Download or read book Memory Efficient Approaches of Second Order for Optimal Control Problems written by Julia Sternberg and published by . This book was released on 2005 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Memory Efficient Approaches of Second Order for Optimal Control Problems written by and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Consider a time-dependent optimal control problem, where the state evolution is described by an initial value problem. There are a variety of numerical methods to solve these problems. The so-called indirect approach is considered detailed in this thesis. The indirect methods solve decoupled boundary value problems resulting from the necessary conditions for the optimal control problem. The so-called Pantoja method describes a computationally efficient stage-wise construction of the Newton direction for the discrete-time optimal control problem. There are many relationships between multiple shooting techniques and Pantoja method, which are investigated in this thesis. In this context, the equivalence of Pantoja method and multiple shooting method of Riccati type is shown. Moreover, Pantoja method is extended to the case where the state equations are discretised using one of implicit numerical methods. Furthermore, the concept of symplecticness and Hamiltonian systems is introduced. In this regard, a suitable numerical method is presented, which can be applied to unconstrained optimal control problems. It is proved that this method is a symplectic one. The iterative solution of optimal control problems in ordinary differential equations by Pantoja or Riccati equivalent methods leads to a succession of triple sweeps through the discretised time interval. The second (adjoint) sweep relies on information from the first (original) sweep, and the third (final) sweep depends on both of them. Typically, the steps on the adjoint sweep involve more operations and require more storage than the other two. The key difficulty is given by the enormous amount of memory required for the implementation of these methods if all states throughout forward and adjoint sweeps are stored. One of goals of this thesis is to present checkpointing techniques for memory reduced implementation of these methods. For this purpose, the well known aspect of checkpointing has to be extended to a `nest.
Download or read book Structure Exploiting Numerical Algorithms for Optimal Control written by Isak Nielsen and published by Linköping University Electronic Press. This book was released on 2017-04-20 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical algorithms for efficiently solving optimal control problems are important for commonly used advanced control strategies, such as model predictive control (MPC), but can also be useful for advanced estimation techniques, such as moving horizon estimation (MHE). In MPC, the control input is computed by solving a constrained finite-time optimal control (CFTOC) problem on-line, and in MHE the estimated states are obtained by solving an optimization problem that often can be formulated as a CFTOC problem. Common types of optimization methods for solving CFTOC problems are interior-point (IP) methods, sequential quadratic programming (SQP) methods and active-set (AS) methods. In these types of methods, the main computational effort is often the computation of the second-order search directions. This boils down to solving a sequence of systems of equations that correspond to unconstrained finite-time optimal control (UFTOC) problems. Hence, high-performing second-order methods for CFTOC problems rely on efficient numerical algorithms for solving UFTOC problems. Developing such algorithms is one of the main focuses in this thesis. When the solution to a CFTOC problem is computed using an AS type method, the aforementioned system of equations is only changed by a low-rank modification between two AS iterations. In this thesis, it is shown how to exploit these structured modifications while still exploiting structure in the UFTOC problem using the Riccati recursion. Furthermore, direct (non-iterative) parallel algorithms for computing the search directions in IP, SQP and AS methods are proposed in the thesis. These algorithms exploit, and retain, the sparse structure of the UFTOC problem such that no dense system of equations needs to be solved serially as in many other algorithms. The proposed algorithms can be applied recursively to obtain logarithmic computational complexity growth in the prediction horizon length. For the case with linear MPC problems, an alternative approach to solving the CFTOC problem on-line is to use multiparametric quadratic programming (mp-QP), where the corresponding CFTOC problem can be solved explicitly off-line. This is referred to as explicit MPC. One of the main limitations with mp-QP is the amount of memory that is required to store the parametric solution. In this thesis, an algorithm for decreasing the required amount of memory is proposed. The aim is to make mp-QP and explicit MPC more useful in practical applications, such as embedded systems with limited memory resources. The proposed algorithm exploits the structure from the QP problem in the parametric solution in order to reduce the memory footprint of general mp-QP solutions, and in particular, of explicit MPC solutions. The algorithm can be used directly in mp-QP solvers, or as a post-processing step to an existing solution.
Download or read book Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 written by Spencer J. Sherwin and published by Springer Nature. This book was released on 2020-08-11 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.
Download or read book Practical Methods for Optimal Control and Estimation Using Nonlinear Programming written by John T. Betts and published by SIAM. This book was released on 2010-01-01 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: A focused presentation of how sparse optimization methods can be used to solve optimal control and estimation problems.
Download or read book Numerical Methods for Optimal Control Problems with State Constraints written by Radoslaw Pytlak and published by Springer. This book was released on 2006-11-14 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: While optimality conditions for optimal control problems with state constraints have been extensively investigated in the literature the results pertaining to numerical methods are relatively scarce. This book fills the gap by providing a family of new methods. Among others, a novel convergence analysis of optimal control algorithms is introduced. The analysis refers to the topology of relaxed controls only to a limited degree and makes little use of Lagrange multipliers corresponding to state constraints. This approach enables the author to provide global convergence analysis of first order and superlinearly convergent second order methods. Further, the implementation aspects of the methods developed in the book are presented and discussed. The results concerning ordinary differential equations are then extended to control problems described by differential-algebraic equations in a comprehensive way for the first time in the literature.
