A Framework for Extremum Seeking Control of Systems With Parameter Uncertainties

A framework for a class of hybrid extremum seeking controllers with dynamic inclusions

“…Since dynamical systems described by set-valued mappings usually lack of the uniqueness of solutions property, we do not insist on it, but rather we analyze all the possible solutions that may emerge from a given compact set of initial conditions. Our main result is that, under some mild technical assumptions on the plant and the HESCs, the optimal operation set of the plant can be rendered practically asymptotically stable in the parameters of the control system, paralleling and extending classic results in extremum seeking control for continuous-time systems, such as those in Krstić and Wang (2000) and Nesić et al (2013).…”

“…Theorem 1 is a type of ''semi-global'' practical stability result, similar to those in Nesić et al (2013), Nesić et al (2010) and Tan et al (2006), for purely continuous-time systems. However, some subtle differences emerge for the hybrid case.…”

“…When D u := ∅, no solutions with jumps exist, and the HESC reduces to a constrained continuous-time set-valued extremum seeking control. If additionallyF δ is a Lipschitz continuous function, and C u = R n , we recover the standard gradient based extremum seeking control for black-box optimization of Nesić et al (2013), Tan et al (2006), and Nesić et al (2010).…”

“…This result was later extended in Tan, Nesić, and Mareels (2006) to obtain a semi-global practical stability result, whose foundation exploits the ''two-time scale'' setting analyzed in Teel, Moreau, and Nesić (2003). In general, these methods of analysis have proven to be instrumental for the design of several different extremum seeking controllers during the last years, e.g., , Dürr, Stanković, Ebenbauer, and Johansson (2013), Ghods and Krstić (2012), Ghaffari, Krstić, and Nesić (2012), Haring, Wouw, and Nesić (2013), Mills and Krstić (2014), Moase and Manzie (2012), Nesić, Mohammadi, and Manzie (2013), Nesić, Tan, Moase, and Manzie (2010) and Poveda and Quijano (2015), with applications in ABS break control (Yu & Ozguner, 2002), formation flight optimization, (Binetti, Ariyur, Krstić, & Bernelli, 2003), learning in non-cooperative games (Frihauf, Krstić, & Başar, 2012;Kutadinata, Moase, & Manzie, 2015), dynamic resource allocation (Poveda & Quijano, 2012, robot source seeking (Cochran, Kanso, Kelly, Xiong, & Krstić, 2009), optimization of wind turbines (Ghaffari, Krstić, & Seshagiri, 2014), and human exercise machine control (Zhang, Dawson, Dixon, & Xian, 2006), for example. One of the main limitations of existing ESCs based on averaging and singular perturbation theory is that, in general, they cannot deal with the presence of hybrid dynamics during the seeking process, i.e., dynamics that exhibit characteristics typical of both continuous-time systems and discrete-time systems.…”

Extremum-seeking control of a supercritical carbon-dioxide closed Brayton cycle in a direct-heated solar thermal power plant

“…Under this framework, ES (extremum-seeking) algorithms require minimal knowledge of the plant being controlled, largely treating the plant as a 'black box', and therefore avoiding the complications due to model mismatch that may face other modelbased approaches. Alternative ESC variants include methods that include partial plant information [21], in a 'grey box' framework. An ESC method with the ability to be tuned for a wide range of operating conditions and independent of the plant map has also been experimentally demonstrated for the reduction of thermoacoustic oscillations in premixed, gas-turbine combustors [22].…”