## Abstract

Of interest are the limiting forms of the optimum stochastic regulator which minimize the steady-state expectation, E_{s} (x’Qx-f-u’Ru), for the linear process, x = A x + B u + G v, given noisy observations y = H x + w (with v and w being independent white noise processes) as the control weighting matrix, R and /or the spectral density matrix W of the observation noise wtend to zero. It is found that as R vanishes, the optimum regulator can be synthesized by a system using at most n-k integrators, where n is the order of the system and k is the rank of B. Similarly, when W vanishes, the regulator can sometimes be realized with at most n-r integrators, where r is the rank of H. The structure of the regulator is given for each of these cases.

Original language | English (US) |
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Pages (from-to) | 134-141 |

Number of pages | 8 |

Journal | Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME |

Volume | 93 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1971 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Information Systems
- Instrumentation
- Mechanical Engineering
- Computer Science Applications