Journal Article10.1109/TAC.1986.1104364
A second-order algorithm for continuous-time nonlinear optimal control problems
Masao Fukushima,Yutaka Yamamoto +1 more
TL;DR: In this paper, a second-order trust region modification of Newton's method is proposed to solve continuous-time nonlinear optimal control problems with a global convergence property under some assumptions.
read more
Abstract: A second-order algorithm is presented for the solution of continuous-time nonlinear optimal control problems. The algorithm is an adaptation of the trust region modifications of Newton's method and solves at each iteration a linear-quadratic control problem with an additional constraint. Under some assumptions, the proposed algorithm is shown to possess a global convergence property. A numerical example is presented to illustrate the method.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Perspectives in Mathematical System Theory, Control, and Signal Processing
Jan C. Willems,Shinji Hara,Yoshito Ohta,Hisaya Fujioka +3 more
- 01 Jan 2010
TL;DR: A Unified Approach to Decentralized Cooperative Control for Large-Scale Networked Dynamical Systems and an Optimization Approach to Weak Approximation of Levy-Driven Stochastic Differential Equations are discussed.
59
Optimal control of a class of discrete-continuous non-linear systems-decomposition and hierarchical structure
P.D. Roberts,Victor M. Becerra +1 more
TL;DR: An analysis of the optimality and convergence properties of the algorithm is presented and the effectiveness of the technique is demonstrated using a simulation example with a non-separable performance index.
31
Trust region subproblem with an additional linear inequality constraint
Maziar Salahi,Saeed Fallahi +1 more
TL;DR: Preliminary numerical experiments show that, the new approach is much faster in finding the global optimal solution than the known semidefinite relaxation approach, especially when solving large scale problems.
21
A second-order algorithm for continuous-time nonlinear optimal control problems
Masao Fukushima,Yutaka Yamamoto +1 more
TL;DR: In this paper, a second-order trust region modification of Newton's method is proposed to solve continuous-time nonlinear optimal control problems with a global convergence property under some assumptions.
An algorithm for solving control constrained optimal control problems
Baoming Ma,William S. Levine +1 more
- 15 Dec 1993
TL;DR: In this paper, an approach similar to the Han-Powell method in finite-dimensional optimization is devised to solve continuous-time optimal control problems where the control variables are constrained, based on a second-order approximation to the change of the cost functional due to a change in the control.
16
References
Newton's method with a model trust region modification
TL;DR: This report contains a thorough analysis of the locally constrained quadratic minimizations that arise as subproblems in the modified Newton iteration.
Calculus of Variations and Optimal Control Theory
TL;DR: Hestenes as mentioned in this paper has been a leading researcher on optimization theory since the early 1930's and this book contains much of his original work in the field, including the classical, calculus of variations, approach of first and second variations.
574
Newton's Method
Jorge J. Moré,Danny C. Sorensen +1 more
- 01 Feb 1982
TL;DR: Two main approaches to Newton's method for unconstrained minimization are presented: the line search approach and the trust region approach and it is shown how quasi-Newton methods can be derived quite naturally from Newton's methods.