Adaptive control for uncertain nonlinear multi-input multi-output systems

• US 8,712,559 B2
• Filed: 02/09/2011
• Issued: 04/29/2014
• Est. Priority Date: 02/10/2010
• Status: Active Grant

• Current Assignee: Board of Trustees of The University of Illinois, University of Connecticut (State of Connecticut)
• Original Assignee: Board of Trustees of The University of Illinois, University of Connecticut (State of Connecticut)
• Inventors: Hovakimyan, Naira, Xargay, Enric, Cao, Chengyu
• Primary Examiner(s): Bahta, Kidest
• Application Number:
  US13/023,965
• Publication Number:
  US 20110196514A1
• Time in Patent Office: 1,175 Days
• Field of Search: 700/50, 700/51, 700/48, 700/31, 700/28, 700/20, 706/15, 706/48, 706/31, 708/304
• US Class Current: 700/48
• CPC Class Codes: G05B 13/048 using a predictor

Abstract

Systems and methods of adaptive control for uncertain nonlinear multi-input multi-output systems in the presence of significant unmatched uncertainty with assured performance are provided. The need for gain-scheduling is eliminated through the use of bandwidth-limited (low-pass) filtering in the control channel, which appropriately attenuates the high frequencies typically appearing in fast adaptation situations and preserves the robustness margins in the presence of fast adaptation.

Claims

1. A method of adaptive control for an uncertain nonlinear multi-input multi-output system, the method comprising:

providing a processor operable to execute a control law residing in a memory, the control law including a bandwidth-limited filter configuration, the control law configured to generate a control signal u_c as an output of the bandwidth-limited filter configuration;

measuring a system state signal x;

generating a prediction of the system state {circumflex over (x)};

subtracting the prediction of the system state {circumflex over (x)} from the measured system state signal x, and producing an error signal {tilde over (x)};

generating estimates of uncertainties in the multi-input multi-output system; and

generating the control signal u_c as an output of the bandwidth-limited filter configuration based on the generated estimates of uncertainties and the measured system state x.

2. The method according to claim 1 further including generating the estimates of uncertainties based on the measured system state signal x and the control signal u_c.

3. The method according to claim 1 further including providing a state-predictor configured for mimicking the multi-input multi-output system and for specifying desired system behavior.

4. The method according to claim 1 further including updating the estimates of the uncertainties at a high adaptation rate.

5. The method according to claim 1 wherein the adaptive control system is a closed-loop system.

6. The method according to claim 1 wherein the multi-input multi-output system is in the presence of significant unmatched uncertainty.

7. The method according to claim 1 wherein the bandwidth-limited filter configuration comprises m×

m strictly-proper and stable bandwidth-limited filters, wherein m system outputs and m control signals are included in the m×

m strictly-proper and stable bandwidth-limited filters.

8. An adaptive control system for controlling a nonlinear multi-input multi-output system with uncertainties, the adaptive control system comprising:

a fast estimation scheme, the fast estimation scheme including a state predictor and an adaptive law, the fast estimation scheme configured to generate estimates of the uncertainties in the multi-input multi-output system; and

a control law, the control law including a bandwidth-limited filter configuration, the control law configured to generate a control signal u_c as an output of the bandwidth-limited filter configuration.

9. The system according to claim 8 wherein the estimates of the uncertainties are generated based on a measured system state x and the control signal u_c.

10. The system according to claim 8 wherein the state-predictor is configured to mimic the multi-input multi-output system and to specify desired system behavior.

11. The system according to claim 9 wherein the state-predictor is configured to generate a prediction of the system state {circumflex over (x)}, the prediction of the system state {circumflex over (x)} then being subtracted from the measured system state x, to produce an error signal {tilde over (x)};

and

the error signal {tilde over (x)} together with the measured system state signal x and the control signal u_c, drives the adaptive process.

12. The system according to claim 9 wherein the control law generates the control signal u_c based on the estimates of uncertainties and the measured system state x.

13. The system according to claim 8 wherein the adaptive law is configured to update the estimates of the uncertainties at a high adaptation rate.

14. The system according to claim 8 wherein the adaptive control system is a closed-loop system.

15. The system according to claim 8 wherein the multi-input multi-output system is in the presence of significant unmatched uncertainty.

16. An adaptive control system comprising:

a processor operable to execute a control law residing in a memory, the control law including a bandwidth-limited filter configuration, the control law configured to generate a control signal u_c as an output of the bandwidth-limited filter configuration; and

a state predictor configured to generate a prediction of a nonlinear multi-input multi-output system state {circumflex over (x)}, such that when the system state {circumflex over (x)} is subtracted from an actual system state x, an error signal is produced that, together with the actual system state x and the control signal u_c, drives an adaptation process.

17. The system according to claim 16 wherein the bandwidth-limited filter comprises a feedback structure in the control law.

18. The system according to claim 16 wherein the control signal u_c equals K_g(s)r(s)−

C₁(s){circumflex over (η

)}₁(s)−

C₂(s)H_m<sup>−

1</sup>(s)H_um(s){circumflex over (η

)}₂(s), wherein

K_g(s) is a prefilter,

r(s) is a bounded setpoint,

C₁(s) and C₂(s) are bandwidth-limited filters,

{circumflex over (η

)}₁(s) and {circumflex over (η

)}₂(s) are adaptive laws,

H_m<sup>−

1</sup>(s) is an inverse of a matched transfer matrix, and

H_um(s) is an unmatched transfer matrix.

19. The system according to claim 18 wherein C₁(s) and C₂(s) are stable bandwidth-limited filters.