Optimal control theory with economic applications
Optimal control theory with economic applications
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Pseudospectral Chebyshev Optimal Control of Constrained Nonlinear Dynamical Systems
Computational Optimization and Applications
The Euler approximation in state constrained optimal control
Mathematics of Computation
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Second-Order Runge--Kutta Approximations in Control Constrained Optimal Control
SIAM Journal on Numerical Analysis
Automatic differentiation of explicit Runge-Kutta methods for optimal control
Computational Optimization and Applications
Computational Optimization and Applications
Numerical Approximation of Partial Differential Equations
Numerical Approximation of Partial Differential Equations
A First Course in the Numerical Analysis of Differential Equations
A First Course in the Numerical Analysis of Differential Equations
Discretization methods for optimal control problems with state constraints
Journal of Computational and Applied Mathematics
Symbolic-numeric efficient solution of optimal control problems for multibody systems
Journal of Computational and Applied Mathematics - Special issue: International workshop on the technological aspects of mathematics
Practical Methods for Optimal Control and Estimation Using Nonlinear Programming
Practical Methods for Optimal Control and Estimation Using Nonlinear Programming
Automatica (Journal of IFAC)
Inexact Restoration for Runge-Kutta Discretization of Optimal Control Problems
SIAM Journal on Numerical Analysis
Brief paper: Pseudospectral methods for solving infinite-horizon optimal control problems
Automatica (Journal of IFAC)
Computational Optimization and Applications
Paper II: Successive approximation methods for the solution of optimal control problems
Automatica (Journal of IFAC)
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The Forward-Backward Sweep Method is a numerical technique for solving optimal control problems. The technique is one of the indirect methods in which the differential equations from the Maximum Principle are numerically solved. After the method is briefly reviewed, two convergence theorems are proved for a basic type of optimal control problem. The first shows that recursively solving the system of differential equations will produce a sequence of iterates converging to the solution of the system. The second theorem shows that a discretized implementation of the continuous system also converges as the iteration and number of subintervals increases. The hypotheses of the theorem are a combination of basic Lipschitz conditions and the length of the interval of integration. An example illustrates the performance of the method.