Abstract

The primary goal of this paper is to develop a formal foundation to design an adaptive output feedback predictor for a class of unknown systems where parameters and order are unknown or high-dimensional. We present a reduced-order adaptive output-predictor scheme based on modal reduction and Lyapunov's method. Moreover, the credibility of the proposed reduced-order adaptive output-predictor scheme is validated by mathematical proof and numerical studies.

References

1.
Ioannou
,
P. A.
, and
Sun
,
J.
,
2012
,
Robust Adaptive Control
,
Courier Corporation
,
Upper Saddle River, NJ
.
2.
Davidson
,
B. S.
,
Madigan
,
M. L.
,
Southward
,
S. C.
, and
Nussbaum
,
M. A.
,
2011
, “
Neural Control of Posture During Small Magnitude Perturbations: Effects of Aging and Localized Muscle Fatigue
,”
IEEE Trans. Biomed. Eng.
,
58
(
6
), pp.
1546
1554
.10.1109/TBME.2010.2095500
3.
Chen
,
K.
, and
Astolfi
,
A.
,
2018
, “
Adaptive Control of Linear Systems With Time-Varying Parameters
,” 2018 Annual American Control Conference (
ACC
), Milwaukee, WI, June 27–29, pp.
80
85
.10.23919/ACC.2018.8431444
4.
Åström
,
K. J.
, and
Wittenmark
,
B.
,
2013
,
Adaptive Control
,
Courier Corporation
,
Upper Saddle River, NJ
.
5.
Tangirala
,
A. K.
,
2018
,
Principles of System Identification: Theory and Practice
,
CRC Press
,
Boca Raton, FL
.
6.
Ljung
,
L.
, et al.,
1987
, “
Theory for the User
,”
System Identification
,
Prentice Hall
,
Upper Saddle River, NJ
.
7.
Khalil
,
H. K.
,
2015
,
Nonlinear Control
, Vol.
3
,
Pearson
,
Upper Saddle River, NJ
.
8.
Leonessa
,
A.
,
Haddad
,
W. M.
,
Hayakawa
,
T.
, and
Morel
,
Y.
,
2009
, “
Adaptive Control for Nonlinear Uncertain Systems With Actuator Amplitude and Rate Saturation Constraints
,”
Int. J. Adapt. Control Signal Process.
,
23
(
1
), pp.
73
96
.10.1002/acs.1065
9.
Davison
,
E.
,
1966
, “
A Method for Simplifying Linear Dynamic Systems
,”
IEEE Trans. Autom. Control
,
11
(
1
), pp.
93
101
.10.1109/TAC.1966.1098264
10.
Knüpfer
,
C.
, and
Beckstein
,
C.
,
2013
, “
Function of Dynamic Models in Systems Biology: Linking Structure to Behaviour
,”
J. Biomed. Semant.
,
4
(
1
), p.
24
.10.1186/2041-1480-4-24
11.
Krstic
,
M.
, and
Kokotovic
,
P. V.
,
1995
, “
Adaptive Nonlinear Design With Controller-Identifier Separation and Swapping
,”
IEEE Trans. Autom. Control
,
40
(
3
), pp.
426
440
.10.1109/9.376055
12.
Nguyen
,
C. H.
, and
Leonessa
,
A.
,
2017
, “
Adaptive Predictor-Based Output Feedback Control for a Class of Unknown MIMO Linear Systems
,”
J. Nonlinear Sci.
,
27
(
4
), pp.
1257
1290
.10.1007/s00332-017-9368-3
13.
Cao
,
C.
, and
Hovakimyan
,
N.
,
2008
, “
L1 Adaptive Output Feedback Controller for Non Strictly Positive Real Reference Systems With Applications to Aerospace Examples
,”
AIAA
Paper No. 2008-7288.10.2514/6.2008-7288
14.
Cao
,
C.
, and
Hovakimyan
,
N.
,
2007
, “
Guaranteed Transient Performance With L1 Adaptive Controller for Systems With Unknown Time-Varying Parameters and Bounded Disturbances: Part I
,”
2007 American Control Conference
, New York, July 9–13, pp.
3925
3930
.10.1109/ACC.2007.4282485
15.
Cao
,
C.
, and
Hovakimyan
,
N.
,
2007
, “
Stability Margins of L1 Adaptive Controller: Part II
,”
2007 American Control Conference
,
New York
, July 9–13, pp.
3931
3936
.10.1109/ACC.2007.4282486
16.
Cao
,
C.
, and
Hovakimyan
,
N.
,
2007
, “
L1 Adaptive Output Feedback Controller for Systems With Time-Varying Unknown Parameters and Bounded Disturbances
,”
2007 American Control Conference
,
New York
, July 9–13, pp.
486
491
.10.1109/ACC.2007.4282994
17.
Lee
,
H.
,
Cichella
,
V.
, and
Hovakimyan
,
N.
,
2014
, “
L1 Adaptive Output Feedback Augmentation of Model Reference Control
,”
2014 American Control Conference
,
Portland, OR
, June 4–6, pp.
697
702
.10.1109/ACC.2014.6859348
18.
Nguyen
,
C. H.
, and
Leonessa
,
A.
,
2015
, “
Adaptive Predictor-Based Output Feedback Control for a Class of Unknown MIMO Systems: Experimental Results
,” 2015 American Control Conference (
ACC
), Chicago, IL, July 1–3, pp.
3515
3521
.10.1109/ACC.2015.7171875
