An infinite horizon linear quadratic optimal control problem for analytic semigroup with unbounded control in Hilbert space is considered.The state weight operator is allowed to be inddefinite while the control weight...An infinite horizon linear quadratic optimal control problem for analytic semigroup with unbounded control in Hilbert space is considered.The state weight operator is allowed to be inddefinite while the control weight operator is coercive.Under the exponential stabilization condition,it is proved that any optimal control and its optimal trajectory are continuous.The positive real lemma as a necessary and sufficient condition for the unique solvability of this problem is established.The closed-loop synthesis of optimal control is given via the solution to the algebraic Riccati equation.展开更多
基金This work is partially supported by the National Key Project of Chinathe National Nature Science Foundation of China No.19901030NSF of the Chinese State Education Ministry and Lab.of Math.for Nonlinear Sciences at Fudan University
文摘An infinite horizon linear quadratic optimal control problem for analytic semigroup with unbounded control in Hilbert space is considered.The state weight operator is allowed to be inddefinite while the control weight operator is coercive.Under the exponential stabilization condition,it is proved that any optimal control and its optimal trajectory are continuous.The positive real lemma as a necessary and sufficient condition for the unique solvability of this problem is established.The closed-loop synthesis of optimal control is given via the solution to the algebraic Riccati equation.
