Control Synergies for Rapid Stabilization and Enlarged Region of Attraction for a Model of Hopping
Abstract
:1. Introduction
2. Biological Relevance and Novelty
3. Model
3.1. Running Model
3.2. Equations of Motion
4. Methods
4.1. Step-to-Step Analysis Using Poincaré Map
4.2. Control Synergies for Enlarging the Region of Attraction
4.2.1. Key Ideas Behind Control Synergies
4.2.2. Exponential Convergence Using Orbital Control Lyapunov Function
4.2.3. Region of Attraction
Algorithm 1: ROA() |
Input: fixed point Output: Initial conditions ’s 1 FIND() such that intersects 2 foreach do // is a small positive number 3 COMPUTE(’s) on the level set . 4 FIND( for each by solving optimization problem described by Equation (10). 5 if then 6 continue 7 else 8 break 9 end 10 end |
4.2.4. Using Optimization for Exponential Stabilization
5. Results
6. Discussion
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Zamani, A.; Bhounsule, P.A. Control Synergies for Rapid Stabilization and Enlarged Region of Attraction for a Model of Hopping. Biomimetics 2018, 3, 25. https://doi.org/10.3390/biomimetics3030025
Zamani A, Bhounsule PA. Control Synergies for Rapid Stabilization and Enlarged Region of Attraction for a Model of Hopping. Biomimetics. 2018; 3(3):25. https://doi.org/10.3390/biomimetics3030025
Chicago/Turabian StyleZamani, Ali, and Pranav A. Bhounsule. 2018. "Control Synergies for Rapid Stabilization and Enlarged Region of Attraction for a Model of Hopping" Biomimetics 3, no. 3: 25. https://doi.org/10.3390/biomimetics3030025