Download or read book NBS Special Publication written by and published by . This book was released on 1968 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Neural Network Control of a Parallel Hybrid electric Propulsion System for a Small Unmanned Aerial Vehicle written by Frederick G. Harmon and published by . This book was released on 2005 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: Parallel hybrid-electric propulsion systems would be beneficial for small unmanned aerial vehicles (UAVs) used for military, homeland security, and disaster monitoring missions involving intelligence, surveillance, or reconnaissance (ISR). The benefits include increased time-on-station and range than electric-powered UAVs and stealth modes not available with gasoline-powered UAVs. A conceptual design of a small UAV with a parallel hybrid-electric propulsion system, an optimization routine for the energy use, the application of a neural network to approximate the optimization results, and simulation results are provided. The two-point conceptual design includes an internal combustion engine sized for cruise and an electric motor and lithium-ion battery pack sized for endurance speed. The flexible optimization routine allows relative importance to be assigned between the use of gasoline, electricity, and recharging. The Cerebellar Model Arithmetic Computer (CMAC) neural network approximates the optimization results and is applied to the control of the parallel hybrid-electric propulsion system. The CMAC controller saves on the required memory compared to a large look-up table by two orders of magnitude. The energy use for the hybrid-electric UAV with the CMAC controller during a one-hour and a three-hour ISR mission is 58% and 27% less, respectively, than for a gasoline-powered UAV.
Download or read book First Order and Second Order Numerical Methods for Optimal Control Problems written by A. Miele and published by . This book was released on 1979 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lecture summarizes recent advances in the area of numerical methods for optimal control problems, with particular emphasis on the work performed by the Aero-Astronautics Group of Rice University. The following basic problems are considered; problems with general boundary conditions, problem with nondifferential constraints, and problem with multiple subarcs. First-order alogrithms are reviewed, in particular, the sequential ordinary gradient-restoration algorithm and the sequential conjugate gradient-restoration algorithm. Second-order algorithms are also reviewed, in particular, the modified quasilinearization algorithm. Here, the optimal initial choice of the multipliers is discussed. Transformation techniques are presented by means of which a great variety of problems of optimal control can be reduced to one of the formulations presented. Specifically, the following topics are treated; time normalization, free initial state, problems with bounded control, problems with bounded state, and Chebyshev minimax problems. (Author).
Download or read book Dynamic Optimization Second Edition written by Morton I. Kamien and published by Courier Corporation. This book was released on 2013-04-17 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its initial publication, this text has defined courses in dynamic optimization taught to economics and management science students. The two-part treatment covers the calculus of variations and optimal control. 1998 edition.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1970 with total page 796 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book FOCAPD 19 Proceedings of the 9th International Conference on Foundations of Computer Aided Process Design July 14 18 2019 written by Salvador Garcia Munoz and published by Elsevier. This book was released on 2019-07-09 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: FOCAPD-19/Proceedings of the 9th International Conference on Foundations of Computer-Aided Process Design, July 14 - 18, 2019, compiles the presentations given at the Ninth International Conference on Foundations of Computer-Aided Process Design, FOCAPD-2019. It highlights the meetings held at this event that brings together researchers, educators and practitioners to identify new challenges and opportunities for process and product design. - Combines presentations from the Ninth International Conference on Foundations of Computer-Aided Process Design, FOCAPD-2019
Download or read book Topics in Modal Analysis Volume 10 written by Michael Mains and published by Springer. This book was released on 2015-04-15 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics in Modal Analysis, Volume 10: Proceedings of the 33rd IMAC, A Conference and Exposition on Structural Dynamics, 2015, the tenth volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Experimental Techniques Processing Modal Data Rotating Machinery Acoustics Adaptive Structures Biodynamics Damping
Download or read book A Direct Second Order Computational Method for Solving Optimal Control Problems written by Peter Thomas Rutishauser and published by . This book was released on 1968 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimal Control Theory with Applications in Economics written by Thomas A. Weber and published by MIT Press. This book was released on 2011-09-30 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous introduction to optimal control theory, with an emphasis on applications in economics. This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely self-contained, it provides an introduction to the use of optimal control theory for deterministic continuous-time systems in economics. The theory of ordinary differential equations (ODEs) is the backbone of the theory developed in the book, and chapter 2 offers a detailed review of basic concepts in the theory of ODEs, including the solution of systems of linear ODEs, state-space analysis, potential functions, and stability analysis. Following this, the book covers the main results of optimal control theory, in particular necessary and sufficient optimality conditions; game theory, with an emphasis on differential games; and the application of control-theoretic concepts to the design of economic mechanisms. Appendixes provide a mathematical review and full solutions to all end-of-chapter problems. The material is presented at three levels: single-person decision making; games, in which a group of decision makers interact strategically; and mechanism design, which is concerned with a designer's creation of an environment in which players interact to maximize the designer's objective. The book focuses on applications; the problems are an integral part of the text. It is intended for use as a textbook or reference for graduate students, teachers, and researchers interested in applications of control theory beyond its classical use in economic growth. The book will also appeal to readers interested in a modeling approach to certain practical problems involving dynamic continuous-time models.
Download or read book A Parallel Method for Discrete time Optimal Control Problems written by Daniel Ralph and published by . This book was released on 1993 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
