Control Lyapunov function (CLF) methodology tries to minimize a quadratic cost-function as; V(x)=x^2, through a point-wise setup. However, optimal control minimizes a quadratic cost-function through a time-interval as; J(x)=int(x^2.dt,0..infinity), through the time axis.
Therefore, we may conclude CLF is equivalent to proportional-control, while optimal control is an integral-control methodology. The robustness of optimal-control is attributable to its integral format.
Dear Saeb AmirAhmadi Chomachar ,
Technical CFL is the basis of the main loop design methods such as Bellman's dynamic programming in optimal control. We can consider a CFL as an optimal tracking control (finite or infinite) with more robustness by the introduction of LMI.
For more details and information about this subject i suggest you see links and attached file on topic.
https://arxiv.org/pdf/1803.08980.pdf
http://ames.gatech.edu/cdc_2012_agg_v_10_final.pdf
http://ames.gatech.edu/CFL_Robotics_TAC.pdf
Article Nonlinear Control of Interior PMSM Using Control Lyapunov Functions
https://shishirny.github.io/pages/publications/theses/NADUBETTUYADUKUMAR-DISSERTATION-2016.pdf
Article Nonlinear analysis and control of a reaction wheel pendulum:...
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It seems I have made a breakthrough. Please see the image and PDF attached here for your perusal. Thank You.
Salam Saeb,
Certainly the performance of a PI controller is significantly better than the integral action alone, which is why in practice one does not find a pure integral controller alone in the industry. Proportional action tends to upset the system in rapidity and integral action tends to reduce error asymptotically.
Best regards
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