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200 Library Papers/farzanRobustControlSynthesis2020.md
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---
readstatus: false
dateread:
title: "Robust Control Synthesis and Verification for Wire-Borne Underactuated Brachiating Robots Using Sum-of-Squares Optimization"
readstatus: true
dateread:
title: Robust Control Synthesis and Verification for Wire-Borne Underactuated Brachiating Robots Using Sum-of-Squares Optimization
year: 2020
authors:
- "Farzan, Siavash"
- "Hu, Ai-Ping"
- "Bick, Michael"
- "Rogers, Jonathan"
citekey: "farzanRobustControlSynthesis2020"
- Farzan, Siavash
- Hu, Ai-Ping
- Bick, Michael
- Rogers, Jonathan
citekey: farzanRobustControlSynthesis2020
pages: 7744-7751
---
# Indexing Information
## DOI
@ -45,6 +30,12 @@ pages: 7744-7751
# Annotations
### Imported: 2024-10-16 10:34 am
>[!fail] Possibly Incorrect
> *A. Robust Control Synthesis and Verification Results The iterative optimization algorithm described in (15) to (17) was carried out for the brachiating robot system detailed above. We used polynomials of degree 4 for the Lagrange multipliers L, Lu, Lw and Lt, while the degree of the controller polynomial u ̄ is set to 1. The computing time required for the offline optimization convergence was approximately 4 hours. The long time required for convergence is not an issue for practical implementation of the controller, as the resulting feedback control policy u ̄(y ̄, t) (represented by time-varying gains on measurable states) will be hard-coded into the robot. To visualize the resulting robust backward reachable set, we project its 2-dimensional subspaces (out of the full 6dimensional state-space) on 2D plots. Fig. 4 shows the projections of each state vs. θ1, and compares the innerapproximation of the robust backward reachable sets for both the SOS-based controller and the time-varying LQR controller. As shown on the plots, the resulting invariant sets for the SOS-based controller cover a larger part of the statespace compared to TVLQR. The inner-approximation of the backward reachable set for the TVLQR controller is computed by solving the SOS program in (14a) without including the controller u ̄ in the optimization decision variables, eliminating the need for the second step optimization in (16). Furthermore, as depicted in Fig. 5, the verified set of initial conditions X0 which is driven to the desired set Xf by the SOS-based controller is larger in every dimension compared to the corresponding set for the TVLQR controller.*
>
> >[!note] Note
> >I don't think any of this actually means anything about being 'Robust'. They're saying the backwards sets are 'robust' but what does that even mean..? There is no mention of plant perturbation at all.
### Imported: 2024-10-16 10:48 am