Mad Product Sheet

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MAD - MATLAB Automatic Differential package. MATLAB Automatic Differentiation (MAD) is a professionally maintained and developed automatic differentiation tool for MATLAB. Many new features are added continuously since the development and additions are made in close cooperation with the user base. Automatic differentiation is generally defined as (after Andreas Griewank, Evaluating Derivatives - Principles and Techniques of Algorithmic Differentiation, SIAM 2000): “Algorithmic, or automatic, differentiation (AD) is concerned with the accurate and efficient evaluation of derivatives for functions defined by computer programs. No truncation errors are incurred, and the resulting numerical derivative values can be used for all scientific computations that are based on linear, quadratic, or even higher order approximations to nonlinear scalar or vector functions.” MAD is a MATLAB library of functions and utilities for the automatic differentiation of MATLAB functions and statements. MAD utilizes an optimized class library “derivvec”, for the linear combination of derivative vectors. Key Features MAD Example A variety of trigonometric functions. >> x = fmad(3,1); FFT functions available (FFT, IFFT). >> y = x^2 + x^3; >> getderivs(y) interp1 and interp2 optimized for differentiation. ans = 33 Delivers floating point precision derivatives (better robustness). A new MATLAB class fmad which overloads the builtin MATLAB arithmetic and some intrinsic functions. More than 100 built-in MATLAB operators have been implemented. The classes allow for the use of MATLAB’s sparse matrix representation to exploit sparsity in the derivative calculation at runtime. Normally faster or equally fast as numerical differentiation. Complete integration with all TOMLAB solvers. Possible to use as plug-in for modeling class tomSym and optimal control package PROPT. Tomlab Optimization Inc. Tomlab Optimization AB 93 S Jackson St #95594, Seattle, WA 98104, USA Västerås Tech Park, Trefasgatan 4, SE-721 30 Västerås, Sweden Tel: +1 (509) 320-4213, Fax: +1 (619) 245-2476 Tel: +46 (21) 495 1260, Fax: +1 (619) 245-2476 Email: [email protected], http://tomopt.com Email: [email protected], http://tomopt.com.

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Propt Product Sheet
PROPT - The world’s fastest Optimal Control platform for MATLAB. PROPT - ONE OF A KIND, LIGHTNING FAST SOLUTIONS TO YOUR OPTIMAL CONTROL PROBLEMS! NOW WITH WELL OVER 100 TEST CASES! The PROPT software package is intended to When using PROPT, optimally coded analytical solve dynamic optimization problems. Such first and second order derivatives, including problems are usually described by: problem sparsity patterns are automatically generated, thereby making it the first MATLAB • A state-space model of package to be able to fully utilize a system. This can be NLP (and QP) solvers such as: either a set of ordinary KNITRO, CONOPT, SNOPT and differential equations CPLEX. (ODE) or differential PROPT currently uses Gauss or algebraic equations (PAE). Chebyshev-point collocation • Initial and/or final for solving optimal control conditions (sometimes problems. However, the code is also conditions at other written in a more general way, points). allowing for a DAE rather than an ODE formulation. Parameter • A cost functional, i.e. a estimation problems are also scalar value that depends possible to solve. on the state trajectories and the control function. PROPT has three main functions: • Sometimes, additional equations and variables • Computation of the that, for example, relate constant matrices used for the the initial and final differentiation and integration conditions to each other. of the polynomials used to approximate the solution to the trajectory optimization problem. The goal of PROPT is to make it possible to input such problem • Source transformation to turn descriptions as simply as user-supplied expressions into possible, without having to worry optimized MATLAB code for the about the mathematics of the cost function f and constraint actual solver.
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A Toolchain for Solving Dynamic Optimization Problems Using Symbolic and Parallel Computing Evgeny Lazutkin Siegbert Hopfgarten Abebe Geletu Pu Li Group Simulation and Optimal Processes, Institute for Automation and Systems Engineering, Technische Universität Ilmenau, P.O. Box 10 05 65, 98684 Ilmenau, Germany. {evgeny.lazutkin,siegbert.hopfgarten,abebe.geletu,pu.li}@tu-ilmenau.de Abstract shown in Fig. 1. Based on the current process state x(k) obtained through the state observer or measurement, Significant progresses in developing approaches to dy- resp., the optimal control problem is solved in the opti- namic optimization have been made. However, its prac- mizer in each sample time. The resulting optimal control tical implementation poses a difficult task and its real- strategy in the first interval u(k) of the moving horizon time application such as in nonlinear model predictive is then realized through the local control system. There- control (NMPC) remains challenging. A toolchain is de- fore, an essential limitation of applying NMPC is due to veloped in this work to relieve the implementation bur- its long computation time taken to solve the NLP prob- den and, meanwhile, to speed up the computations for lem for each sample time, especially for the control of solving the dynamic optimization problem. To achieve fast systems (Wang and Boyd, 2010). In general, the these targets, symbolic computing is utilized for calcu- computation time should be much less than the sample lating the first and second order sensitivities on the one time of the NMPC scheme (Schäfer et al., 2007). Al- hand and parallel computing is used for separately ac- though powerful methods are available, e.g.
