Modeling Nonlinear Systems

Abstract

Systems and techniques, including machine-readable instructions, for modeling of nonlinear systems. In one aspect, an apparatus includes a collection of two or more inputs configured and arranged to receive input signals, a collection of two or more outputs configured and arranged to output output signals, a processing unit configured to transform the input signals into the output signals, wherein the transformation is non-linear and treats the non-linear system as a collection of multiple input, single output non-linear systems, and a data storage that stores characteristics of the transformation.

1 . An apparatus for modeling a non-linear system, comprising:
 a collection of two or more inputs configured and arranged to receive input signals;   a collection of two or more outputs configured and arranged to output output signals;   a processing unit configured to transform the input signals into the output signals, wherein the transformation is non-linear; and   a data storage that stores characteristics of the non-linear transformation, including
 a first characterization of an impact of a first input signal received on a first of the inputs on an effect that a second input signal received on a second of the inputs has on an output signal output by a first of the outputs, and 
 a second characterization of an impact of the same first input signal on an effect that a third input signal on the same first of the inputs has on the same output signal output by the same first of the outputs. 
   
     
     
         2 . The apparatus of  claim 1 , wherein the inputs, the outputs, and the processing unit are configured as a hippocampal-cortical neural prostheses. 
     
     
         3 . The apparatus of  claim 1 , wherein the processing unit comprises a stochastic noise source that stochastically changes the transformation of the input signals into the output signals. 
     
     
         4 . The apparatus of  claim 2 , wherein the processing unit comprises a threshold configured to discretize the output signals. 
     
     
         5 . The apparatus of  claim 2 , wherein the processing unit is configured to use self-kernels to describe nonlinear dynamic interactions within same inputs of the collection of two or more inputs, and the processing unit is configured to use cross-kernels to describe nonlinear dynamic interactions between different inputs of the collection of two or more inputs. 
     
     
         6 . The apparatus of  claim 5 , wherein the processing unit is configured to use a feedback kernel to capture output-dependent system dynamics. 
     
     
         7 . The apparatus of  claim 6 , wherein the processing unit is configured to use a Laguerre expansion technique. 
     
     
         8 . (canceled) 
     
     
         9 . The apparatus of  claim 6 , wherein at least one of the self-kernels and the cross-kernels comprises a decaying feedforward kernel. 
     
     
         10 . (canceled) 
     
     
         11 . The apparatus of  claim 1 , wherein the characteristics stored by the data storage further comprise a third characterization of a linear transformation of the first input signal received on the first of the inputs into the output signal output by the first of the outputs. 
     
     
         12 . (canceled) 
     
     
         13 . The apparatus of  claim 2 , wherein:
 the hippocampal-cortical neural prostheses comprises an implantable neural stimulator;   the collection of two or more inputs comprises a collection of input electrodes; and   the collection of two or more outputs comprises a collection of output electrodes.   
     
     
         14 . A method for modeling a non-linear system, comprising:
 receiving, at a data processing apparatus, machine-readable information characterizing a collection of two or more inputs and two or more outputs from a multiple input, multiple output non-linear system; and   estimating, by the data processing apparatus, a collection of parameters for modeling the non-linear system by considering the multiple input, multiple output non-linear system to be a collection of multiple input, single output systems.   
     
     
         15 . The method of  claim 14 , wherein estimating the collection of parameters comprises estimating a parameter characterizing an impact of a first input signal received on a first of the multiple inputs on an effect that a second input signal received on a second of the multiple inputs has on an output signal output by a first of the multiple outputs. 
     
     
         16 . The method of  claim 14 , wherein estimating the collection of parameters comprises estimating a parameter characterizing an impact of a first input signal received on a first of the multiple inputs on an effect that a second input signal received on the first of the multiple inputs has on an output signal output by a first of the multiple outputs. 
     
     
         17 . The method of  claim 14 , wherein estimating the collection of parameters comprises estimating a parameter characterizing a linear transformation of a first input signal received on a first of the multiple inputs on an output signal output by a first of the multiple outputs. 
     
     
         18 . The method of  claim 14 , wherein estimating the collection of parameters comprises estimating a collection of kernels to effect a hippocampal-cortical neural prostheses. 
     
     
         19 . The method of  claim 18 , wherein estimating the collection of kernels comprises estimating a collection of feedforward cross kernels. 
     
     
         20 . The method of  claim 18 , wherein estimating the collection of kernels comprises estimating a collection of feedforward self kernels. 
     
     
         21 . The method of  claim 14 , wherein estimating the collection of parameters comprises modeling at least some of the multiple input, single output systems as including a stochastic noise source. 
     
     
         22 . The method of  claim 14 , further comprising:
 receiving, at the data processing apparatus, a collection of input signals; and   transforming, by the data processing apparatus, the input signals into a collection of output signals based on the estimating parameters for modeling the non-linear system.   
     
     
         23 . The method of  claim 14 , further comprising outputting, from the data processing apparatus, a collection of output signals based of the estimated collection of parameters. 
     
     
         24 . The method of  claim 23 , wherein outputting the collection of output signals comprises performing deep tissue stimulation. 
     
     
         25 . An apparatus for modeling a non-linear system, comprising:
 a collection of two or more inputs configured and arranged to receive input signals;   a collection of two or more outputs configured and arranged to output output signals;   a processing unit configured to transform the input signals into the output signals, wherein the transformation is non-linear and treats the non-linear system as a collection of multiple input, single output non-linear systems; and   a data storage that stores characteristics of the transformation.   
     
     
         26 . The apparatus of  claim 25 , wherein a first characteristic of the non-linear transformation stored by the data storage comprises a characterization of an impact of a first input signal received on a first of the inputs on an effect that a second input signal received on a second of the inputs has on an output signal output by a first of the outputs. 
     
     
         27 . The apparatus of  claim 25 , wherein a first characteristic of the non-linear transformation stored by the data storage comprises a first characterization of an impact of a first input signal on a first of the inputs on an effect that a second input signal on the first of the inputs has on an output signal output by a first of the outputs. 
     
     
         28 . The apparatus of  claim 25 , wherein the processing unit comprises a stochastic noise source that stochastically changes the transformation of the input signals into the output signals. 
     
     
         29 . The apparatus of  claim 25 , wherein the processing unit comprises a threshold configured to discretize the output signals. 
     
     
         30 . The apparatus of  claim 25 , comprising a hippocampal-cortical neural prostheses comprising a collection of kernels configured to estimate parameters of the transformation. 
     
     
         31 . The apparatus of  claim 30 , wherein the collection of kernels comprises a feedforward self kernel to describe nonlinear dynamic interaction within an input. 
     
     
         32 . The apparatus of  claim 31 , wherein the collection of kernels comprises a feedforward cross kernel to describe nonlinear dynamic interaction between different inputs. 
     
     
         33 . The apparatus of  claim 32 , wherein the collection of kernels comprises a feedback kernel to capture output-dependent system dynamics.