Semidefinite programming approaches to multi-contact feedback control
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.
Russell L. Tedrake.
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We consider the feedback design for stabilizing a rigid body system by making and breaking multiple contacts with the environment without prespecifying the timing or the number of occurrence of the contacts. We examine several different models of such systems and the roles of semidefinite programming and sums-of-squares programming in designing and verifying stabilizing controllers. First the system is modelled as a discrete-time piecewise affine system and we use semidefinite programming to design stabilizing controllers according to Lyapunov theory. Second the system is modelled as a discrete-time piecewise polynomial system and we use sums-of-squares programming to design feedback controllers. Third the system is modelled as a discrete-time polynomial system with linear complimentarity constraints for contacts and we use sums-of-squares to verify the controllers according to Lyapunov theory.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2019Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages 71-77).
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology
Electrical Engineering and Computer Science.