A Model Problem.- Semiconcave Functions.- Generalized Gradients and Semiconcavity.- Singularities of Semiconcave Functions.- Hamilton-Jacobi Equations.- Calculus of Variations.- Optimal Control Problems.- Control Problems with Exit Time.

/pdf/semiconcave-functions-hamilton-jacobi-equations-and-optimal-1vuumifya9.pdf

Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control

The design of nonrobust and robust time-optimal controllers for linear systems in the frequency domain is presented. The bang-bang profile is represented as the superposition of time-delayed step inputs or the output of a time-delay filter subject to a step input. A parameter optimization problem is formulated to minimize the final time of the maneuver with the constraint that the time-delay filter cancels all of the poles of the system. The issue of robustness to errors in the model is addressed by placing multiple zeros of the time-delay filter at the estimated locations of the poles of the system. The design technique is illustrated on representative models of large space structures, for rest-to-rest, time-optimal, and robust time-optimal maneuvers. Spin-up maneuvers are shown to be special cases of the general formulation. IME-OPTIMAL control of flexible spacecraft is a topic of current interest.1 Many computational approaches and analyses have been presented in the recent literature to deal with the effects of flexibility. Most of these works deal with planar (singleaxis) rest-to-rest maneuvers under two categories: near-minimumtime control and exact-minimum-time control. The first category of methods is based on smooth approximations to minimum-time control for an equivalent rigid body. This class of methods has been shown to be well suited when applied moments or torques are produced by either throttlable thrusters or reaction wheels.2'3 Higher modes of the system are not excited due to the smoothness of the control profile. The second category of methods deals with on-off thrusters directly. Rajan4 formulates the problem including

/pdf/robust-time-optimal-control-frequency-domain-approach-4szlalemmo.pdf

Robust time-optimal control - Frequency domain approach

Numerical methods for mixed-integer optimal control problems

Minimum principles in motor control

Compressed sensing is a relatively recent area of research that refers to the recovery of high-dimensional but low-complexity objects from a limited number of measurements. The topic has applications to signal/image processing and computer algorithms, and it draws from a variety of mathematical techniques, such as graph theory, probability theory, linear algebra, and optimization. This book aims to provide an in-depth initiation to the field of compressed sensing. Specific topics include material on graph theory and the design of binary-measurement matrices, matrix recovery and completion, and optimization algorithms. The core audience for this book consists of engineers, computer scientists, and statisticians who are interested in compressed sensing. Professionals working in image processing, speech processing, or seismic signal processing should also find the book of interest.

D. Bushaw

Papers

Functional analysis and time optimal control