ax + Bu.We first derive a generalized Riccati differential equation (GRDE) for the finite-horizon nonsingular (det E0)descriptor regulator problem.Then we show that for the singular case (det E=0), a solution of the GRDE can be used for computing an optimal control and the optimal cost.For the infinite-horizon case, a generalized algebraic Riccati equation (GARS) is derived as a steady-state version of the GRDE.Based on the generalized eigenproblem associated with the Hamiltonian equation, we present a method of computing admissible solutions to the GARE and optimal feedback gains.Numerical examples are included.

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This paper considers an LQ regulator problem for a continuous-time descriptor system Ex =Ax + Bu.We first derive a generalized Riccati differential equation (GRDE) for the finite-horizon nonsingular (det E0)descriptor regulator problem.Then we show that for the singular case (det E=0), a solution of the GRDE can be used for computing an optimal control and the optimal cost.For the infinite-horizon case, a generalized algebraic Riccati equation (GARS) is derived as a steady-state version of the GRDE.Based on the generalized eigenproblem associated with the Hamiltonian equation, we present a method of computing admissible solutions to the GARE and optimal feedback gains.Numerical examples are included.

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Available abstract

This paper considers an LQ regulator problem for a continuous-time descriptor system Ex =Ax + Bu.We first derive a generalized Riccati differential equation (GRDE) for the finite-horizon nonsingular (det E0)descriptor regulator problem.Then we show that for the singular case (det E=0), a solution of the GRDE can be used for computing an optimal control and the optimal cost.For the infinite-horizon case, a generalized algebraic Riccati equation (GARS) is derived as a steady-state version of the GRDE.Based on the generalized eigenproblem associated with the Hamiltonian equation, we present a method of computing admissible solutions to the GARE and optimal feedback gains.Numerical examples are included.

Key concepts: Linear-quadratic regulator, Algebraic Riccati equation, Riccati equation, Mathematics, Optimal control, Regulator, Invertible matrix, Applied mathematics

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