Optimal control of a co-rotating vortex pair: averaging and impulsive control

Nonlinear Dynamics and Ergodic Theory Methods in Control

“…Another student (Zoran Levnajid) worked on problems in visualization of dynamical ffj^tems [9]. A postdoc (Dmitri Vainchtein) continued working on the problem of flow control using tools from dynamical systems theory and vdrtex dynamics [35,33] and pursued a problem in control of nanoparticle separation [34]. The PI worked on ergodic theory methods for control of systems with drift [14,15] and optimization of mixing in a paper appeared in the journal Nature [25].…”

“…A specific problem of great interest in fluid dynamics is that of vortex merger, that we studied in [35]. Two-dimensional incompressible flows tend to generate coherent vortical structures.…”

“…), is that of vortex merger. We studied the case when vortices are at a large distance compared with the core radius in [35]. The case when the vortices are in close proximity can be studied using the vortex patch model, as done in [33].…”

Stabilization of vortices in the wake of a circular cylinder using harmonic forcing

“…Active control seeks to stabilize the flow with the use of an actuator. The various actuators that have been proposed in the literature include a blowing-suction mechanism [6][7][8][9], transverse oscillation of the cylinder [10], rotation of the cylinder about itself [11][12][13], rotation of parts of the cylinder's walls [14], electromagnetic devices [15], piezo-ceramic materials [16], and rotary devices [17]. Refer to [18] for a recent review of the literature on flow control.…”

p-moment stability of stochastic impulsive differential equations and its application in impulsive control

“…For the abrupt change, there may emerge jumps in the evolution, which lead to the non-smooth effects of the system. In recent years, significant progress has been made in the study of impulsive differential equations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] : Lakshmikantham et al [1] brought forward a lot of basic methods firstly, which were used in the study of impulsive differential equations. And an important theory, the stability of an impulsive control scheme is equivalent to the stability of trivial solution of an impulsive differential equation, was proved in ref.…”