Extremum Seeking Adaptive Control of Beam Envelope in Particle Accelerators

Stochastic Averaging and Stochastic Extremum Seeking

“…ES has also been used in many diverse applications with unknown/uncertain systems, such as steering vehicles toward a source in GPS-denied environments [28,30,146], active flow control [15,16,24,53,63,64], aeropropulsion [104,144], colling systems [82,84] wind energy [32], photovoltaics [81], human exercise machines [148], optimizing the control of nonisothermal valve actuator [113], controlling Tokamak plasmas [25], and enhancing mixing in magnetohydrodynamic channel flows [96], timing control of HCCI engine combustion [62], formation flight optimization [20], control of aircraft endurance based on atmospheric turbulence [69], beam matching adaptive control [123], optimizing bioreactors [141], control of combustion instability [9], control of nonisothermal continuous stirred reactors [49], control of swirl-stabilized spray combustion [105], optimal control of current profile in the DIII-D tokamak [110], laser pulse shaping [115], control of beam envelope in particle accelerators [122], control of an axial-flow compressor [142], and stabilization of neoclassical tearing modes in tokamak fusion plasmas [143].…”

Constrained extremum seeking stabilization of systems not affine in control

“…Initial analytic studies paved the way for local and global stability results . Recent developments include the application of ES to PID tuning, the control of a tunable thermoacoustic cooler, control of beam envelope in particle accelerators, has been applied to moderately unstable systems, has been used for optimizing engine fuel consumption, a non‐gradient approach to global ES, stabilization of a nonlinear system with parametric uncertainties when a system model is available, fluctuation mitigation and velocity profile regulation in magnetically confined plasmas, power optimization of photovoltaic micro‐converters via Newton‐based ES, Newton‐based stochastic ES, a time‐varying approach for discrete‐time systems, constrained extremum seeking, gradient seeking, control of electromagnetic actuators, and multi‐parametric gain tuning for nonlinear control; a broad review is summarized in . In Fu and Ozguner, a model‐based ES approach is considered for control affine systems with unknown performance functions, which is robust to model uncertainties and disturbances.…”

Stochastic Averaging in Discrete Time and its Applications to Extremum Seeking

“…Extremum seeking is a non-model based real-time optimization tool and also a method of adaptive control. Since the first proof of the convergence of extremum seeking [11], the research on extremum seeking has triggered considerable interest in the theoretical control community ( [34], [6], [33], [31], [19], [32], [16]) and in applied communities ( [20], [21], [25]). According the choice of probing signals, the research on the extremum seeking method can be simply classified into two types: deterministic ES method ( [6], [1], [33], [31], [19], [32]) and stochastic ES method ( [18], [15], [14]).…”