Methods and systems for nonlinear adaptive control and filtering

An adaptive controller for a system, the controller comprising:

• a command module configured to provide an initial control output signal wherein the initial control output signal is usable to define the operation of the system;
• an output module coupled to the command module;
• a feedback module configured to provide a system state input;
• and
• an adaptive module coupled to the command module and the feedback module, the adaptive module comprising at least one adaptive sub-module coupled to the output module, each adaptive sub-module being configured to provide an output modifier to the output module;
• wherein
• each adaptive sub-module comprises a plurality of nonlinear components, each nonlinear component is configured to generate a response to the system state input and is coupled to the output module by at least one weighted coupling, and each weighted coupling has a corresponding connection weight;
• the response from each nonlinear component is weighted by the connection weights of the corresponding weighted couplings and the weighted responses are provided to the output module to form the output modifier;
• each adaptive sub-module further comprises a learning module configured to update the connection weights for each weighted coupling in that adaptive sub-module based on the initial control output signal, the learning module being configured to receive the initial control output signal and to determine the update to the connection weights using the initial control output signal;
• and
• the output module is configured to:
• generate a final control output signal by modifying the initial control output signal using the output modifiers;
• and
• transmit the final control output signal to the system, wherein the operation of the system is defined by the final control output signal;
• further wherein
• the at least one adaptive sub-module comprises a transformative adaptation sub-module configured to provide a transformative output modifier directly using the weighted responses from the nonlinear components;
• the initial control output signal defines a control signal in a first system space that is defined in relation to the operation of the system;
• modifying the initial control output signal using the transformative output modifier transforms the final control output signal to a second system space;
• and
• the second system space is also defined in relation to the operation of the system.

An adaptive filter for a system, the adaptive filter comprising:

• a command module configured to provide an initial future system state estimate, wherein the initial future system state estimate is usable to define a future system state input for a future point in time;
• an output module coupled to the command module;
• a feedback module configured to provide a system state input to the system, wherein the system uses the system state input in controlling the operation of the system;
• and
• an adaptive module coupled to the command module and the feedback module, the adaptive module comprising at least one adaptive sub-module coupled to the output module, each adaptive sub-module being configured to provide an output modifier to the output module;
• wherein
• each adaptive sub-module comprises a plurality of nonlinear components, wherein each nonlinear component is configured to generate a scalar output in response to the system state input and is coupled to the output module by at least one weighted coupling, each weighted coupling has a corresponding connection weight;
• the scalar output from each nonlinear component is weighted by the connection weights of the corresponding weighted couplings and the weighted outputs are provided to the output module to form the output modifier;
• each adaptive sub-module further comprises a learning module configured to update the connection weights for each weighted coupling in that adaptive sub-module based on the initial future system state estimate, the learning module being configured to receive the initial future system state estimate and to determine the update to the connection weights using the initial future system state estimate;
• the at least one adaptive sub-module comprises a particular adaptive sub-module configured to account for changes in one of the system dynamics and the system kinematics;
• and
• the learning module for the particular adaptive sub-module is configured to update the connection weights for each weighted coupling in that adaptive sub-module so that the output modifier from that particular adaptive sub-module is usable to modify the initial future system state estimate to account for the changes in the one of the system dynamics and the system kinematics;
• and
• the output module is configured to:
• generate a final future system state estimate by modifying the initial future system state estimate using the output modifiers, and
• transmit the final future system state estimate to the feedback module, wherein the feedback module uses the final future system state estimate to define the future system state input for the future point in time.