![]() From these, we obtain the new definition of the instantaneous velocity which is pseudo-translation symmetry in both time and position and formulate the mechanics which are pseudo-linear and pseudo-translation invariant. Cauchy, Mthode gnrale pour la rsolution des systmes d'quations simultanes. Besides, we demand that the displacement should be invariant under the pseudo-translation. Cadzow, Discrete-Time Systems: An Introduction With Interdisciplinary Applications. Cadzow, J.A.: Discrete calculus of variations. Using this we consider a special type of the non-uniform discrete times with the pseudo-translation symmetry. discrete variational calculus in time, which sidesteps the endpoint constraint problem. Discrete Green's functions and strong stability properties of the finite. Journal of Applied Mathematics and Physics,ĪBSTRACT: In this paper, we will consider the simplest pseudo-addition where pseudo-multiplication and pseudo-division are the same as the ordinary ones and distributivity hold. Optimal control problems for underactuatedmechanical systems can be seen as a higher-order variational problemsubject to higher-order constraints (that is, when the Lagrangianfunction and the constraints depend on higher-order derivatives suchas the acceleration, jerk or jounces). ![]() Pseudo-Multiplication, Pseudo-Addition, Pseudo-Translation Symmetry, Pseudo-Linear Pseudo-Linear Mechanics with Pseudo-Translation SymmetryĪUTHORS: Wonsang Chung, Yeounju Kim, Seohyeon Kim, Jeongmin Kwon We show, using Gteaux differentials, that the so-called Euler equation and a transversality condition are necessary conditions for optimality. ![]() We are concerned with deterministic and stochastic nonstationary discrete-time optimal control problems in infinite horizon. International Journal of Control, 11, 393-407. Mathematics Department, CINVESTAV-IPN, A.
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