Dear All,
When I do my project, I need add a constraint to the trajectory at a certain time within nonlinear optimal control design. For example, there are two dimensional system , x and y. I would like to set x(3) = 5 and y(3) = 6 (the time interval is [0, 5]s), which means I want the trajectory travel (5, 6) at 3 second.
Is there any way to formulate that ?
If there are some papers or materials can be recommends , that would be great.
thanks
Jie
One powerful tool that you can use is “Nonlinear model predictive control”. To this aim, you need to incorporate your constraints, which in your case is pointwise, in the optimization problem. See the below link for more details
“https://folk.ntnu.no/torarnj/nonlinear.pdf”
Another category of tools that you can use is “Reference and command governors”. Roughly speaking, the main idea for this type of tool is modifying the reference of the closed-loop system or some parameters so that the transient behavior is always compatible with the system constraints (including pointwise constraints). Generally, reference and command governor’s schemes have a tendency to be easy to understand, systematic to utilize, and computationally inexpensive to run, which makes them a great candidate for augmenting to existing optimal solutions that were not specifically designed to handle constraints. See the below paper for more details
“Kolmanovsky, E. Garone and S. Di Cairano, "Reference and command governors: A tutorial on their theory and automotive applications," 2014 American Control Conference, 2014, pp. 226-241, doi: 10.1109/ACC.2014.6859176.”
Another way to handle your problem is to design a proper safety filter (reactive or proactive) to satisfy your pointwise constraints. For example, see
“Wabersich, Kim Peter, and Melanie N. Zeilinger. "A predictive safety filter for learning-based control of constrained nonlinear dynamical systems." Automatica 129 (2021): 109597.”
Hi Jie Yao,
Please find attached some articles on this point, I hope they can help you.
With regards,
- Badges
- Science topic
- Similar topics
- Geoscience
- Asia
- India