NONLINEAR CONTROLLABILITY AND INVOLUTORY ACTUATOR ORBITS,
Abstract
The general multi-dimensional linear optimal control problem with quadratic cost functional and nonquadratic weighting on the final states is completely solved in closed form by utilizing Caratheodory's construct on of C sup 2 solutions to the Hamilton-Jacobi equation associated with the control problem. The same method is also applied to a broad spectrum of nonlinear control processes with nonquadratic cost functionals. Necessary and sufficient conditions for complete controllability of a general class of nonlinear control systems are derived. The derivation of these conditions makes use of properties of certain Pfaffian equations associated with the control system and properties of the Penrose pseudo-inverse of matricies. The idea of 'involutory actuator orbits' is introduced. A class of nonlinear control processes with involutory actuator orbits is shown to have an equivalent class of linear systems with non quadratic cost functionals. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1970
- Accession Number
- AD0712716
Entities
People
- Alexander Chen-che Liang
Organizations
- University of Southern California