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**Closed-form solutions for a class of optimal quadratic regulator problems with terminal constraints.**
*(English)*
Zbl 0596.49002

The paper describes three new developments related to a class of optimal finite-time quadratic regulator problems with terminal constraints instead of penalizing the terminal states. First, analytical solutions are obtained for the feedback gains by means of three coupled Riccati- like matrix differential equations and then a closed form expression for the closed-loop system state trajectory is derived. A new way of implementing these solutions is also developed, leading to considerably simplified computational procedures, based on matrix transformations.

Examples including a first-order system and a simple spacecraft are used to demonstrate the validity of all the analytical solutions presented in the paper.

Examples including a first-order system and a simple spacecraft are used to demonstrate the validity of all the analytical solutions presented in the paper.

Reviewer: O.Pastravanu

### MSC:

49J15 | Existence theories for optimal control problems involving ordinary differential equations |

34A05 | Explicit solutions, first integrals of ordinary differential equations |

34B30 | Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) |

34H05 | Control problems involving ordinary differential equations |

93B17 | Transformations |

93C15 | Control/observation systems governed by ordinary differential equations |

93D15 | Stabilization of systems by feedback |

93B40 | Computational methods in systems theory (MSC2010) |

65K10 | Numerical optimization and variational techniques |