Neural networks for prediction and control
First Claim
1. A method for estimation, comprising the steps of:
- (a) specifying an estimation error criterion, a class of allowed estimation functions, an initial estimation function selected from said class, and an initial measurement estimate, (b) inputting at least one measurement vector, (c) determining an updated estimation function using said estimation error criterion, a previously determined estimation function, a previous measurement estimate, and said at least one measurement vector, (d) determining an updated measurement estimate using an estimation function and said measurement vector, (e) outputting said updated measurement estimate, and (f) iterating steps (b) through (e) a plurality of times, wherein the step of determining an updated estimation function is performed using a neural network equivalent system (NNES).
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Abstract
Neural networks for optimal estimation (including prediction) and/or control involve an execution step and a learning step, and are characterized by the learning step being performed by neural computations. The set of learning rules cause the circuit'"'"'s connection strengths to learn to approximate the optimal estimation and/or control function that minimizes estimation error and/or a measure of control cost. The classical Kalman filter and the classical Kalman optimal controller are important examples of such an optimal estimation and/or control function. The circuit uses only a stream of noisy measurements to infer relevant properties of the external dynamical system, learn the optimal estimation and/or control function, and apply its learning of this optimal function to input data streams in an online manner. In this way, the circuit simultaneously learns and generates estimates and/or control output signals that are optimal, given the network'"'"'s current state of learning.
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Citations
47 Claims
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1. A method for estimation, comprising the steps of:
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(a) specifying an estimation error criterion, a class of allowed estimation functions, an initial estimation function selected from said class, and an initial measurement estimate, (b) inputting at least one measurement vector, (c) determining an updated estimation function using said estimation error criterion, a previously determined estimation function, a previous measurement estimate, and said at least one measurement vector, (d) determining an updated measurement estimate using an estimation function and said measurement vector, (e) outputting said updated measurement estimate, and (f) iterating steps (b) through (e) a plurality of times, wherein the step of determining an updated estimation function is performed using a neural network equivalent system (NNES). - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16)
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12. In an estimation method comprising the steps of:
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(a) determining a first estimation function, (b) determining a vector, (c) applying said estimation function to said vector, and (d) determining a second estimation function, the improvement comprising determining said second estimation function as a function of said first estimation function and said vector by means of a neural network equivalent system (NNES).
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17. A method for control, comprising the steps of:
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(a) specifying a control cost criterion, a class of allowed control functions, and an initial control function selected from said class, (b) specifying a sequence of time values, (c) for each time value in said sequence of time values, determining an updated control function corresponding to said time value using said control cost criterion and a previously determined control function, (d) inputting state data comprising at least one of a plant state vector, a measurement vector, or a measurement estimate, (e) determining a control vector using one of said updated control functions and said state data, (f) outputting said control vector, (g) optionally iterating steps (d) through (f) one or more times, (h) iterating steps (b) through (g) one or more times, wherein step (c) is performed using a neural network equivalent system (NNES). - View Dependent Claims (18, 19, 20, 21, 22, 23, 24, 25)
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26. A method for combined estimation and control, comprising the steps of:
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an estimation step comprising the steps of;
(a) specifying an estimation error criterion, a class of allowed estimation functions, an initial estimation function selected from said class, and an initial measurement estimate, (b) inputting at least one measurement vector, (c) determining an updated estimation function using said estimation error criterion, a previously determined estimation function, a previous measurement estimate, and said at least one measurement vector, (d) determining an updated measurement estimate using an estimation function and said measurement vector, (e) outputting said updated measurement estimate, and (f) iteration of steps (b) through (e) a plurality of times, wherein the step of determining an updated estimation function is performed using a neural network equivalent system, and a control step comprising the steps of;
(g) specifying a control cost criterion, a class of allowed control functions, and an initial control function selected from said class, (h) specifying a sequence of time values, (i) for each time value in said sequence of time values, determining an updated control function corresponding to said time value using said control cost criterion and a previously determined control function, (j) inputting state data comprising at least one of a plant state vector, a measurement vector, or a measurement estimate, (k) determining a control vector using one of said updated control functions and said state data, (l) outputting said control vector, (m) optionally iterating steps (j) through (l) one or more times, (n) iterating steps (h) through (m) one or more times, wherein step (i) is performed using a neural network equivalent system (NNES), wherein said estimation and control steps are performed by a single neural network equivalent system (NNES).
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27. In a method for estimation, control, system identification, reinforcement learning, supervised learning, unsupervised learning, and/or classification, comprising a step of iteratively transforming a first matrix into a second matrix, the improvement comprising the steps of:
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(a) specifying a functional relationship between said first matrix and a first set of vectors, (b) specifying a transformation of each vector in said first set of vectors into a vector of a second set of vectors, (c) implementing said first set of vectors as a first set of activity vectors in a neural network equivalent system (NNES), (d) implementing an approximation of said first matrix as a first set of connection strength values in said NNES, (e) determining, by means of neural computations, a second set of connection strength values as a function of said first set of activity vectors, and (f) determining, by means of neural computations, a second set of activity vectors as a function of said first set of activity vectors and of said first set of connection strength values, wherein said second set of connection strength values approximates said second matrix. - View Dependent Claims (28, 29, 30)
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- 31. A neural network equivalent system (NNES) comprising a plurality of activity vectors and at least one set of connection strength values, wherein said set of connection strength values is updated using a learning rule that comprises the application of a ganging operation to said plurality of activity vectors.
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36. A neural network equivalent system (NNES) for estimation and/or control comprising:
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(a) a plurality of nodes connected to perform a sequence of steps in a prescribed order, (b) said plurality of nodes comprising processors programmed or constructed to perform an execution step and/or a learning step using neural computations, (c) input means for providing measurement values to said plurality of nodes, (d) neural computation means for determining a plurality of measurement estimates, plant state estimates, and/or control vector signals using said measurement signals, and (e) means for outputting said plurality of measurement estimates, plant state estimates, and/or control vector signals. - View Dependent Claims (37, 38, 39, 40, 41, 42)
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43. A recurrent neural network equivalent system (NNES) for estimation, wherein a measurement vector is input to the network at a plurality of distinct locations and/or distinct times.
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44. A recurrent neural network equivalent system (NNES) for estimation and/or control, comprising time-sequencing means whereby
(a) the data flow is organized in time using major and minor time steps, (b) each of said major time steps corresponds to the input of at least one measurement vector, (c) each of said major time steps is divided into a plurality of minor time steps, and (d) the data flow is organized so that specified network functions are carried out at specified locations and at specified minor time steps.
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45. A recurrent neural network equivalent system (NNES) for estimation and/or control comprising:
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(a) means for inputting a plurality of measurement vectors, (b) means for learning an estimation and/or control function using said measurement vectors, and (c) means for performing system identification using said measurement vectors.
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46. A recurrent neural network equivalent system (NNES) for estimation and/or control comprising:
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(a) means for storing, as a set of connection strengths, the values of a matrix, (b) means for updating said values of said matrixt and (c) means for computing the result of multiplying an activity vector by a member selected from the group consisting of said matrix and the inverse of said matrix. - View Dependent Claims (47)
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Specification