Optimal control problems over large time intervals.

*(English)*Zbl 0623.49010Consider a linear quadratic optimal control problem with prescribed initial and final states, in which the time interval T is large - it does not appear that a criterion is given to determine when this condition actually occurs. The authors show that most of the transient activity occurs near \(t=0\) and \(t=T\), that the state vector remains small away from these points, and that the optimal trajectory and control for the original problem can be approximately obtained by piecing together the optimal trajectories and controls for two infinite-time problems.

Reviewer: J.Rubio

##### MSC:

49K15 | Optimality conditions for problems involving ordinary differential equations |

49M99 | Numerical methods in optimal control |

93C05 | Linear systems in control theory |

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

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

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\textit{B. D. O. Anderson} and \textit{P. V. Kokotovic}, Automatica 23, 355--363 (1987; Zbl 0623.49010)

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##### References:

[1] | Anderson, B.D.O., Stability results for optimal systems, Electronics lett., 5, (1969) |

[2] | Asseo, S.J., Optimal control of a servo derived from nonquadratic performance criteria, IEEE trans aut. control, AC-14, 404, (1969) |

[3] | Bass, R.W.; Weber, R.F., Optimal nonlinear feedback control derived from quartic and higher-order performance criteria, IEEE trans aut. control, AC-11, 448, (1966) |

[4] | Glad, S.T., On the gain margin of nonlinear and optimal regulators, IEEE trans aut. control, AC-29, 615, (1984) · Zbl 0547.93017 |

[5] | Kokotovic, P.V., Applications of singular perturbation techniques to control problems, SIAM rev., 26, 501, (1984) · Zbl 0548.93001 |

[6] | Kokotovic, P.V.; Khalil, H.K.; O’Reilly, J., () |

[7] | Kokotovic, P.V.; O’Malley, R.E.; Sannuti, P., Singular perturbations and order reduction in control theory—an overview, Automatica, 12, 123, (1976) · Zbl 0323.93020 |

[8] | Moylan, P.J.; Anderson, B.D.O., Nonlinear regulator theory and an inverse optimal control problem, IEEE trans. aut. control, AC-18, 460, (1973) · Zbl 0283.49007 |

[9] | Rekasius, Z.V., Suboptimal design of intentionally nonlinear controllers, IEEE trans aut. control, AC-9, 380, (1964) |

[10] | Tsitsiklis, J.N.; Athans, M., Guaranteed robustness properties of multivariable nonlinear stochastic optimal regulators, IEEE trans aut. control, AC-29, 690, (1984) · Zbl 0544.93079 |

[11] | Wilde, R.R.; Kokotovic, P.V., A dichotomy in linear control theory, IEEE trans aut. control, AC-17, 382, (1972) · Zbl 0261.93014 |

[12] | Wilde, R.R.; Kokotovic, P.V., Optimal open- and closed-loop control of singularly perturbed linear systems, IEEE trans aut. control, AC-18, 616, (1973) · Zbl 0273.49053 |

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