QUADRATIC OPTIMAL CONTROL OF DISTRIBUTED PARAMETER SYSTEMS WITH STOCHASTIC INPUTS,

Abstract

The report concerns the design of a quadratic optimal regulator for systems described by time-invariant linear partial differential equations with Gaussian white noise disturbance of the state and measurement. Point control at the boundary or interior points is treated as a special case of distributed control. Such a system is shown to separate into independent design of the best feedback controller and state estimator. Sufficient conditions are established in terms of solutions to a Hamilton-Jacobi equation which is solved by eigenfunction expansion of Hamilton-Jacobi canonical systems associated with controller and estimator Ricatti equations. A finite series representation of the state and co-state in terms of the low frequency eigenfunctions of the canonical systems is shown to provide an approximation to the optimal regulator. Examples are presented for controlling scalar diffusion processes in cases of distributed and point control and observation. (Author)

Document Details

Document Type
Technical Report
Publication Date
May 01, 1970
Accession Number
AD0709710

Entities

People

  • Merriman Staton Sholar

Organizations

  • University of California, Los Angeles

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Differential Equations
  • Diffusion
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Estimators
  • Feedback
  • Frequency
  • Mathematical Analysis
  • Mathematics
  • Measurement
  • Noise
  • Partial Differential Equations
  • Regulators
  • White Noise

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Calculus or Mathematical Analysis