This work points out that the costates are actually discontinuous functions of time for optimal control problems with Coulomb friction. In particular these discontinuities occur at the time points where the velocity of the system changes sign. To our knowledge, this has not been noted before. This phenomenon is demonstrated on a minimum-time problem with Coulomb friction and the consistency of discontinuous costates and switching functions with respect to the input switches is shown.
In this paper an optimization-based method of drift prevention is presented for learning control of underdetermined linear and weakly nonlinear time-varying dynamic systems. By defining a fictitious cost function and the associated model-based sub-optimality conditions, a new set of equations results, whose solution is unique, thus preventing large drifts from the initial input. Moreover, in the limiting case where the modeling error approaches zero, the input that the proposed method converges to is the unique feasible (zero error) input that minimizes the fictitious cost function, in the linear case, and locally minimizes it in the (weakly) nonlinear case. Otherwise, under mild restrictions on the modeling error, the method converges to a feasible sub-optimal input.
In this paper we present a very simple modification of the iterative learning control algorithm of Arimoto et al [1] to the case where the inputs are bounded. The Jacobian condition presented in Avrachenkov [2] is specified instead of the usual condition specified by Arimoto et al [1]. (See also Moore [11].) In particular, the former is a condition for monotonicity in the distance to the solution instead of monotonicity in the output error. This observation allows for a simple extension of the methods of Arimoto et al [1] to the case of bounded inputs since the process of moving an input back to a bound if it exceeds it does not affect the contraction mapping property; in fact, the distance to the solution, if anything, can only decrease even further. The usual Jacobian error condition, on the other hand, is not sufficient to guarantee the chopping rule will converge to the solution, as proved herein. To the best of our knowledge, these facts have not been previously pointed out in the iterative learning control literature.
As computational needs for structural finite element analysis increase, a robust implicit structural dynamics code is needed which can handle millions of degrees of freedom in the model and produce results with quick turn around time. A parallel code is needed to avoid limitations of serial platforms. Salinas is an implicit structural dynamics code specifically designed for massively parallel platforms. It computes the structural response of very large complex structures and provides solutions faster than any existing serial machine. This paper gives a current status of Salinas and uses demonstration problems to show Salinas' performance.
In this work, a method is proposed for modifying the standard master-slave stiffness matrix so that linear consistency across the interface of the master and slave meshes is achieved. The existence of such a local stiffness modification is implied by the work of [Dohrmann, et al, to appear]. The present work aims at achieving the same linear consistency through a different method of stiffness modification that is based on simply ensuring zero residual force at the interior interface nodes for all non-zero-stress linear displacement fields and zero residual force at all interface nodes for all rigid-body linear displacement fields. These zero residuals ensure that the local stiffness modification results in an interface that passes the patch test. Numerical examples herein demonstrate that the maximum stress error at the interface goes to zero with the proposed method while it does not for the standard master-slave method.