Singular Perturbation of Nonlinear Regulators and Systems with Oscillatory Modes.
Abstract
This report applies singular perturbation techniques to nonlinear optimal control problems and systems with high frequency oscillatory behavior. For a class of nonlinear regulator problems the Hamilton-Jacobi equation is solved as a power series expansion whose coefficients are solved from equations involving the slow variables only. Consequently we obtain near-optimal feedback controls. Through the construction of a composite Lyapunov function, these controls can stabilize large disturbances of the fast variables. A fixed endpoint nonlinear control problem is decomposed into three lower order problems, namely, the nonlinear reduced order problem and the linear quadratic left and right boundary layer problems. For systems with high frequency oscillatory behavior, the original system is decomposed into a slowly varying system and a fast oscillatory system. This procedure provides physical interpretations for the high frequency oscillations occurring in a mass-spring-damper system and an interconnected power system.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1977
- Accession Number
- ADA057644
Entities
People
- Joe H. Chow
Organizations
- University of Illinois Urbana–Champaign