# Difference between revisions of "EECI08: Optimization-Based Control"

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In this lecture we describe how real-time optimization can be used to design feedback control algorithms for nonlinear, constrained systems. The receding horizon control (RHC) principle is described and the main ingredients required for its stability are discussed. Efficient numerical methods can then be used to find trajectories that satify the system dynamics and constraints, as well as minimizing a cost function. We concentrate on methods for real-time trajectory generation, and in particular the [[NTG]] software package. | In this lecture we describe how real-time optimization can be used to design feedback control algorithms for nonlinear, constrained systems. The receding horizon control (RHC) principle is described and the main ingredients required for its stability are discussed. Efficient numerical methods can then be used to find trajectories that satify the system dynamics and constraints, as well as minimizing a cost function. We concentrate on methods for real-time trajectory generation, and in particular the [[NTG]] software package. | ||

== Lecture Materials == | |||

* Lecture slides: {{eeci-sp08 pdf|L5_optimal.pdf|Optimization-Based Control}} | * Lecture slides: {{eeci-sp08 pdf|L5_optimal.pdf|Optimization-Based Control}} | ||

* Lecture notes: {{obc08|Chapter 3 - Receding Horizon Control}} | * Lecture notes: {{obc08|Chapter 3 - Receding Horizon Control}} |

## Revision as of 01:00, 29 March 2008

Prev: Trajectory Generation | Course home | Next: Sensor Fusion |

In this lecture we describe how real-time optimization can be used to design feedback control algorithms for nonlinear, constrained systems. The receding horizon control (RHC) principle is described and the main ingredients required for its stability are discussed. Efficient numerical methods can then be used to find trajectories that satify the system dynamics and constraints, as well as minimizing a cost function. We concentrate on methods for real-time trajectory generation, and in particular the NTG software package.

## Lecture Materials

- Lecture slides: Optimization-Based Control
- Lecture notes: Chapter 3 - Receding Horizon Control

## Reading

Constrained model predictive control: Stability and optimality, D. Q. Mayne, J. B. Rawlings, C. V. Rao and P. O. M. Scokaert. Automatica, 2000, Vol. 36, No. 6, pp. 789-814. This is one of the most referenced comprehensive survey papers on MPC. Gives a nice overview about its history and explains the most important issues and various approaches.

Online Control Customization via Optimization-Based Control, R. M. Murray et al. In Software-Enabled Control: Information Technology for Dynamical Systems, T. Samad and G. Balas (eds.), IEEE Press, 2001. This paper talks about the CLF-based nonlinear RHC approach and its application on the Caltech ducted fan using NTG.

## Additional Resources

Constrained Control and Estimation - An Optimisation Approach, G. C. Goodwin, M. M. Seron, J. A. De Dona. Springer Verlag, 2005. This is a recent book treating constrained control and estimation in a unified framework (including finite horizon optimal control and RHC) using discrete-time formulation. The website has a lot of additional useful and interesting material.

Unconstrained Receding-Horizon Control of Nonlinear Systems, A. Jadbabaie, J. Yu and J. Hauser. IEEE Transactions on Automatic Control, May 2001, Vol. 46, No. 5, pp. 776-783. This paper might be a little dense for the first read, but contains an essence of A. Jadbabaie's PhD thesis on CLF-based nonlinear RHC.

Nonlinear Receding Horizon Control: A Control Lyapunov Function Approach, A. Jadbabaie. PhD Thesis, 2000.

Real-Time Optimal Trajectory Generation for Constrained Dynamical Systems, M. Milam. PhD Thesis, 2003.

NTG software, version 2.2a, 2002. This is the last publically released version of NTG. The documentation is a bit sparse, but the examples are heavily commented.

Optragen, version 1.0, 2006. This is a new MATLAB toolbox for optimal trajectory generation written by Raktim Bhattacharya, a former postdoc at Caltech. This version does not run in real-time, but has a much more user-friendly interface than NTG.