The evaluation and visualization of system performance in chaotic dynamical systems

Fractal regularities of sub-harmonic motions perspective for pulse dynamics monitoring

“…Any fractal diagram volume can be reconstructed with necessary accuracy by use of interpolation and approximation of a fragment row. Now different fractal properties are used to characterise motion types (for instance, [6,7,[17][18][19][20]). As the result, it has begun possible to realize identification algorithms for all motion types from general viewpoint.…”

“…In this case, one is forced to use a priori information about the PECS dynamics, as it is impossible to partition the phase or parameter system spaces into the domains of particular motion existence or their groups in an on-line mode. For instance, there can be a priori partitions of the parameter space into the ''stable'' and ''unstable'' domains [5], or the ''stable'', ''unstable'', ''quazi-'', ''chaos'' domains [6], or of the phase space into the ''chaos'' and ''non-chaos'' domains [7], and in the last two cases fractal sets have been used.…”

Controller tuning via performance maps

“…A full description of performance map generation (PM) appeared in [17]. The major concepts of this are presented herein by permission.…”

Visualization ofN-dimensional performance maps

“…1 Although there are no formalized techniques employed in rule generation, some general heuristics can be employed. Normally, at least some a priori knowledge is held about the expected response of a system.…”

“…was developed in an effort to bring intuitive, graphical information conveyance to control and other dynamical systems. [1][2][3] A PM is a color-coded, graphical, computer representation of the performance of a dynamical system as its system parameters are varied. In effect, it provides an intuitive graphical description of the effects of parameter tuning.…”