in this paper mathematical structure of time-dependent lagrangian systems and their symmetries are extended and the explicit relation between constants of motion and infinitesimal symmetries of time-dependent lagrangian systems are considered. starting point is time-independent lagrangian systems ,then we extend mathematical concepts of these systems such as equivalent lagrangian systems to the...

Controlled Lagrangian and matching techniques are developed for the stabilization of relative equilibria and equilibria of discrete mechanical systems with symmetry as well as broken symmetry. Interesting new phenomena arise in the controlled Lagrangian approach in the discrete context that are not present in the continuous theory. In particular, to make the discrete theory effective, one can m...

This paper obtains feedback stabilization of an inverted pendulum on a rotor arm by the “method of controlled Lagrangians”. This approach involves modifying the Lagrangian for the uncontrolled system so that the Euler-Lagrange equations derived from the modified or “controlled” Lagrangian describe the closed-loop system. For the closed-loop equations to be consistent with available control inpu...

We extend the theory of controlled Lagrangian systems to include systems with symmetry and the Lagrangian reduction theory. This extension is crucial to study examples such as spacecraft control, underwater vehicle control, etc.

In this paper, we apply Dirac structures and the associated theory of implicit Lagrangian systems to electric networks. We show how a Dirac structure on the flux linkage phase space can be induced from a KCL (Kirchhoff Current Law) constraint distribution on a configuration charge space in analogy with mechanics. In this context, a notion of implicit port–controlled Lagrangian systems is develo...

This paper extends the λ-method, which was developed in (Auckly et al., 2000; Auckly and Kapitanski, 2003) to solve effectively PDE’s involved in the method of controlled Lagrangian systems, by taking into account a gyroscopic term. The gyroscopic force provides more free parameters when one designs stabilizing controllers in the method of controlled Lagrangian systems. We illustrate the extend...

This paper approaches optimal control problems for discrete-time controlled Markov processes by representing the value of the problem in a dual Lagrangian form; the value is expressed as an infimum over a family of Lagrangian martingales of an expectation of a pathwise supremum of the objective adjusted by the Lagrangian martingale term. This representation opens up the possibility of numerical...