A Technique of Quasi-Optimum Control

[+] Author and Article Information
B. Friedland

Aerospace Research Center, General Precision, Inc., Little Falls, N. J.

J. Basic Eng 88(2), 437-443 (Jun 01, 1966) (7 pages) doi:10.1115/1.3645876 History: Received July 07, 1965; Online November 03, 2011


To find the optimum control law u = u(x) for the process ẋ = f(x, u), the Hamiltonian H = p′ f is formed. The optimum control law can be expressed as u = u* = σ(p, x), where u* maximizes H. The transformation from the state x to the “costate” p entails the analytic solution of the nonlinear system: ẋ = f(x, σ(p, x)); ṗ = −fxp with boundary conditions at two points. Since such a solution generally can not be found, we seek a quasi-optimum control law of the form u = σ(P + Mξ, x), where x = X + ξ with ‖ξ‖ small, and X, P are the solutions of a simplified problem, obtained by setting ξ = 0 in the above two-point boundary-value problem. We assume that P(X) is known. It is shown that the matrix M satisfies a Riccati equation, −Ṁ = MHXP + HPX M + MHPP M + HXX , and can be computed by solving a linear system of equations. A simple example illustrates the application of the technique to a problem with a bounded control variable.

Copyright © 1966 by ASME
Your Session has timed out. Please sign back in to continue.





Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In