First and second order optimality conditions for optimal control problems of state constrained integral equations

This paper deals with optimal control problems of integral equations, with initial-final and running state constraints. The order of a running state constraint is defined in the setting of integral dynamics, and we work here with constraints of arbitrary high orders. First and second-order necessary conditions of optimality are obtained, as well as second-order sufficient conditions

Inverse dynamics of serial and parallel underactuated multibody systems using a DAE optimal control approach

peer reviewedThe inverse dynamics analysis of underactuated multibody systems aims at determining the control inputs in order to track a prescribed trajectory. This paper studies the inverse dynamics of non-minimum phase underactuated multibody systems with serial and parallel planar topology, e.g. for end-effector control of flexible manipulators or manipulators with passive joints. Unlike for minimum phase systems, the inverse dynamics of non-minimum phase systems cannot be solved by adding trajectory constraints (servoconstraints) to the equations of motion and applying a forward time integration. Indeed, the inverse dynamics of a non-minimum phase system is known to be non-causal, which means that the control forces and torques should start before the beginning of the trajectory (preactuation phase) and continue after the end-point is reached (post-actuation phase). The existing stable inversion method roposed for general nonlinear non-minimum phase systems requires to derive explicitly the equations of the internal dynamics and to solve a boundary value problem. This paper proposes an alternative solution strategy which is based on an optimal control approach using a direct transcription method. The method is illustrated for the inverse dynamics of an underactuated serial manipulator with rigid links and four degrees-of-freedom and an underactuated parallel machine. An important advantage of the proposed approach is that it can be applied directly to the standard equations of motion of multibody systems either in ODE or in DAE form. Therefore, it is easier to implement this method in a general purpose simulation software

Thermal-tempering analysis of bulk metallic glass plates using an instant-freezing model

The viscoelastic nature of bulk metallic glasses (BMGs), their low thermal conductivity, and the fast cooling used in their processing subject them to thermal tempering. This process leads to a residual stress state in which compression on the surface is balanced by tension in the interior. For the first time, we have calculated such stresses in metallic glasses by adapting an analytical instant-freezing model previously developed for silicate glasses. This model has been demonstrated to be reasonably accurate in predicting the final residual stresses, although, due to its very nature, it neglects transient effects. For an infinite plate geometry and employing processing parameters often used for metallic glasses, we predict that significant residual stresses can be generated in these materials during thermal tempering. Preliminary measurements conducted using the layer-removal method yield compressive residual stress values close to model predictions