CROSS-FEEDBACK-CONTROLLED HYSTERON SYNTHESIZED HYSTERESIS NETWORKS FOR SIGNAL PROCESSING, CONTROLLERS, MUSIC, AND COMPUTER SIMULATIONS IN PHYSICS, ENGINEERING, AND ECONOMICS
A method for synthesis of an advanced hysteresis function of a plurality of inputs providing cross-feedback-controlled hysteron synthesized hysteresis networks for signal processing, controllers, music, and computer simulations in physics, engineering, and economics is described. The method includes receiving and processing of a plurality of input signals with at least two parameterized multivariable nonlinearities, each parameterized multivariable nonlinearity serving as a parameterized hysteron, to produce at least one associated output signal. The output signals are processed by controller functions, each controller function comprising memory and producing at least one control signal responsive to at least one of the output signals and for controlling an associated parameterized hysteron. The resulting system provides a hysteretic response to at least one of the plurality of input signals, and can be used in the modeling and nonlinear control of systems involving networks of gears, electrical transformers, economic processes, or other networked hysteretic elements.
1 . A computer-implemented method for synthesis of a hysteresis function of a plurality of inputs, the method comprising:
receiving a plurality of input signals;
processing selected input signals from the plurality of input signals with at least two parameterized multivariable nonlinearities, each parameterized multivariable nonlinearity serving as a parameterized hysteron and configured to produce at least one associated output signal; and
processing the plurality of input signals with at least one computing device, the at least one computing device comprising a numerical processor, the numerical processor for computing at least two controller functions comprising a memory function; and
configuring the first controller function to produce at least one first control signal responsive to at least one of the output signals from a first of the parameterized multivariable nonlinearities, the at least one first control signal for controlling the parameterized hysteron of a first other of the parameterized multivariable nonlinearities,
configuring the second controller function to produce at least one second control signal responsive to at least one of the output signals from a second of the parameterized multivariable nonlinearities, the at least one first control signal for controlling the parameterized hysteron of a second other of the parameterized multivariable nonlinearities,
wherein the at least one first control signal is used to control the parameterized hysteron of the first other of the parameterized multivariable nonlinearities so as to create a an associated output signal comprising a hysteretic response to at least one of the plurality of input signals, and
wherein the at least one second control signal is used to control the parameterized hysteron of the second other of the parameterized multivariable nonlinearities so as to create an associated output signal comprising a hysteretic response to at least one of the plurality of input signals.
2 . The method of claim 1 wherein the first control signal comprises a single control signal.
3 . The method of claim 1 wherein the first control signal comprises a plurality of control signals.
4 . The method of claim 1 wherein the controller function is responsive to at least one extremal value of the amplitude of at least one of the plurality of input signals.
5 . The method of claim 1 wherein the controller function is responsive to at least an integration of the amplitude of at least one of the plurality of input signals.
6 . The method of claim 1 wherein the controller function is responsive to at least one time-derivative of the amplitude of at least one of the plurality of input signals.
7 . The method of claim 1 wherein the controller function is responsive to the sign of the time derivative of at least one of the plurality of input signals but independent of the rate of change of at least one of the plurality of input signals.
8 . The method of claim 1 wherein the controller function is responsive to the sign of the time derivative of at least one of the plurality of input signals and responsive to the rate of change of at least one of the plurality of input signals.
9 . The method of claim 1 wherein the controller function is responsive to at least one extremal value of the phase of at least one of the plurality of input signals.
10 . The method of claim 1 wherein the controller function is responsive to at least an integration of the phase of at least one of the plurality of input signals.
11 . The method of claim 1 wherein the controller function is responsive to at least one time-derivative of the phase of at least one of the plurality of input signals.
12 . The method of claim 1 wherein the controller function is responsive to at least one extremal value of a quantity responsive to the signal spectrum of at least one of the plurality of input signals.
13 . The method of claim 1 wherein the controller function is responsive to at least an integration of a quantity responsive to the signal spectrum of at least one of the plurality of input signals.
14 . The method of claim 1 wherein the controller function comprises fractional-order dynamics.
15 . The method of claim 1 wherein the controller function is responsive to at least one time-derivative of a quantity responsive to the signal spectrum of at least one of the plurality of input signals.
16 . The method of claim 1 wherein the parameterized hysteron comprises a parameterized all-pass filter imposing phase modulation on at least one input signal, the phase modulation responsive to the at least one control signal.
17 . The method of claim 1 wherein the parameterized hysteron comprises a parameterized filter imposing at least amplitude modulation on at least one input signal, the amplitude modulation if further responsive to spectral content of the at least one input signal.
18 . The method of claim 16 wherein the phase modulation if further responsive to spectral content of the at least one input signal.
19 . The method of claim 1 wherein the first other of the parameterized multivariable nonlinearities is the second of the parameterized multivariable nonlinearities.
20 . The method of claim 1 wherein the second other of the parameterized multivariable nonlinearities is the first of the parameterized multivariable nonlinearities.