Abstract
The existence of linear quadratic optimal control of ship automatic steering instruments is studied. Firstly, the sufficient conditions for the quadratic integrability of the solutions of linear second order time-variant differential equations are developed. Secondly, the optimal control form of the ship automatic steering instrument is obtained by using the dynamic programming method, which guarantees a minimal ship sway range, during long-distance navigation, by using as little energy as possible. Finally, based on the above mentioned sufficient conditions, the conditions for the realization of optimal control are obtained, which provides a foundation for choosing the weighted coefficients for optimal control in engineering.
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