Optimal Shortcuts to Adiabatic Control by Lagrange Mechanics
1International Center of Quantum Artificial Intelligence for Science and Technology (QuArtist), Department of Physics, Shanghai University, Shanghai 200444, China.
Entropy (Basel, Switzerland)
|May 27, 2023
Summary
Researchers designed an optimal cartpole trajectory using inverse engineering and optimal control theory. This method ensures fast, stable transport with the pendulum upright at start and end.
Area of Science:
- Robotics and Control Systems
- Mechanical Engineering
- Applied Mathematics
Background:
- Cartpole systems are classic challenges in control theory.
- Achieving fast and stable transport requires advanced control strategies.
- Anharmonic effects in cartpole dynamics can complicate control.
Purpose of the Study:
- To design an optimal trajectory for fast and stable cartpole transport.
- To apply inverse engineering and optimal control theory to cartpole dynamics.
- To investigate the anharmonic effects on cartpole control.
Main Methods:
- Utilized inverse engineering based on Lagrange mechanics.
- Applied optimal control theory, specifically time minimization.
- Employed relative displacement between the cart and pole as a controller.
- Analyzed the anharmonic effect of the cartpole system.
Main Results:
- Developed an optimal trajectory for cartpole transport.
- The derived optimal trajectory has a bang-bang form.
- Ensured the pendulum is in a vertical upward position at initial and final moments.
- Demonstrated oscillation within a small angle range.
Conclusions:
- The combination of inverse engineering and optimal control provides an effective method for designing fast and stable cartpole trajectories.
- The bang-bang control strategy derived from time minimization is suitable for achieving desired cartpole states.
- The approach successfully addresses anharmonic effects for improved system performance.
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