초록 ▼

An adaptive control system (ACS) uses direct output feedback to control a plant. The ACS uses direct adaptive output feedback control developed for highly uncertain nonlinear systems, that does not rely on state estimation. The approach is also applicable to systems of unknown, but bounded dimension

An adaptive control system (ACS) uses direct output feedback to control a plant. The ACS uses direct adaptive output feedback control developed for highly uncertain nonlinear systems, that does not rely on state estimation. The approach is also applicable to systems of unknown, but bounded dimension, whose output has known, but otherwise arbitrary relative degree. This includes systems with both parameter uncertainty and unmodeled dynamics. The result is achieved by extending the universal function approximation property of linearly parameterized neural networks to model unknown system dynamics from input/output data. The network weight adaptation rule is derived from Lyapunov stability analysis, and guarantees that the adapted weight errors and the tracking error are bounded.

대표청구항 ▼

That which is claimed: 1. An adaptive control system (ACS) for controlling a plant having a number of unknown internal states, said plant comprising at least one sensor and at least one actuator, said ACS comprising an adaptive controller operatively connected to the at least one sensor to receive

That which is claimed: 1. An adaptive control system (ACS) for controlling a plant having a number of unknown internal states, said plant comprising at least one sensor and at least one actuator, said ACS comprising an adaptive controller operatively connected to the at least one sensor to receive a plant output signal y and operatively connected to the at least one actuator to generate at least one control signal δc to control the plant based on a plant output signal y, the adaptive controller being operatively connected to receive the plant output signal y from at least one sensor without knowledge of the internal states by output feedback from the plant and generating the control signal δc to regulate the plant output signal y, the plant output signal y being a function of the full plant state x having known but unrestricted relative degree r. 2. An ACS as claimed in claim 1 wherein the adaptive controller comprises a linear controller contributing to generation of the control signal δc to control the plant based on the plant output signal y and an approximate linear dynamic model of the plant, and further comprises an adaptive element contributing to generation of the control signal δc based on the plant output signal y to control unmodeled plant dynamics using adaptive control. 3. An ACS as claimed in claim 2 wherein the adaptive element comprises a neural network implementing adaptive control of the plant via the control signal δc based on the plant output signal y. 4. An ACS as claimed in claim 3 wherein the adaptive element uses at least one time-delayed version yd of the plant output signal y, that is supplied together with the plant output signal y as inputs to the neural network, the neural network generating an adaptive control signal vad contributing to generation of the control signal δc to control the plant output y despite unmodeled plant dynamics, based on the time-delayed signal yd and the plant output signal y, the time-delayed version signal yd and the plant output signal y, to ensure boundedness of the tracking error signal {tilde over (y)}, the tracking error signal {tilde over (y)} being a difference of the plant output signal y and a commanded plant output signal yc. 5. An ACS as claimed in claim 3 wherein the neural network of the adaptive element comprises at least one basis function φ and at least one connection weight W used to generate an adaptive control signal vad contributing to generation of the command control signal δc, the adaptive element further comprising an error conditioning element coupled to receive the basis function φ, the error conditioning element filtering the basis function φ with a transfer function T-1(s) to produce filtered basis function φf used to modify the connection weight(s) W of the neural network through feedback to ensure boundedness of the tracking error signal {tilde over (y)}. 6. An ACS as claimed in claim 1 wherein the adaptive controller comprises a command filter unit generating an rth derivative yc(r) of the plant output signal y in which r is an integer indicating the number of times the plant output signal y must be differentiated with respect to time before an explicit dependence on the control variable is revealed. 7. An ACS as claimed in claim 1 wherein the adaptive controller comprises: an error signal generator generating a tracking error signal {tilde over (y)} indicating the difference between the plant output signal y and a commanded output signal yc; a linear controller coupled to receive the tracking error signal {tilde over (y)}, the linear controller generating a transformed signal {tilde over (y)}ad based on the tracking error signal {tilde over (y)}; and an adaptive element coupled to receive the transformed signal {tilde over (y)}ad and generating an adaptive control signal vad based thereon, the adaptive element operating on the transformed signal {tilde over (y)}ad to generate the adaptive signal vad such that the transfer function from vad to {tilde over (y)}ad is strictly positive real (SPR). 8. An ACS as claimed in claim 1 wherein sensed variables affecting the state of the plant, in addition to the plant output signal y, are fed back to the ACS to control the plant. 9. A linear controller coupled to receive a tracking error signal {tilde over (y)} that is a vector difference of a plant output signal y that is a function of a full plant state having known but unrestricted relative degree r, and a commanded output signal yc, the linear controller generating a pseudo-control component signal vdc based on a transfer function Ndc(s)/Ddc(s) and the tracking error signal {tilde over (y)}, the pseudo-control component signal vdc used by the linear controller to control the plant based on an approximate linear model of the plant, and the linear controller generating a transformed signal {tilde over (y)}ad based on a transfer function Nad(s)/Ddc(s) and the tracking error signal {tilde over (y)}, the transformed signal {tilde over (y)}ad supplied by the linear controller and used for adaptive control of the plant, the transfer functions Ndc(s)/Ddc(s) and Nad(s)/Ddc(s) selected to assure boundedness of the tracking error signal {tilde over (y)}. 