Abstract
This paper exploits the equivalence between constrained dynamics problems and a class of tracking control problems. An alternative derivation of the modern formulation of Parczewski and Blajer [J. Appl. Math. 56 (1989) 676–684] is presented, including some new analysis on the “almost singular” case, followed by a critique of the classical Lagrangian formulation. In addition, a new formulation which allows the constraints to be satisfied approximately is presented. A general closed-loop control law which depends on a user-specified threshold of constraint errors, ϵ, is proposed, transforming the default DAE problem into a stiff ODE initial-value problem which can be routinely solved on computers. It is shown that certain explosively unstable open-loop systems may be stabilized by the use of closed-loop control using a small but finite ϵ. An example is worked out using both the open-loop and the closed-loop control formulations.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
