Method for feedback linearization of neural networks and neural network incorporating same
First Claim
1. A method of adaptively controlling a plant having at least one measurable state and at least first and second unknown functions of said measurable state, comprising:
- sensing said at least one measurable state;
comparing said sensed state with a desired state in a first feedback loop to produce an error signal;
calculating, as a function of said sensed state, a first unknown function estimate using a first multi-layer neural network process in a second feedback loop, said first multi-layer neural network process having multiple layers of neurons with tunable weights;
calculating, as a function of said sensed state, a second unknown function estimate using a second multi-layer neural network process in a third feedback loop, said second multi-layer neural network process having multiple layers of neurons with tunable weights;
calculating a smooth control action as a function of said error signal, and as a function of said first and second unknown function estimates;
applying said smooth control action to said plant to maintain said at least one measurable state at said desired state; and
adaptively adjusting said tunable weights of said first and second multi-layer neural network processes as a function of said error signal.
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Abstract
A method for linearization of feedback in neural networks, and a neural network incorporating the feedback linearization method are presented. Control action is used to achieve tracking performance for a state-feedback linearizable, but unknown nonlinear control system. The control signal comprises a feedback linearization portion provided by neural networks, plus a robustifying portion that keep the control magnitude bounded. Proofs are provided to show that all of the signals in the closed-loop system are semi-globally uniformly ultimately bounded. This eliminates an off-line learning phase, and simplifies the initialization of neural network weights.
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Citations
5 Claims
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1. A method of adaptively controlling a plant having at least one measurable state and at least first and second unknown functions of said measurable state, comprising:
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sensing said at least one measurable state; comparing said sensed state with a desired state in a first feedback loop to produce an error signal; calculating, as a function of said sensed state, a first unknown function estimate using a first multi-layer neural network process in a second feedback loop, said first multi-layer neural network process having multiple layers of neurons with tunable weights; calculating, as a function of said sensed state, a second unknown function estimate using a second multi-layer neural network process in a third feedback loop, said second multi-layer neural network process having multiple layers of neurons with tunable weights; calculating a smooth control action as a function of said error signal, and as a function of said first and second unknown function estimates; applying said smooth control action to said plant to maintain said at least one measurable state at said desired state; and adaptively adjusting said tunable weights of said first and second multi-layer neural network processes as a function of said error signal. - View Dependent Claims (2, 3, 4)
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5. An adaptive controller for a plant including at least one measurable state and at least first and second unknown functions of said measurable state, comprising:
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means for sensing said at least one measurable state of said plant; a first multi-layer neural network having multiple layers of neurons with tunable weights, for receiving said at least one measurable state of said plant, for calculating a first unknown function estimate based on said at least one measurable state; a second multi-layer neural network having multiple layers of neurons with tunable weights, for receiving said at least one measurable state of said plant, for calculating a second unknown function estimate based on said at least one measurable state; an error amplifier for calculating a difference between said at least one measurable state and a desired state; means for calculating a smooth control action as a function of said difference, and as a function of said first and second unknown function estimates, and for applying said control action to said plant; and means for adaptively adjusting said tunable weights of said first and second multi-layer neural networks as a function of said difference.
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Specification