Title :
A controllability theory for nonlinear systems
Author :
Gershwin, Stanley B. ; Jacobson, David H.
Author_Institution :
Bell Telephone Laboratories, Holmdel, NJ, USA
fDate :
2/1/1971 12:00:00 AM
Abstract :
A Lyapunov-like approach to the controllability of nonlinear dynamic systems is presented. A theory is developed which yields sufficient conditions for complete controllability for some classes of nonlinear systems; feedback controllers which drive the systems to desired terminal conditions, at a specified final time, are also obtained. Well-known controllability conditions for linear dynamic systems are derived using this general controllability theory. Elliptical regions are found which contain (bound) the trajectories of a class of systems controlled according to these methods. These regions are used in synthesizing controllers for nonlinear systems and for a class of state-variable inequality constrained problems. An uncontrollability theorem, based also upon Lyapunov-like notions, is presented; this yields sufficiency conditions for uncontrollability for some types of nonlinear systems. Relationships of the theories to other nonlinear controllability approaches are indicated.
Keywords :
Controllability; Lyapunov methods; Nonlinear systems, continuous-time; Terminal control; Control system synthesis; Control systems; Controllability; Jacobian matrices; Nonlinear control systems; Nonlinear dynamical systems; Nonlinear systems; Physics; Student members; Sufficient conditions;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.1971.1099624