Mikil Foss

A direct Lyapunov approach for a class of underactuated mechanical systems

A Lyapunov direct method is proposed for a class of underactuated, mechanical systems. The direct method is derived in general for systems having n degrees of freedom of which only m < n are actuated. The applications consist of a class of systems where the elements of the mass/inertia matrix and the gravitational forces/torques are either constants or functions of a single generalized position variable and where n is two and m is one. The time derivative of the candidate Lyapunov function produces a relation that is solved via a matching method. Some of the matching equations consist of linear differential and partial differential equations. It is shown for this class of systems, that the solutions of these linear differential and partial differential equations necessary for assuring asymptotic stability can be evaluated numerically as part of the feedback process. Examples are presented involving an inverted pendulum cart and an inertia wheel pendulum

Global Morrey regularity results for asymptotically convex variational problems

Abstract We prove some global, up to the boundary of a domain Ω ⊂ ℝ n , continuity and Morrey regularity results for almost minimizers of functionals of the form . The main assumptions are that g is asymptotically convex and that it has superlinear polynomial growth with respect its third argument. The integrand is only required to be locally bounded with respect to its third argument. Some discontinuous behavior with respect to its other arguments is also allowed. We also provide an application of our results to a class of variational problems with obstacles.

A Direct Lyapunov Approach for Stabilization of Underactuated Mechanical Systems

Control of underactuated systems is treated from a Lyapunov direct method approach. The method results in a set of three matching conditions, the solution of which is easily accomplished. The method developed is capable of treating more complicated systems than that reported in an earlier publication. The suitability of the Lyapunov candidate function is demonstrated through mathematical proofs. An application of the method to the ball and beam is presented.

Improvements in direct Lyapunov stabilization of underactuated, mechanical systems

A Lyapunov direct method is presented for the stabilization of underactuated, mechanical systems. The Lyapunov approach provides the tools for control law design. This work represents a continued development of previously published techniques. The major contribution of the presentation is that a method is demonstrated for assuring the positive definiteness of certain matrices associated with the formulation. A stabilization example using the rotary inverted pendulum is included.