## Control of Distributed Parameter and Stochastic SystemsIn the mathematical treatment of many problems which arise in physics, economics, engineering, management, etc., the researcher frequently faces two major difficulties: infinite dimensionality and randomness of the evolution process. Infinite dimensionality occurs when the evolution in time of a process is accompanied by a space-like dependence; for example, spatial distribution of the temperature for a heat-conductor, spatial dependence of the time-varying displacement of a membrane subject to external forces, etc. Randomness is intrinsic to the mathematical formulation of many phenomena, such as fluctuation in the stock market, or noise in communication networks. Control theory of distributed parameter systems and stochastic systems focuses on physical phenomena which are governed by partial differential equations, delay-differential equations, integral differential equations, etc., and stochastic differential equations of various types. This has been a fertile field of research with over 40 years of history, which continues to be very active under the thrust of new emerging applications. Among the subjects covered are: - Control of distributed parameter systems;
- Stochastic control;
- Applications in finance/insurance/manufacturing;
- Adapted control;
- Numerical approximation
It is essential reading for applied mathematicians, control theorists, economic/financial analysts and engineers. |

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### Contents

III | 3 |

IV | 13 |

V | 21 |

VI | 31 |

VII | 39 |

VIII | 47 |

IX | 55 |

X | 63 |

XXIII | 173 |

XXIV | 181 |

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XXX | 231 |

XI | 71 |

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XIII | 85 |

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XV | 103 |

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XX | 143 |

XXI | 153 |

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XXXI | 239 |

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XXXVI | 283 |

XXXVII | 291 |

XXXVIII | 299 |

XXXIX | 307 |

XL | 315 |

XLI | 323 |

### Common terms and phrases

adapted solution adaptive control adjoint apply approximation assume assumption asymptotic Banach space Bellman equation boundary conditions boundary control bounded Brownian motion BSDE Chen coefficient compact consider constant constraints continuous convergence convex corresponding cost functional damping defined Definition denote Department of Mathematics deterministic Dirichlet eigenvalues elliptic ergodic control problem estimate exact controllability exists feedback control finite dimensional forward-backward given Hamilton-Jacobi-Bellman equation Hilbert space inequality inner product inverse problem Lasiecka Lemma linear quadratic Lipschitz Markov chain Math matrix maximum principle membrane shell equation nonlinear norm obtain optimal control optimal control problem paper parabolic partial differential equations Peng perturbations portfolio proof properties Proposition random resp Riccati equation satisfies semigroup semilinear SIAM solvable solve stabilizability stochastic control stochastic differential equations Theorem theory Triggiani unique solution University USA email value function variable vector viscosity solution Yong Zhou