Practical Direct Collocation Methods for Computational Optimal Control

2012 ◽  
pp. 33-60 ◽  
Author(s):  
Victor M. Becerra
Keyword(s):  
Optimal Control ◽  
Collocation Methods ◽  
Direct Collocation

scholarly journals Partitioned Quasi-Newton Approximation for Direct Collocation Methods and Its Application to the Fuel-Optimal Control of a Diesel Engine

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Jonas Asprion ◽  
Oscar Chinellato ◽  
Lino Guzzella
Keyword(s):  
Optimal Control ◽  
Diesel Engine ◽  
Collocation Methods ◽  
Nonlinear Program ◽  
Turbocharged Diesel Engine ◽  
Sparsity Pattern ◽  
Direct Collocation ◽  
First Results ◽  
Curvature Information ◽  
Quasi Newton

The numerical solution of optimal control problems by direct collocation is a widely used approach. Quasi-Newton approximations of the Hessian of the Lagrangian of the resulting nonlinear program are also common practice. We illustrate that the transcribed problem is separable with respect to the primal variables and propose the application of dense quasi-Newton updates to the small diagonal blocks of the Hessian. This approach resolves memory limitations, preserves the correct sparsity pattern, and generates more accurate curvature information. The effectiveness of this improvement when applied to engineering problems is demonstrated. As an example, the fuel-optimal and emission-constrained control of a turbocharged diesel engine is considered. First results indicate a significantly faster convergence of the nonlinear program solver when the method proposed is used instead of the standard quasi-Newton approximation.

scholarly journals Optimal Control for Bufferbloat Queue Management Using Indirect Method with Parametric Optimization

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Amr Radwan ◽  
Hoang-Linh To ◽  
Won-Joo Hwang
Keyword(s):  
Optimal Control ◽  
Queue Length ◽  
Network Performance ◽  
Parametric Optimization ◽  
Collocation Methods ◽  
Queue Management ◽  
Indirect Approach ◽  
Direct Collocation ◽  
Short Queue ◽  
The Cost

Because memory buffers become larger and cheaper, they have been put into network devices to reduce the number of loss packets and improve network performance. However, the consequences of large buffers are long queues at network bottlenecks and throughput saturation, which has been recently noticed in research community as bufferbloat phenomenon. To address such issues, in this article, we design a forward-backward optimal control queue algorithm based on an indirect approach with parametric optimization. The cost function which we want to minimize represents a trade-off between queue length and packet loss rate performance. Through the integration of an indirect approach with parametric optimization, our proposal has advantages of scalability and accuracy compared to direct approaches, while still maintaining good throughput and shorter queue length than several existing queue management algorithms. All numerical analysis, simulation in ns-2, and experiment results are provided to solidify the efficiency of our proposal. In detailed comparisons to other conventional algorithms, the proposed procedure can run much faster than direct collocation methods while maintaining a desired short queue (≈40 packets in simulation and80 (ms) in experiment test).

Comparison of Global and Local Collocation Methods for Optimal Control

2008 ◽  
Vol 31 (2) ◽  
pp. 432-436 ◽  
Author(s):  
Geoffrey T. Huntington ◽  
Anil V. Rao
Keyword(s):  
Optimal Control ◽  
Collocation Methods ◽  
Global And Local

Trajectory Optimization for Spacecraft Proximity Rendezvous Using Direct Collocation Method

2012 ◽  
Vol 433-440 ◽  
pp. 6652-6656 ◽  
Author(s):  
Tao Liu ◽  
Yu Shan Zhao ◽  
Peng Shi ◽  
Bao Jun Li
Keyword(s):  
Nonlinear Programming ◽  
Control Problem ◽  
Programming Problem ◽  
Collocation Method ◽  
Trajectory Optimization ◽  
Collocation Methods ◽  
Nonlinear Programming Problem ◽  
Reference Orbit ◽  
Direct Collocation ◽  
Direct Collocation Method

Trajectory optimization problem for spacecraft proximity rendezvous with path constraints was discussed using direct collocation method. Firstly, the model of spacecraft proximity rendezvous in elliptic orbit optimization control problem was presented, with the dynamic equations established in the target local orbital frame, and the performance index was minimizing the total fuel consumption. After that the optimal control problem was transcribed into a large scale problem of Nonlinear Programming Problem (NLP) by means of Hermite-Simpson discretization, which was one of the direct collocation methods. Then the nonlinear programming problem was solved using MATLAB software package SNOPT. Finally, to verify this method, the fuel-optimal trajectory for finite thrust was planned for proximity rendezvous with elliptic reference orbit. Numerical simulation results demonstrate that the proposed method was feasible, and was not sensitive to the initial condition, having good robustness.

scholarly journals Evaluation of Direct Collocation Optimal Control Problem Formulations for Solving the Muscle Redundancy Problem

2016 ◽  
Vol 44 (10) ◽  
pp. 2922-2936 ◽  
Author(s):  
Friedl De Groote ◽  
Allison L. Kinney ◽  
Anil V. Rao ◽  
Benjamin J. Fregly
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Direct Collocation ◽  
Redundancy Problem ◽  
Problem Formulations

Trajectory Optimization for Nonholonomic Vehicles on Non-Flat Terrains Using Shooting and Collocation Methods

2013 ◽  
Author(s):  
Dimitris M. Chatzigeorgiou
Keyword(s):  
Optimal Control ◽  
Mobile Robots ◽  
Performance Index ◽  
Trajectory Optimization ◽  
Optimization Problem ◽  
Control Policy ◽  
Collocation Methods ◽  
Governing Equations ◽  
Nonholonomic Mobile Robots ◽  
Nonholonomic Vehicles

In this paper we focus on the trajectory optimization problem for a specific family of robots; nonholonomic mobile robots. We study the particular case where such robots operate on smooth, non-flat terrains, i.e. terrains with large differences in elevation. Initially we present the governing equations of such robots and then study the trajectory optimization problem in order to solve for the optimal control policy. We test two different approaches for this problem, namely a shooting and a collocation method, for evaluating and optimizing a performance index.

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