10. A method comprising the step of: a) generating at least one control signal δc to control a plant having a number of unknown internal states based on a plant output signal y using an adaptive control system (ACS), the ACS connected to receive the plant output signal y from at least one sensor without knowledge of the internal states by output feedback from the plant to the ACS, the ACS generating the control signal δc to regulate the plant output signal y, the plant output signal y being a function of the full plant state x having known but unrestricted relative degree r; and b) supplying the control signal δc to at least one actuator used to control the plant. 11. A method as claimed in claim 10 wherein the control signal δc is generated in step (a) so as to control the plant output based on an approximate linear dynamic model, and so as to control the plant despite unmodeled plant dynamics based on an adaptive control technique. 12. A method as claimed in claim 10 wherein the adaptive control technique is implemented with a neural network. 13. A method as claimed in claim 10 wherein the command control signal δc is generated in step (a) based on sensed variables affecting the state x of the plant in addition to the plant output signal y. 14. A method comprising the steps of: a) selecting a transfer function Ndc(s)/Ddc(s) used in control of a plant based on a plant output signal y that is a function of states x existing in the plant, Ndc(s) being the numerator and Ddc(s) being the denominator of the transfer function Ndc(s)/Ddc(s) relating the tracking error signal {tilde over (y)} representing a vector difference between the plant output signal y and a commanded output signal yc, to a linear portion of a pseudo-control signal vdc used to control the plant; b) selecting a transfer function Nad(s)/Ddc(s) used in adaptive control of the plant based on the plant output signal y, Nad(s) being the numerator and Ddc(s) being the denominator of the transfer function Nad(s)/Ddc(s) relating the tracking error signal y to an adaptive portion of the tracking error signal {tilde over (y)}ad used to generate an adaptive portion of the pseudo-control signal vad; said steps (a) and (b) assuring boundedness of the tracking error signal {tilde over (y)}; and c) physically controlling the plant based on the linear portion of the pseudo-control signal vdc and the adaptive portion of the pseudo-control signal vad based on the selected transfer functions Ndc(s)/Ddc(s) and Nad(s)/Ddc(s) and the plant output signal y. 15. A method comprising the steps of: a) generating a tracking error signal {tilde over (y)} that is a vector difference of a plant output signal y that is a function of states x existing in a plant, and a commanded output signal yc; b) generating a pseudo-control component signal vdc based on a transfer function Ndc(s)/Ddc(s) and the tracking error signal {tilde over (y)}; c) generating a transformed signal {tilde over (y)}ad based on a transfer function Nad(s)/Ddc(s) and the tracking error signal {tilde over (y)}; d) controlling the plant with the pseudo-control component signal vdc, the pseudo-control component signal vdc controlling the plant based on an approximate linear model; and e) controlling the plant adaptively based on the transformed signal {tilde over (y)}ad used for adaptive control of the plant. 16. A method as claimed in claim 15 further comprising the steps of: f) receiving a plant output signal y that is a function of states x existing in a plant; g) delaying the plant output signal y to produce a delayed signal yd; h) receiving a pseudo-control signal v used to control the plant; i) delaying the pseudo-control signal v to produce a delayed signal vd; and j) supplying the signals y, yd, v, vd to a neural network to generate an adaptive control signal vad to control the plant. 17. A method as claimed in claim 16 further comprising the steps of: k) filtering at least one basis function φ to generate a filtered basis function φf; l) multiplying the filtered basis function φf by the transformed signal {tilde over (y)}ad to produce an error signal δ; and m) modifying at least one connection weight W of the neural network based on the error signal δ. 18. A method as claimed in claim 17 further comprising the steps of: n) differentiating the plant output signal y r times to produce an rth derivative signal y(r)c of the plant output signal y, r being the relative degree of the plant output signal; o) summing the rth derivative signal, the pseudo-control component signal vdc, and the adaptive control signal vad, to generate a pseudo-control signal v; and p) generating a command control signal δc based on the pseudo-control signal v and the plant output signal y by model inversion. 19. A method comprising the steps of: a) receiving a plant output signal y that is a function of states existing in a plant; b) delaying the plant output signal y to produce a delayed signal yd; c) receiving a pseudo-control signal v used to control the plant; d) delaying the pseudo-control signal v to produce a delayed signal vd; and e) supplying the signals y, yd, v, vd to a neural network to generate an adaptive control signal vad to assist a linear controller in controlling the plant. 20. A method as claimed in claim 19 further comprising the steps of: f) filtering at least one basis function φ to generated a filtered basis function φf; g) multiplying the filtered basis function φ by the transformed signal {tilde over (y)}ad to produce an error signal δ; and h) modifying at least one connection weight W of the neural network based on the error signal δ.