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Sequential Gradient Restoration Algorithm For Optimal Control Problems With Bounded State Variables
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Book Synopsis Sequential Gradient-restoration Algorithm for Optimal Control Problems with Bounded State Variables by : G. R. Hennig
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).
Book Synopsis Sequential Gradient-restoration Algorithm for Optimal Control Problems with Bounded State Variables by : G. R. Hennig
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).
Book Synopsis Sequential Gradient-restoration Algorithm for Optimal Control Problems with Bounded State Variables by : G. R. Hennig
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 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Some Properties of the Sequential Gradient-Restoration Algorithm and the Modified Quasilinearization Algorithm for Optimal Control Problems with Bounded State by : H. Y. Huang
Download or read book Some Properties of the Sequential Gradient-Restoration Algorithm and the Modified Quasilinearization Algorithm for Optimal Control Problems with Bounded State written by H. Y. Huang and published by . This book was released on 1972 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: The sequential gradient-restoration algorithm and the modified quasilinearization algorithm were developed for optimal control problems with bounded state. These algorithms have a basic property: for a subarc lying on the state boundary, the state boundary equations are satisfied at every iteration, if they are satisfied at the beginning of the computational process. Thus, the subarc remains anchored on the state boundary. In the paper, the anchoring conditions are derived. (Author).
Book Synopsis Sequential Gradient-Restoration Algorithm for Optimal Control Problems with Nondifferential Constraints, Part 3. Examples by : A. Miele
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).
Book Synopsis Sequential Gradient-Restoration Algorithm for Optimal Control Problems with Nondifferential Constraints. Part 2. Examples by : A. Miele
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).
Book Synopsis A Hybrid Approach to Optimal Control Problems with Bounded State. Part 2, Examples by : A. Miele
Download or read book A Hybrid Approach to Optimal Control Problems with Bounded State. Part 2, Examples written by A. Miele and published by . This book was released on 1974 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: In another paper, Miele, Tietze, and Cloutier developed a modification of the sequential gradient-restoration algorithm for minimizing a functional subject to different constraints. In this report, five numerical examples are presented, some pertaining to the fixed-final-time case and some pertaining to the free-final-time case. The numerical results show the rapid convergence characteristics of the modification of the sequential gradient-restoration algorithm.
Book Synopsis New Transformation Technique for Optimal Control Problems with Bounded State. Part II. Examples by : A. Miele
Download or read book New Transformation Technique for Optimal Control Problems with Bounded State. Part II. Examples written by A. Miele and published by . This book was released on 1974 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Part I (AD/A-004 333), Miele and Cloutier developed a new transformation technique for optimal control problems with bounded state. This transformation technique was employed in conjunction with the sequential gradient-restoration algorithm. In this report, five numerical examples are presented, some pertaining to the fixed-final-time case and some pertaining to the free-final-time case. The numerical results show the rapid convergence characteristics of the algorithm discussed in Part I.
Book Synopsis Sequential Gradient-restoration Algorithm for Optimal Control Problems with Nondifferential Constraints by : Angelo Miele (Civil engineer, Aircraft designer, Italy, United States)
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:
Book Synopsis Sequential Gradient-restoration Algorithm for Optimal Control Problems with Nondifferential Constraints and General Boundary Conditions by : S. Gonzalez
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:
Book Synopsis Sequential Gradient-restoration Algorithm for Optimal Control Problems with General Boundary Conditions by : S. Gonzalez
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:
Book Synopsis Sequential Gradient-Restoration Algorithm for Optimal Control Problems with Nondifferential Constraints. Part I. Theory by : A. Miele
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).
Book Synopsis New Transformation Technique for Optimal Control Problems with Bounded State. Part I. Theory by : A. Miele
Download or read book New Transformation Technique for Optimal Control Problems with Bounded State. Part I. Theory written by A. Miele and published by . This book was released on 1974 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: The numerical solution of optimal control problems involving a state inequality constraint of the form L(x, theta) = or> 0 is considered. The approach employed is of the hybrid type, in an attempt to combine some of the best features of the indirect approach and the direct approach. While a predetermined number and sequence of subarcs are assumed (a feature of direct methods), enforcement of the state inequality constraint is obtained through a Valentine-type representation (a feature of indirect methods). A new transformation technique is developed by applying the Valentine-type representation to the kth derivative of the function L(x, theta), assumed to have a constant sign in each of the subarcs composing the extremal arc. The algorithm developed belongs to the class of sequential gradient-restoration algorithms. The principal property of the algorithm is that it produces a sequence of feasible suboptimal solutions: the functions x(t), u(t), pi obtained at the end of each cycle satisfy the constraints to a predetermined accuracy. Five numerical examples illustrating the theory are given in Part 2 (AD/A-004 334) and demonstrate the feasibility as well as the rapidity of convergence of the technique developed in this paper.
Book Synopsis Sequential Conjugate Gradient-Restoration Algorithm for Optimal Control Problems with General Boundary Conditions by : A. K. Wu
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.
Book Synopsis Sequential Conjugate Gradient-Restoration Algorithm for Optimal Control Problems. Part I. Theory by : J. C. Heideman
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.
Book Synopsis Sequential Conjugate Gradient-restoration Algorithm for Optimal Control Problems with Nondifferential Constraints and General Boundary Conditions by : A. K. Wu
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.
Book Synopsis Sequential Conjugate Gradient-restoration Algorithm for Optimal Control Problems with Nondifferental Constraints : Part 1, Theory by :
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:
