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The optimal control of a mechanical system is of crucial importance in many realms. 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, infinite-dimensional(More)
SUMMARY The equations of motion of a controlled mechanical system subject to holonomic constraints may be formulated in terms of the states and controls by applying a constrained version of the Lagrange-d'Alembert principle. This paper derives a structure-preserving scheme for the optimal control of such systems using, as one of the key ingredients, a(More)
To Henri Poincaré on the 150th anniversary of his birth. Abstract. The title of this paper is inspired by the work of Poincaré [1890, 1892], who introduced many key dynamical systems methods during his research on celestial mechanics and especially the three body problem. Since then, many researchers have contributed to his legacy by developing and applying(More)
— This paper introduces a hierarchical, decentralized , and parallelizable method for dealing with optimization problems with many agents. It is theoretically based on a hierarchical optimization theorem that establishes the equivalence of two forms of the problem, and this idea is implemented using DMOC (Discrete Mechanics and Optimal Control). The result(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)
— 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)