Download or read book Sequential Conjugate Gradient restoration Algorithm for Optimal Control Problems with Nondifferential Constraints and General Boundary Conditions written by A. K. Wu and published by . This book was released on 1978 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper considers the numerical solution of the problem of minimizing a functional subject to differential constraints, nondifferential constraints, and general boundary conditions. The approach taken is a sequence of two-phase cycles, composed of a conjugate gradient phase and a restoration phase. The conjugate gradient phase involves one iteration: the first variation of the functional is minimized, subject to the linearized constraints and a quadratic constraint imposed on the variations of the control, the parameter, and the missing components of the initial state. The restoration phase involves one or more iterations: in each iteration, the norm squared of the variations of the control, the parameter, and the missing components of the initial state is minimized, subject to the linearized constraints. Twelve numerical examples are presented in order to illustrate the performance of the algorithm. The numerical results show the feasibility as well as the convergence characteristics of the present algorithm.
Download or read book Sequential Conjugate Gradient Restoration Algorithm for Optimal Control Problems with General Boundary Conditions written by A. K. Wu and published by . This book was released on 1978 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper considers the numerical solution of the problem of minimizing a functional subject to differential constraints and general boundary conditions. The approach taken is a sequence of two-phase cycles, composed of a conjugate gradient phase and a restoration phase. The conjugate gradient phase involves one iteration and is designed to decrease the value of the functional, while the constraints are satisfied to first order. During this iteration, the first variation of the functional is minimized, subject to the linearized constraints and to a quadratic constraint imposed on the variations of the control, the parameter, and the missing components of the initial state. The restoration phase involves one or more iterations and is designed to force constraint satisfaction to a predetermined accuracy, while the norm squared of the variations of the control, the parameter, and the missing components of the initial state is minimized.
Download or read book Sequential Conjugate Gradient Restoration Algorithm for Optimal Control Problems with Nondifferential Constraints Part 1 Theory written by J. R. Cloutier and published by . This book was released on 1977 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: A sequential conjugate gradient-restoration algorithm is developed in order to solve optimal control problems involving a functional subject to differential constraints, nondifferential constraints, and terminal constraints. The algorithm is composed of a sequence of cycles, each cycle consisting of two phases, a conjugate gradient phase and a restoration phase. The conjugate gradient phase involves a single iteration and is designed to decrease the value of the functional while satisfying the constraints to first order. The restoration phase involves one or more iterations and is designed to restore the constraints to a predetermined accuracy, while the norm of the variations of the variations of the control and the parameter is minimized, subject to the linearized constraints. The sequential conjugate gradient-restoration algorithm is characterized by two main properties. First, at the end of each cycle, the trajectory satisfies the constraints to a given accuracy. Second, the conjugate gradient stepsize and the restoration stepsize can be chosen so that the restoration phase preserves the descent property of the conjugate gradient phase.
Download or read book Technical Abstract Bulletin written by and published by . This book was released on with total page 1048 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sequential Conjugate Gradient Restoration Algorithm for Optimal Control Problems with Nondifferential Constraints Part 2 Examples written by J. R. Cloutier and published by . This book was released on 1977 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first volume the sequential conjugate gradient-restoration alogorithm was developed for minimizing a functional subject to differential constraint, nondifferential constraints, and terminal constraints. In this report, sixteen numerical examples are presented, four pertaining to a quadratic functional subject to linear constraints and twelve pertaining to a nonquadratic functional subject to nonlinear constraints. These examples demonstrate the feasibility as well as the rapid convergence characteristics of the sequential conjugate gradient-restoration algorithm.
