NONLINEAR SYSTEM ANALYSIS AND SYNTHESIS. PART II. STUDY OF THE LUR'E PROBLEM AND OF STOCHASTIC OPTIMAL CONTROL,

Abstract

Research was mainly concerned with: (a) The construction of Lyapunov functions by machine methods, especially as regards the so-called problem of Lur'e. (b) The formulation of stochastic optimization problems. Research topics presented in this report are: General Discussion; On the absolute stability of sampled-data control systems; On the absolute stability of a system of finite difference equations; On the absolute stability of a nonlinear sampled-data system; Irreducible realizations and the degree of a matrix of rational functions; Resolution of the Problem of Lur'e; General Discussion; Near Optimal control in the presence of small stochastic perturbations; On the differential equations satisfied by conditional probability densities of Markov processes, with applications; On the stochastic maximum principle; fixed-time of control; A 'time-domain' successive approximation method for some linear optimal stochastic systems. (Author)

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1964
Accession Number
AD0610197

Entities

People

  • R. E. Kalman

Organizations

  • Glenn L. Martin Company

Tags

DTIC Thesaurus Topics

  • Control Systems
  • Difference Equations
  • Differential Equations
  • Equations
  • Lyapunov Functions
  • Markov Processes
  • Nonlinear Systems
  • Partial Differential Equations
  • Probability
  • Rational Functions
  • Time Domain

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Control Systems Engineering.