scholarly journals Direct trajectory optimization and costate estimation of finite-horizon and infinite-horizon optimal control problems using a Radau pseudospectral method

2009 ◽  
Vol 49 (2) ◽  
pp. 335-358 ◽  
Author(s):  
Divya Garg ◽  
Michael A. Patterson ◽  
Camila Francolin ◽  
Christopher L. Darby ◽  
Geoffrey T. Huntington ◽  
...  
Keyword(s):  
Optimal Control ◽  
Trajectory Optimization ◽  
Optimal Control Problems ◽  
Infinite Horizon ◽  
Pseudospectral Method ◽  
Finite Horizon ◽  
Control Problems

scholarly journals A pseudospectral method for budget-constrained infinite horizon optimal control problems

2021 ◽  
Vol 71 ◽  
pp. 145-154
Author(s):  
Angie Burtchen ◽  
Valeriya Lykina ◽  
Sabine Pickenhain
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Numerical Solutions ◽  
Infinite Horizon ◽  
Pseudospectral Method ◽  
Linear Quadratic Regulator ◽  
Approximate Solutions ◽  
Control Problems ◽  
Linear Quadratic ◽  
Weighted Functional Spaces

In this paper a generalization of the indirect pseudo-spectral method, presented in [17], for the numerical solution of budget-constrained infinite horizon optimal control problems is presented. Consideration of the problem statement in the framework of weighted functional spaces allows to arrive at a good approximation for the initial value of the adjoint variable, which is inevitable for obtaining good numerical solutions. The presented method is illustrated by applying it to the budget-constrained linear-quadratic regulator model. The quality of approximate solutions is demonstrated by an example.

scholarly journals The effect of the terminal penalty in Receding Horizon Control for a class of stabilization problems

2020 ◽  
Vol 26 ◽  
pp. 58
Author(s):  
Karl Kunisch ◽  
Laurent Pfeiffer
Keyword(s):  
Optimal Control ◽  
Value Function ◽  
Optimal Control Problems ◽  
Infinite Horizon ◽  
Receding Horizon Control ◽  
Finite Horizon ◽  
Dynamic Programming Principle ◽  
Control Problems ◽  
Receding Horizon ◽  
Taylor Approximation

The Receding Horizon Control (RHC) strategy consists in replacing an infinite-horizon stabilization problem by a sequence of finite-horizon optimal control problems, which are numerically more tractable. The dynamic programming principle ensures that if the finite-horizon problems are formulated with the exact value function as a terminal penalty function, then the RHC method generates an optimal control. This article deals with the case where the terminal cost function is chosen as a cut-off Taylor approximation of the value function. The main result is an error rate estimate for the control generated by such a method, when compared with the optimal control. The obtained estimate is of the same order as the employed Taylor approximation and decreases at an exponential rate with respect to the prediction horizon. To illustrate the methodology, the article focuses on a class of bilinear optimal control problems in infinite-dimensional Hilbert spaces.

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