摘要 : We study a linear-quadratic optimal control problem in a Hilbert space where the state equation is unsolvable with respect to the derivative and contains an unbounded operator. The performance index is the sum of the integral of a... 展开 We study a linear-quadratic optimal control problem in a Hilbert space where the state equation is unsolvable with respect to the derivative and contains an unbounded operator. The performance index is the sum of the integral of a quadratic form with respect to the control and the state variable on a finite or infinite time interval and also quadratic forms with respect to the differences between the state variable values at fixed points and given values. The optimal control is presented in the feedback form using the implicit differential operator Riccati equation or the operator equation of the Riccati type under a special symmetry condition for the solution. The minimal value of the minimized functional is calculated. Some illustrative examples are also given. 收起