Download or read book Sequential Gradient restoration Algorithm for Optimal Control Problems with General Boundary Conditions written by S. Gonzalez and published by . This book was released on 1978 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sequential Conjugate Gradient restoration Algorithm for Optimal Control Problems with Nondifferental Constraints Part 1 Theory written by and published by . This book was released on 1977 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Control and Dynamic Systems V16 written by C.T. Leonides and published by Elsevier. This book was released on 2012-12-02 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Control and Dynamic Systems: Advances in Theory and Application, Volume 16 is concerned with applied dynamic systems control techniques. It describes various techniques for system modeling, which apply to several systems issues. This book presents a comprehensive treatment of powerful algorithmic techniques for solving dynamic-system optimization problems. It also describes approaches for systems model that apply to system issues such as time delays. The remaining chapters of this book explore the simulation of large closed-loop systems and optimization of low-order feedback controllers for discrete-time systems. Researchers who wish to broaden their understanding of dynamic systems control techniques will find this book invaluable.
Download or read book Sequential Conjugate Gradient Restoration Algorithm for Optimal Control Problems Part 2 Examples written by J. C. Heideman and published by . This book was released on 1974 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt: In another paper Heideman and Levy developed the sequential conjugate gradient-restoration algorithm for minimizing a functional subject to differential constraints and terminal constraints. In this report, several numerical examples are presented, some pertaining to a quadratic functional subject to linear constraints and some pertaining to a nonquadratic functional subject to nonlinear constraints. These examples demonstrate the feasibility as well as the rapid convergence characteristic of the sequential conjugate gradient-restoration algorithm.
Download or read book Sequential Gradient restoration Algorithm for Optimal Control Problems with Nondifferential Constraints written by Angelo Miele (Civil engineer, Aircraft designer, Italy, United States) and published by . This book was released on 1973 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sequential Gradient Restoration Algorithm for Optimal Control Problems with Nondifferential Constraints Part 3 Examples written by A. Miele and published by . This book was released on 1973 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: Miele, Damoulakis, and Cloutier developed the sequential gradient-restoration algorithm for minimizing a functional subject to differential constraints, nondifferential constraints, and terminal constraints. In the report, several numerical examples are presented, some pertaining to the fixed-final-time case and some pertaining to the free-final-time case. Both problems with bounded state and problems with bounded time rate of change of the state are investigated. The numerical results show the rapid convergence characteristics of the sequential gradient-restoration algorithm. (Author).
Download or read book Sequential Gradient Restoration Algorithm for Optimal Control Problems with Nondifferential Constraints Part 2 Examples written by A. Miele and published by . This book was released on 1973 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: Miele, Damoulakis and Cloutier developed the sequential gradient-restoration algorithm for minimizing a functional subject to differential constraints, nondifferential constraints, and terminal constraints. In the report, several numerical examples are presented, some pertaining to the fixed-final-time case and some pertaining to the free-final-time case. Both equality constrained optimization problems and problems with bounded control are investigated. The numerical results show the rapid convergence characteristics of the sequential gradient-restoration algorithm. (Author).
Download or read book Numerical Solution of Optimal Control Problems with State Constraints by Sequential Quadratic Programming in Function Space written by Kees C. P. Machielsen and published by . This book was released on 1988 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sequential Conjugate Gradient restoration Algorithm for Optimal Control Problems written by J. C. Heideman and published by . This book was released on 1974 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Recent Advances in Gradient Algorithms for Optimal Control Problems written by Angelo Miele and published by . This book was released on 1975 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a survey paper which summarizes recent advances in the area of gradient algorithms for optimal control problems, with particular emphasis on the work performed by the Aero-Astronautics Group of Rice University. The following topics are treated: sequential gradient-restoration algorithm, family of gradient-restoration algorithms, hybrid modification of the sequential gradient-restoration algorithm, sequential conjugate gradient-restoration algorithm, nondifferential constraints, multiple subarcs, transformation techniques. (Author).
Download or read book Sequential Conjugate Gradient Restoration Algorithm for Optimal Control Problems Part I Theory written by J. C. Heideman and published by . This book was released on 1974 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper considers the problem of minimizing a functional I which depends on the state x(t), the control u(t), and the parameter pi. Here, I is a scalar, x an n-vector, u an m-vector, and pi a p-vector. At the initial point, the state is prescribed. At the final point, the state and the parameter are required to satisfy q scalar relations. Along the interval of integration, the state, the control, and the parameter are required to satisfy n scalar differential equations.
