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A new approach to the solution of optimal control problems for mechanical systems is proposed. It is based on a direct discretization of the Lagrange-d'Alembert principle for the system (as opposed to using, for example, collocation or multiple shooting to enforce the equations of motion as constraints). The resulting forced discrete Euler-Lagrange… (More)

The optimal control of a mechanical system is of crucial importance in many application areas. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion sequences in robotics and biomechanics. In most cases, some sort of discretization of the original,… (More)

— Switching time optimization (STO) arises in systems that have a finite set of control modes, where a particular mode can be chosen to govern the system evolution at any given time. The STO problem has been extensively studied for switched systems that consists of time continuous ordinary differential equations with switching laws. However, it is rare that… (More)

— The problem of showing that Lagrangian Coherent Structures (LCS) are useful in determining near optimal trajectories for autonomous underwater vehicles (AUVs) known as gliders is investigated. This paper extends our preliminary results in couple ways. First, the ocean current flows are modeled by 3D B-spline functions in which the input variables are… (More)

Variational integrators are symplectic-momentum preserving integrators that are based on a discrete variational formulation of the underlying system. So far, variational integrators have been mainly developed and used for a wide variety of mechanical systems. In this work, we develop a variational integrator for the simulation of electric circuits. An… (More)

— Many different numerical methods have been developed to compute trajectories of optimal control problems on the one hand and to approximate Pareto sets of multiobjective optimization problems on the other hand. However, so far only few approaches exist for the numerical treatment of the combination of both problems leading to multiobjective optimal… (More)

In this contribution, we introduce an optimal control problem for hybrid Lagrangian control systems. The dynamics of these systems and their discrete approximations are derived via a hybrid variational principle which is based on the Lagrange-d'Alembert principle for continuous Lagrangian control systems. Optimal control problems are stated in a continuous… (More)