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An Algorithm for Bang–Bang Control of Fixed-Head Hydroplants
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Optimal Steering Control Input Generation for Vehicle's Entry Speed Maximization in a Double-Lane Change Manoeuvre
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Basic Implementation of Multiple-Interval Pseudospectral Methods to Solve Optimal Control Problems
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Real-Time Trajectory Planning to Enable Safe and Performant Automated Vehicles Operating in Unknown Dynamic Environments
Real-time Trajectory Planning to Enable Safe and Performant Automated Vehicles Operating in Unknown Dynamic Environments by Huckleberry Febbo A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Mechanical Engineering) at The University of Michigan 2019 Doctoral Committee: Associate Research Scientist Tulga Ersal, Co-Chair Professor Jeffrey L. Stein, Co-Chair Professor Brent Gillespie Professor Ilya Kolmanovsky Huckleberry Febbo [email protected] ORCID iD: 0000-0002-0268-3672 c Huckleberry Febbo 2019 All Rights Reserved For my mother and father ii ACKNOWLEDGEMENTS I want to thank my advisors, Prof. Jeffrey L. Stein and Dr. Tulga Ersal for their strong guidance during my graduate studies. Each of you has played pivotal and complementary roles in my life that have greatly enhanced my ability to communicate. I want to thank Prof. Peter Ifju for telling me to go to graduate school. Your confidence in me has pushed me farther than I knew I could go. I want to thank Prof. Elizabeth Hildinger for improving my ability to write well and providing me with the potential to assert myself on paper. I want to thank my friends, family, classmates, and colleges for their continual support. In particular, I would like to thank John Guittar and Srdjan Cvjeticanin for providing me feedback on my articulation of research questions and ideas. I will always look back upon the 2018 Summer that we spent together in the Rackham Reading Room with fondness. Rackham . oh Rackham . I want to thank Virgil Febbo for helping me through my last month in Michigan.
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CME 338 Large-Scale Numerical Optimization Notes 2
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Tomlab Product Sheet
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TACO — a Toolkit for AMPL Control Optimization
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Optimal Control of Isometric Muscle Dynamics
12 J. Math.Fund.Sci. Vol. 47, No. 1, 2015, 12-30 Optimal Control of Isometric Muscle Dynamics Robert Rockenfeller &Thomas Götz Mathematical Institute, University Koblenz-Landau, Campus Koblenz Universitätsstr. 1, 56070 Koblenz, Germany Email: [email protected] Abstract. We use an indirect optimal control approach to calculate the optimal neural stimulation needed to obtain measured isometric muscle forces. The neural stimulation of the nerve system is hereby considered to be a control function (input) of the system ’muscle’ that solely determines the muscle force (output). We use a well-established muscle model and experimental data of isometric contractions. The model consists of coupled activation and contraction dynamics described by ordinary differential equations. To validate our results, we perform a comparison with commercial optimal control software. Keywords: biomechanics; inverse dynamics; muscle model; optimal control, stimulation. 1 Introduction0B Mathematical models for everyday phenomena often ask for a control or input such that a system reacts in an optimal or at least in a desired way. Whether finding the optimal rotation of a stick for cooking potatoes on the open fire such that the potato has a desired temperature, see [1], or computing the optimal neural stimulation of a muscle such that the force output is as close as possible to experimentally measured data. Typical examples for biomechanical optimal control problems occur in the calculation of goal directed movements, see [2- 4] and in robotics [5]. Concerning huge musculoskeletal systems, the load sharing problem of muscle force distribution has to be solved using optimal control [6, 7]. The most common application for solving the load sharing problem is the inverse dynamics of multi-body systems (MBS) as in [8,9].
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