19.
Cao
,
C.
, and
Hovakimyan
,
N.
,
2009
, “
L1 Adaptive Output Feedback Controller for Non Strictly Positive Real Multi-Input Multi-Output Systems in the Presence of Unknown Nonlinearities
,”
2009 American Control Conference
, St. Louis, MO, June 10–12, pp.
5138
5143
.10.1109/ACC.2009.5160620
20.
Gahlawat
,
A.
,
Zhao
,
P.
,
Patterson
,
A.
,
Hovakimyan
,
N.
, and
Theodorou
,
E.
,
2020
, “
L1-GP: L1 Adaptive Control With Bayesian Learning
,”
Learning for Dynamics and Control
, June 11–12, pp.
826
837
.
21.
Pravitra
,
J.
,
Ackerman
,
K. A.
,
Cao
,
C.
,
Hovakimyan
,
N.
, and
Theodorou
,
E. A.
,
2020
, “
L1-Adaptive MPPI Architecture for Robust and Agile Control of Multirotors
,” 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (
IROS
), Las Vegas, NV, Oct. 24–Jan. 24, pp.
7661
7666
.10.1109/IROS45743.2020.9341154
22.
Lee
,
H.
,
Cichella
,
V.
, and
Hovakimyan
,
N.
,
2021
, “
L1 Adaptive Output Feedback for Nonsquare Systems With Arbitrary Relative Degree
,”
IEEE Trans. Autom. Control
,
66
(
2
), pp.
895
901
.10.1109/TAC.2020.2989279
23.
Lavretsky
,
E.
,
2017
, “
Robust and Adaptive Output Feedback Control for Non-Minimum Phase Systems With Arbitrary Relative Degree
,”
AIAA
Paper No. 2017-1490.10.2514/6.2017-1490
24.
Ansari
,
R.
,
Abaid
,
N.
, and
Leonessa
,
A.
,
2022
, “
Reduced-Order Adaptive Output Predictors for a Class of Uncertain Dynamical Systems
,” 2022 American Control Conference (
ACC
), Atlanta, GA, June 8–10, pp.
3394
3399
.10.23919/ACC53348.2022.9867638
25.
Nguyen
,
C. H.
, and
Leonessa
,
A.
,
2016
, “
Predictor-Based Adaptive Output Feedback Control: Application to Functional Electrical Stimulation of a Human Arm Model
,”
ASME J. Dyn. Syst., Meas., Control
,
138
(
11
), p.
111014
.10.1115/1.4033863
26.
Chen
,
B. M.
,
Lin
,
Z.
, and
Shamash
,
Y.
,
2004
,
Linear Systems Theory: A Structural Decomposition Approach
,
Springer Science & Business Media
,
Berlin
.
27.
Chidambara
,
M.
, and
Davison
,
E.
,
1967
, “
Further Remarks on Simplifying Linear Dynamic Systems
,”
IEEE Trans. Autom. Control
,
12
(
2
), pp.
213
214
.10.1109/TAC.1967.1098557
28.
Audley
,
D.
,
Baumgartner
,
S.
, and
Rugh
,
W.
,
1975
, “
Linear System Realization Based on Data Set Representations
,”
IEEE Trans. Autom. Control
,
20
(
3
), pp.
432
433
.10.1109/TAC.1975.1100987
29.
Fossard
,
A.
,
1970
, “
On a Method for Simplifying Linear Dynamic Systems
,”
IEEE Trans. Autom. Control
,
15
(
2
), pp.
261
262
.10.1109/TAC.1970.1099420
30.
Varga
,
A.
,
1995
, “
Enhanced Modal Approach for Model Reduction
,”
Math. Modell. Syst.
,
1
(
2
), pp.
91
105
.10.1080/13873959508837010
31.
Glover
,
K.
,
1984
, “
All Optimal Hankel-Norm Approximations of Linear Multivariable Systems and Their L, -Error Bounds
,”
Int. J. Control
,
39
(
6
), pp.
1115
1193
.10.1080/00207178408933239
32.
Tombs
,
M. S.
, and
Postlethwaite
,
I.
,
1987
, “
Truncated Balanced Realization of a Stable Non-Minimal State-Space System
,”
Int. J. Control
,
46
(
4
), pp.
1319
1330
.10.1080/00207178708933971
33.
Deb
,
P. S.
, and
Leena
,
G.
,
2021
, “
Order Reduction of Linear Time Invariant Large-Scale System by Improved Mixed Approximation Method
,”
Modeling, Simulation and Optimization: Proceedings of CoMSO 2020
, Silchar, India, Aug. 3–5, pp.
635
644
.10.1007/978-981-15-9829-6_50
34.
Obinata
,
G.
, and
Anderson
,
B. D.
,
2012
,
Model Reduction for Control System Design
,
Springer Science & Business Media
,
Berlin
.
35.
Antoulas
,
A. C.
,
2005
, “
An Overview of Approximation Methods for Large-Scale Dynamical Systems
,”
Annu. Rev. Control
,
29
(
2
), pp.
181
190
.10.1016/j.arcontrol.2005.08.002
36.
Schilders
,
W. H.
,
Van der Vorst
,
H. A.
, and
Rommes
,
J.
,
2008
, “
Model Order Reduction: Theory
,”
Research Aspects and Applications
, Vol.
13
,
Springer
,
Berlin
.
37.
Moore
,
B.
,
1981
, “
Principal Component Analysis in Linear Systems: Controllability, Observability, and Model Reduction
,”
IEEE Trans. Autom. Control
,
26
(
1
), pp.
17
32
.10.1109/TAC.1981.1102568
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