Efficient reconstructed Legendre algorithm for solving linear-quadratic optimal control problems

AbstractIn this paper, a new numerical approach via reconstructed Legendre orthogonal polynomials (LOPs) is presented to solve the linear quadratic optimal control problems (LQPs). By using the elegant operational properties of orthogonal polynomials, a computationally attractive algorithm is developed for calculating LQP. A numerical example illustrates the techniques and demonstrates the accuracy and efficiency of these controllers

Cumulative reports and publications through December 31, 1988

This document contains a complete list of ICASE Reports. Since ICASE Reports are intended to be preprints of articles that will appear in journals or conference proceedings, the published reference is included when it is available

Summary of research in applied mathematics, numerical analysis and computer science at the Institute for Computer Applications in Science and Engineering

Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis and computer science during the period October 1, 1983 through March 31, 1984 is summarized

Cumulative reports and publications through December 31, 1990

This document contains a complete list of ICASE reports. Since ICASE reports are intended to be preprints of articles that will appear in journals or conference proceedings, the published reference is included when it is available

Cumulative reports and publications through 31 December 1983

All reports for the calendar years 1975 through December 1983 are listed by author. Since ICASE reports are intended to be preprints of articles for journals and conference proceedings, the published reference is included when available. Thirteen older journal and conference proceedings references are included as well as five additional reports by ICASE personnel. Major categories of research covered include: (1) numerical methods, with particular emphasis on the development and analysis of basic algorithms; (2) computational problems in engineering and the physical sciences, particularly fluid dynamics, acoustics, structural analysis, and chemistry; and (3) computer systems and software, especially vector and parallel computers, microcomputers, and data management

Summary of research in applied mathematics, numerical analysis, and computer sciences

The major categories of current ICASE research programs addressed include: numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; control and parameter identification problems, with emphasis on effective numerical methods; computational problems in engineering and physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and computer systems and software, especially vector and parallel computers

Activities of the Institute for Computer Applications in Science and Engineering (ICASE)

Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science during the period October 1, 1984 through March 31, 1985 is summarized

Forward and Inverse Methods in Optimal Control and Dynamic Game Theory

University of Minnesota M.S.M.E. thesis. August 2019. Major: Mechanical Engineering. Advisors: Andrew Lamperski, Rajesh Rajamani. 1 computer file (PDF); x, 79 pages.Optimal control theory is ubiquitous in mathematical sciences and engineering. However, in a classroom setting we barely move beyond linear quadratic regulator problems, if at all. In this work, we demystify the necessary conditions of optimality associated with nonlinear optimal control by deriving them from first principles. We also present two numerical schemes for solving these problems. Moving forward, we present an extension of inverse optimal control, which is the problem of computing a cost function with respect to which observed state and control trajectories are optimal. This extension helps us to handle systems which are subjected to state and/or control constraints. We then generalize the methodology of optimal control theory to solve constrained non-zero sum dynamic games. Dynamic games are optimization problems involving several players who are trying to optimize their respective cost functions subject to constraints. We present a novel method to compute Nash equilibrium associated with a game by combining aspects from direct and indirect methods of solving optimal control problems. Finally, we study constrained inverse dynamic games, which is a problem analogous to constrained inverse optimal control method. Here, we show that an inverse dynamic game problem can be decoupled and solved as an inverse optimal control problem for each of the players individually. Throughout the work, examples are provided to demonstrate efficacy of the methods developed

Cumulative reports and publications through December 31, 1989

A complete list of reports from the Institute for Computer Applications in Science and Engineering (ICASE) is presented. The major categories of the current ICASE research program are: numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; control and parameter identification problems, with emphasis on effectual numerical methods; computational problems in engineering and the physical sciences, particularly fluid dynamics, acoustics, structural analysis, and chemistry; computer systems and software, especially vector and parallel computers, microcomputers, and data management. Since ICASE reports are intended to be preprints of articles that will appear in journals or conference proceedings, the published reference is included when it is available

Activities of the Institute for Computer Applications in Science and Engineering

Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science during the period April 1, 1985 through October 2, 1985 is summarized