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 I Theory written by A. Miele and published by . This book was released on 1973 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper considers the numerical solution of optimal control problems involving a functional subject to differential constraints, nondifferential constraints, and terminal constraints. The problem is to find the state x(t), the control u(t), and the parameter pi so that the functional is minimized, while the constraints are satisfied to a predetermined accuracy. The approach taken is a sequence of two-phase processes or cycles, composed of a gradient phase and a restoration phase. The gradient phase involves a single iteration and is designed to decrease the functional, while the constraints are satisfied to first order. The restoration phase involves one or several iterations and is designed to restore the constraints to a predetermined accuracy, while the norm of the variations of the control and the parameter is minimized. (Author).
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 Sequential Gradient restoration Algorithm for Optimal Control Problems with Nondifferential Constraints and General Boundary Conditions written by S. Gonzalez and published by . This book was released on 1978 with total page 79 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 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 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 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 Gradient restoration Algorithm for Optimal Control Problems with Bounded State Variables written by G. R. Hennig and published by . This book was released on 1972 with total page 61 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper considers the numerical solution of optimal control problems involving a functional I subject to differential constraints, a state variable inequality constraint, and terminal constraints. The problem is to find the state x(t), the control u(t), and the parameter pi so that the functional is minimized, while the constraints are satisfied to a predetermined accuracy. The approach taken is a sequence of two-phase processes or cycles, composed of a gradient phase and a restoration phase. (Modified author abstract).
Download or read book Sequential Gradient restoration Algorithm for Optimal Control Problems with Bounded State Variables written by G. R. Hennig and published by . This book was released on 1972 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hennig and Miele developed the sequential gradient-restoration algorithm for minimizing a function subject to differential constraints, a state variable inequality constraint, and terminal constraints. In the report, six numerical examples are presented, four pertaining to the fixed-final-time case and two pertaining to the free-final-time case. The numerical results show the rapid convergence characteristics of the sequential gradient-restoration algorithm. (Author).
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 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 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 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 A Modified Sequential Gradient restoration Algorithm for Constrained Optimal Control Problems written by D. Blank and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modifications and Extensions of the Sequential Gradient Restoration Algorithm for Optimal Control Theory written by Angelo Miele (Civil engineer, Aircraft designer, Italy, United States) and published by . This book was released on 1970 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a previous paper, the sequential gradient-restoration algorithm for minimizing a functional subject to certain differential equations and boundary conditions was developed. This algorithm, here called Algorithm (alpha), includes the alternate succession of gradient phases and restoration phases. In the gradient phase, the first-order change of the functional is minimized subject to the linearized differential equations, the linearized boundary conditions, and a quadratic constraint on the variations of the control and the parameter. In the restoration phase, the differential equations and the boundary conditions are restored to a predetermined degree of accuracy, subject to the least-square change of the control and the parameter. In the report, several modifications and extensions of algorithm (alpha) are studied. (Author).
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:
