Nonlinear system observation and control
View Patent ↗An observation system configured to observe at least one known state variable of an observed system includes a plurality of filters that are configured to receive a system input, and generate the at least one unknown state variable. Generating the unknown state variable includes processing the system input, a plurality of known state variables, and a time varying mode vector. An inverse system configured to observe at least one inverse state variable of an original system includes a plurality of filters that are configured to receive a system input, and generate the at least one inverse state variable. Generating the inverse state variable includes processing the system input, a plurality of known state variables associated with the original system, and a time varying mode vector associated with the original system.
1. An observation system configured to observe at least one unknown state variable of an observed system, comprising:
an input interface configured to receive a system input; and
a processing system coupled to the input interface and comprising a plurality of filters, the processing system being configured to
generate the at least one unknown state variable, including by processing the system input, a plurality of known state variables, and a time varying mode vector {tilde over (G)} n , wherein n corresponds to a sequence of integers.
2. An observation system as recited in claim 1 , wherein the system input is associated with the observed system, the plurality of known state variables, correspond to a plurality of states of the observed system, and the time varying mode vector is associated with the observed system.
3. An observation system as recited in claim 1 , wherein the observed system is a nonlinear system.
4. An observation system as recited in claim 1 , wherein the plurality of known state variables corresponds to a plurality of states of the observed system at a given time.
5. An observation system as recited in claim 1 , wherein the plurality of filters form a filter bank that includes a delay stage configured to feed back the at least one unknown state variable that is generated.
6. An observation system as recited in claim 1 , wherein the at least one unknown state variable includes a state variable of the observed system at a future time.
7. An observation system as recited in claim 1 , wherein the time varying mode vector is determined according to a function.
8. An observation system as recited in claim 1 , wherein the time varying mode vector is determined using a mode control signal.
9. An observation system as recited in claim 1 , wherein the time varying mode vector is determined using a mode control signal, and the mode control signal is determined according to stored values.
10. An observation system as recited in claim 1 , wherein at least one of the plurality of filters has an output that is associated with a next state of the filter.
11. An observation system as recited in claim 1 , wherein the unknown state variable is controlled by changing the mode vector.
12. An observation system as recited in claim 1 , wherein the unknown state variable is controlled by changing the system input.
13. An observation system as recited in claim 1 , wherein the plurality of filters is further configured to estimate an output of the observed system.
14. A method of observing at least one unknown state variable of an observed system, comprising:
receiving a system input associated with the observed system; and
generating the at least one unknown state variable, including by processing the system input, a plurality of known state variables that correspond to a plurality of states of the observed system, and a time varying mode vector {tilde over (G)} n associated with the observed system, wherein n corresponds to a sequence of integers.
15. A method as recited in claim 14 , wherein the observed system is a nonlinear system.
16. A method as recited in claim 14 , wherein the system input is a first system input, the time varying mode vector is a first time varying mode vector, and the plurality of known state variables is a first plurality of known state variables; and the method further comprising:
receiving a second system input; and
generating a second plurality of unknown state variables using the second system input, a second time varying mode vector associated with the observed system, and a second system input.
17. A method as recited in claim 14 , wherein the plurality of known state variables corresponds to a plurality of states of the observed system at a given time.
18. A method as recited in claim 14 , further comprising determining the time varying mode vector according to a function.
19. A method as recited in claim 14 , further comprising determining the mode vector based on a mode control signal.
20. A method as recited in claim 14 , further comprising determining the mode vector based on a mode control signal, and wherein the mode control signal is determined according to stored values.
21. A method as recited in claim 14 , wherein the unknown state variable is controlled by changing the mode vector.
22. A method as recited in claim 14 , wherein the unknown state variable is controlled by changing the system input.
23. A method as recited in claim 14 , further comprising identify a correspondence between a constituent mode of the mode vector and a configuration state.
24. A computer program product for observing at least one unknown state variable of an observed system, the computer program product being embodied in a computer readable storage medium and comprising computer instructions for:
receiving a system input associated with the observed system; and
generating the at least one unknown state variable, including by processing the system input, a plurality of known state variables that correspond to a plurality of states of the observed system, and a time varying mode vector {tilde over (G)} n associated with the observed system, wherein n corresponds to a sequence of integers.
25. An inverse system configured to observe at least one inverse state variable of an original system, comprising:
an input interface configured to receive a system input; and
a processing system coupled to the input interface and comprising a plurality of filters, the processing system being configured to
generate the at least one inverse state variable, including by processing the system input, a plurality of known state variables associated with the original system, and a time varying mode vector {tilde over (G)} n associated with the original system, wherein n corresponds to a sequence of integers.
26. An inverse system as recited in claim 25 , wherein the system input corresponds to an output of the original system.
27. An inverse system as recited in claim 25 , wherein the plurality of filters is further configured to estimate an input of the original system.
28. An inverse system as recited in claim 25 , wherein the original system is a nonlinear system.
29. An inverse system as recited in claim 25 , wherein the plurality of filters form a filter bank that includes a delay stage configured to feedback the at least one inverse state variable.
30. An inverse system as recited in claim 25 , wherein the time varying mode vector is determined according to a function.
31. A method of observing at least one inverse state variable of an original system, comprising:
receiving a system input; and
generating the at least one inverse state variable, including by processing the system input, a plurality of known state variables associated with the original system, and a time varying mode vector {tilde over (G)} n associated with the original system, wherein n corresponds to a sequence of integers.
32. A method as recited in claim 31 , wherein the system input corresponds to an output of the original system.
33. A method as recited in claim 31 , further comprising estimating an input of the original system.
34. A method as recited in claim 31 , wherein the original system is a nonlinear system.
35. A method as recited in claim 31 , wherein the plurality of filters form a filter bank that includes a delay stage configured to feedback the at least one inverse state variable.
36. A method as recited in claim 31 , wherein the time varying mode vector is determined according to a function.
37. A computer program product for observing at least one inverse state variable of an original system, the computer program product being embodied in a computer readable storage medium and comprising computer instructions for:
receiving a system input; and
generating the at least one inverse state variable, including by processing the system input, a plurality of known state variables associated with the original system, and a time varying mode vector {tilde over (G)} n associated with the original system, wherein n corresponds to a sequence of integers.