The author considers a mechanical system with generalized coordinates = (q,u), with positive definite kinetic energy as usual. However, when the coordinates are considered as controls, under convenient assumptions, the q-subsystem is governed by the same Euler-Lagrange equations, as developed by Bressan and Rampazzo in previous papers. Moreover, due to the presence of the derivative du/dt of the control in the ODEs for q (and the corresponding momentum p), one does not have an ordinary control system. According to the author, “in a optimal control problem one has to expect an impulsive behaviour of its trajectories. . . in this paper we investigate the existence of Lagrangian coordinates for which the solutions (q, p)(·) of the corresponding control system are independent of the way of bridging the discontinuities of the control u(.)”.
Some remarks on the use of constraints as controls in rational mechanics.
RAMPAZZO, FRANCO
1990
Abstract
The author considers a mechanical system with generalized coordinates = (q,u), with positive definite kinetic energy as usual. However, when the coordinates are considered as controls, under convenient assumptions, the q-subsystem is governed by the same Euler-Lagrange equations, as developed by Bressan and Rampazzo in previous papers. Moreover, due to the presence of the derivative du/dt of the control in the ODEs for q (and the corresponding momentum p), one does not have an ordinary control system. According to the author, “in a optimal control problem one has to expect an impulsive behaviour of its trajectories. . . in this paper we investigate the existence of Lagrangian coordinates for which the solutions (q, p)(·) of the corresponding control system are independent of the way of bridging the discontinuities of the control u(.)”.
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