Constructive tool for orbital stabilization of underactuated nonlinear systems: virtual constraints approach

• Published in: IEEE transactions on automatic control Vol. 50; no. 8; pp. 1164 - 1176
• Main Authors: Shiriaev, A., Perram, J.W., Canudas-de-Wit, C.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.08.2005; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Automatic; Computer science; control theory; systems; Constructive control procedures; Control design; Control system analysis; Control system synthesis; Control theory. Systems; Engineering Sciences; Exact sciences and technology; Feedback; Legged locomotion; Limit-cycles; Mechanical systems; nonlinear and time-varying controllers; Nonlinear dynamical systems; Nonlinear systems; Open loop systems; orbital stabilization; Stability; Vehicle dynamics; orbital stabilization; Constructive mathematics; Orbit; Stabilization; Control program; Non linear control; Feedback regulation; Dynamical system; Controller; Periodic solution; Exponential stability; Constructive control procedures; Periodic control; Time dependence; Time varying system; Underactuation; Mechanical system; Procedure; nonlinear and time-varying controllers; Actuator
• ISSN: 0018-9286; 1558-2523; 1558-2523
• DOI: 10.1109/TAC.2005.852568

We present a constructive tool for generation and orbital stabilization of periodic solutions for underactuated nonlinear systems. Our method can be applied to any mechanical system with a number of independent actuators smaller than the number of degrees of freedom by one. The synthesized feedback control law is nonlinear and time-dependent. It is derived from a feedback structure that explicitly uses the general or full integral of the systems zero dynamics. The control law generates a periodic solution and makes it exponentially orbitally stable.