Abstract
This paper considers control synthesis for polynomial control systems. The developed method leans upon Lyapunov stability and Bernstein certificates of positivity. We strive to develop an algorithm that computes a polynomial control and a polynomial Lyaponov function in the simplicial Bernstein form. Subsequently, we reduce the control synthesis problem to a finite number of evaluations of a polynomial within Bernstein coefficient bounds representing controls and Lyapunov functions. As a consequence, the equilibrium is asymptotically stable with this control.
| Original language | English |
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| Publication date | 2018 |
| Number of pages | 7 |
| DOIs | |
| Publication status | Published - 2018 |
| Event | IFAC Conference on Analysis and Design of Hybrid Systems - University of Oxford, Oxford, United Kingdom Duration: 11 Jul 2018 → 13 Jul 2018 http://www.cs.ox.ac.uk/conferences/ADHS18/ |
Conference
| Conference | IFAC Conference on Analysis and Design of Hybrid Systems |
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| Location | University of Oxford |
| Country/Territory | United Kingdom |
| City | Oxford |
| Period | 11/07/2018 → 13/07/2018 |
| Internet address |
Keywords
- Bernstein basis
- certificates of positivity
- control design
- stability
- subdivision of simplex