Abstract: A control system for controlling an operation of a machine subject to constraints including equality and inequality constraints on state and control variables of the system iteratively solves an optimal control structured optimization problem (OCP), such that each iteration outputs primal variables and dual variables with respect to the equality constraints and dual variables and slack variables with respect to the inequality constraints. For a current iteration, the system classifies each of the inequality constraints as an active, an inactive or an undecided constraint based on a ratio of a slack variable to a dual variable of the corresponding inequality constraint determined by a previous iteration, finds an approximate solution to the set of relaxed optimality conditions subject to the equality constraints and the active and undecided inequality constraints, and update the primal, dual, and slack variables for each of the equality and inequality constraint.

Abstract: A control system for controlling an operation of a machine subject to constraints including equality and inequality constraints on state and control variables of the system iteratively solves an optimal control structured optimization problem (OCP), such that each iteration outputs primal variables and dual variables with respect to the equality constraints and dual variables and slack variables with respect to the inequality constraints. For a current iteration, the system classifies each of the inequality constraints as an active, an inactive or an undecided constraint based on a ratio of a slack variable to a dual variable of the corresponding inequality constraint determined by a previous iteration, finds an approximate solution to the set of relaxed optimality conditions subject to the equality constraints and the active and undecided inequality constraints, and update the primal, dual, and slack variables for each of the equality and inequality constraint.

Abstract: Thin-film solid state batteries architectures and methods of manufacture are provided. Architectures include solid-state batteries with one or more cathodes, electrolytes, anodes deposited onto a substrate. Architectures may be used for solid state lithium batteries. The various fabrication techniques may be used to create a solid state battery is millimeters thick or smaller. These thin-film batteries may be small, light, and have a high energy density.

Abstract: This disclosure describes systems and methods for increasing the usable surface area of electrical contacts within a device, such as a thin film solid state device, through the implementation of electrically conductive interconnects. Embodiments described herein include the use of a plurality of electrically conductive interconnects that penetrate through a top contact layer, through one or more multiple layers, and into a bottom contact layer. The plurality of conductive interconnects may form horizontal and vertical cross-sectional patterns. The use of lasers to form the plurality of electrically conductive interconnects from reflowed layer material further aids in the manufacturing process of a device.

Abstract: The dynamic range of an electrophotographic device may be shifted by calibrating a laser power of a laser source to operate within a first range of power levels during a laser power adjustment operation. At least one laser control parameter is modified after calibrating the laser power so that the laser source is operable within a second range of power levels different from the first range of power levels and a beam emitted by the laser source is controlled within the second range of power levels when the beam is directed towards an image area of a photoconductive surface.