By Magnus Egerstedt

ISBN-10: 0691132968

ISBN-13: 9780691132969

ISBN-10: 1400833876

ISBN-13: 9781400833870

Splines, either interpolatory and smoothing, have an extended and wealthy heritage that has mostly been software pushed. This publication unifies those buildings in a entire and obtainable means, drawing from the most recent tools and functions to teach how they come up evidently within the idea of linear keep an eye on structures. Magnus Egerstedt and Clyde Martin are top innovators within the use of keep an eye on theoretic splines to compile many assorted purposes inside of a standard framework. during this booklet, they start with a sequence of difficulties starting from direction making plans to stats to approximation. utilizing the instruments of optimization over vector areas, Egerstedt and Martin display how all of those difficulties are a part of a similar basic mathematical framework, and the way they're all, to a definite measure, a end result of the optimization challenge of discovering the shortest distance from some extent to an affine subspace in a Hilbert house. They hide periodic splines, monotone splines, and splines with inequality constraints, and clarify how any finite variety of linear constraints should be additional. This booklet finds how the various average connections among keep an eye on thought, numerical research, and facts can be utilized to generate robust mathematical and analytical tools.This e-book is a wonderful source for college kids and execs up to the mark thought, robotics, engineering, special effects, econometrics, and any sector that calls for the development of curves in response to units of uncooked info.

Show description

Read or Download Control Theoretic Splines: Optimal Control, Statistics, and Path Planning (Princeton Series in Applied Mathematics) PDF

Similar robotics & automation books

Innovations in Robot Mobility and Control

There exists rather an enormous literature on cellular robots, masking primary ideas on movement keep an eye on and path-planning in indoor environments utilizing ultrasonic/laser transducers. notwithstanding, there's a shortage of books/collective records on imaginative and prescient established navigation of cellular robots and multi-agent platforms.

The ROV Manual: A User Guide for Observation Class Remotely Operated Vehicles

Many underwater operations that have been as soon as performed via divers can now be performed extra successfully and with much less possibility with Remotely Operated autos (ROVs). this is often the 1st ROV 'how-to' handbook for these concerned with smaller statement category ROVs used for surveying, inspection, remark and examine reasons.

Control in robotics and automation : sensor-based integration

Microcomputer know-how and micromechanical layout have contributed to contemporary swift advances in Robotics. specific advances were made in sensor expertise that let robot structures to assemble information and react "intelligently" in versatile production platforms. The research and recording of the knowledge are important to controlling the robotic.

Vehicle Dynamics and Control

Automobile Dynamics and keep watch over offers a entire assurance of car keep an eye on structures and the dynamic types utilized in the advance of those keep an eye on structures. The keep an eye on process functions lined within the ebook contain cruise regulate, adaptive cruise regulate, ABS, automatic lane conserving, computerized road platforms, yaw balance regulate, engine keep watch over, passive, energetic and semi-active suspensions, tire-road friction coefficient estimation, rollover prevention, and hybrid electrical cars.

Extra resources for Control Theoretic Splines: Optimal Control, Statistics, and Path Planning (Princeton Series in Applied Mathematics)

Sample text

N )T . We first minimize the function H over u, assuming that λ and γ are fixed. This minimum is achieved at the point where the Gateaux derivative of H, with respect to u, is zero. This is found by calculating 1 lim (H(u + v, λ, γ) − H(u, γ, λ)) →0 = T 0 u(t) − N λi i=1 ti (t) + N γi i=1 ti (t) v(t)dt. 18) i=1 where, as before, (t)T = ( T t1 (t), t2 (t), . . , tN (t)) . We now eliminate u from H to obtain H(u , λ, γ) = 1 2 T 0 N ((λT − γ T ) (t))2 dt + λi (ai − Lti (u )) − i=1 N γi (Lti (u ) − bi ) i=1 N N 1 λi Lti (u ) + γi Lti (u ) = (λ − γ)T G(λ − γ) + λT a − γ T b − 2 i=1 i=1 N N 1 T T T = (λ − γ) G(λ − γ) + λ a − γ b − λi λj Lti ( 2 i=1 j=1 + N N λj γi Lti ( i=1 j=1 tj ) + N N λi γj Lti ( tj ) − i=1 j=1 N N tj ) γj γi Lti ( tj ) i=1 j=1 1 = (λ − γ)T G(λ − γ) + λT a − γ T b − λT Gλ + λT Gγ + λT Gγ − γ T Gγ 2 1 = (λ − γ)T G(λ − γ) + λT a − γ T b − (λ − γ)T G(λ − γ) 2 1 = − (λ − γ)T G(λ − γ) + λT a − γ T b.

We will construct u so that the resulting output curve is piecewise smooth and generalizes the classical concept of polynomial splines. For this, we will consider the data set DD. The interpolating conditions can be expressed as αi = y(ti ) = Lti (u), i = 1, . . , N. 13) There are, of course, infinitely many control laws that satisfy these constraints. The problem is to identify a scheme that will select a unique control law in some meaningful way. As already mentioned, linear quadratic optimal control provides a convenient tool for this selection and, in fact, the main objective of this book is to show that optimal control plays a natural role for this.

2 Problem 5 The next problem we consider is the problem of constructing monotone splines. This problem, as we discussed in the beginning of this section, is very important for many practical applications. We will do less than construct monotone splines here, although it is possible to extend the techniques we are using to produce an infinite-dimensional quadratic programming problem that produces monotone splines. We do not make that extension in this section, but restrict ourselves to ensuring that the spline is nondecreasing at each node.

Download PDF sample

Control Theoretic Splines: Optimal Control, Statistics, and Path Planning (Princeton Series in Applied Mathematics) by Magnus Egerstedt


by James
4.0

Rated 4.42 of 5 – based on 31 votes