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All practical control systems are subject to operational
constraints such as
restricted dimensions
and limited control capacity. In many
situations these
constraints are purposely imposed and are
intended to be made as
tight
as possible in order to reduce energy consumption, to minimize
the
utilization
of resources, or to merely reduce the size of a certain device.
Magnetic
suspension
systems, e.g., a fluid pump as depicted below, are
typical examples
with severe constraints:
extremely small clearance, low power
consumption and small size.

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Project Description:
Our project aims to explore the best performances of
control systems with
limited control capacity and resources.
Since constrained
control systems are intrinsically nonlinear,
a simple linear
controller is unlikely to
make full utilization of the available resources and we have to
resort to nonlinear
control strategies, possibly involving switching and hybrid
structures. This project
will develop systematic approaches to the construction of
nonlinear controllers
by using non-quadratic Lyapunov functions whose level sets
reflect the structure
of the constraints better than ellipsoids
generated by quadratic
functions, which are
usually used for the design of linear controllers. To bridge
the
gap between theory
and practice, this work emphasizes the realizablility of the
controller and
numerical
tractability of the design algorithms.
Approaches:
Control design via quadratic Lyapunov functions can be
numerically
implemented
via the Linear Matrix Inequality (LMI) based
methods. We seek to
use functions which are constructed
from several quadratic Lyapunov functions
– Composite Quadratic Lyapunov Functions (CQLF).
These functions
are
potentially numerically tractable while providing more
flexibility and degree
of design freedom for achieving better performances. Three
types of CQLF
have been
constructed and exploited in our recent works and they
have shown
great potential in
performance improvement for uncertain
systems, switched
systems and constrained control systems. |
Our works:
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T. Hu, A. R. Teel and L. Zaccarian, ``Stability and performance for saturated systems
via quadratic and non-quadratic Lyapunov functions," IEEE Transactions on Automatic
Control, 51(11), pp.~1770-1786, 2006.
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T. Hu and Z. Lin, Control Systems with Actuator Saturation: Analysis and Design,
Birkhauser, Boston, xvi, 392 p, July, 2001. (ISBN: 0-8176-4219-6).
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T. Hu, R. Goebel, A.R. Teel and Z. Lin, ``Conjugate Lyapunov functions for saturated
linear systems," Automatica, 41(11), pp.~1949-1956, 2005.
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T. Hu, A. R. Teel and L. Zaccarian, ``Regional anti-windup compensation for linear
systems with input saturation," The 2005 American Control Conference, pp.3397-3402, 2005.
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T. Hu and Z. Lin,``Output regulation of linear systems with bounded continuous feedback,''
IEEE Transactions on Automatic control, Vol.49, No.11, pp.1941-1953, 2004.
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H. Fang, Z. Lin and T. Hu, ``Analysis and control design of linear systems in the presence
of actuator saturation and L2-disturbances,'' Automatica, Vol.40, July, pp.1229-1238, 2004.
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T. Hu and Z. Lin, ``Controlled invariance of ellipsoids: linear vs nonlinear feedback,"
Systems & Control Letters, Vol.53, pp.203-210, 2004.
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T. Hu, Z. Lin and Y. Shamash, ``On maximizing the convergence rate for linear systems
with input saturation," IEEE Transactions on Automatic Control, Vol.48, No.7,
pp.1249-1253, 2003.
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T. Hu and Z. Lin, ``On the tightness of a recent set invariance condition under
actuator saturation," Systems & Control Letters, Vol.49, No.5, pp.389-399, 2003.
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T. Hu and Z. Lin, ``Composite quadratic Lyapunov functions for constrained control systems,"
IEEE Transactions on Automatic Control, Vol.48, No.3, pp.440-450, March 2003.
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T. Hu and Z. Lin,``Output regulation of general discrete-time linear systems with
saturation nonlinearities,'' Int. J. of Robust and Nonlinear Control, Vol.12, No.13,
pp.1129-1143, 2002.
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T. Hu, D. Miller and L. Qiu, ``Null controllable region of LTI discrete-time systems
with input saturation,'' Automatica, Vol.38, No.11, pp.2009-2013, 2002.
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T. Hu and Z. Lin, ``On improving performances with continuous feedback laws,"
IEEE Transactions on Automatic Control, Vol.47, No.9, pp.1570-1575, 2002.
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T. Hu, Z. Lin and L. Qiu, ``An explicit description of the null controllable regions of
linear systems with saturating actuators," Systems & Control Letters, Vol.47, No.1,
pp.65-78, 2002.
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T. Hu and Z. Lin, ``On semi-global stabilizability of anti-stable systems by saturated
linear feedback," IEEE Transactions on Automatic Control, Vol.47, No.7, pp.1193-1198, 2002.
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T. Hu and Z. Lin, ``Exact characterization of invariant ellipsoids for linear systems
with saturating actuators,'' IEEE Transactions on Automatic Control, Vol.47, No.1,
pp.164-169, 2002.
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T. Hu, Z. Lin and B. M. Chen, ``An analysis and design method for linear systems subject
to actuator saturation and disturbance," Automatica, Vol.38, No.2, pp.351-359, 2002.
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T. Hu, Z. Lin and B. M. Chen, ``Analysis and design for linear discrete-time systems
subject to actuator saturation," Systems & Control Letters, Vol.45, No.2,
pp.97-112, 2002.
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Y. Y. Cao, Z. Lin and T. Hu,``Stability analysis of linear time-delay systems subject to
actuator saturation,'' IEEE Transactions on Circuits and Systems - Part I: Fundamental
Theory and Applications, Vol.49, No.2, pp.233-240, 2002.
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T. Hu, Z. Lin and Y. Shamash, ``Semi-global stabilization with guaranteed regional perfor-
mance of linear systems subject to actuator saturation,'' Systems & Control Letters,
Vol.43, No.3, pp.203-210, 2001.
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Z. Lin and T. Hu, ``Semi-global stabilization of linear system subject to output saturation,"
Systems & Control Letters, Vol.43, No.3, pp.211-217, 2001.
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T. Hu and Z. Lin, ``A complete stability analysis of planar discrete-time linear systems
under saturation," IEEE Transactions on Circuits and Systems - Part I: Fundamental Theory
and Applications, Vol.48, No.6, pp.710-725, 2001.
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T. Hu, Z. Lin and L. Qiu, ``Stabilization of exponentially unstable linear systems with
saturating actuators," IEEE Transactions on Automatic Control, Vol.46, No.6,
pp.973-979, 2001.
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T. Hu and Z. Lin, ``Practical stabilization of exponentially unstable linear systems
subject to actuator saturation nonlinearity and disturbance,'' Int. J. of Robust and
Nonlinear Control, Vol.11, pp.555-588, 2001.
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T. Hu and Z. Lin, ``On enlarging the basin of attraction for linear systems under saturated
linear feedback,'' Systems & Control Letters, Vol.40, No.1, pp.59-69, 2000.
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T. Hu and Z. Lin, ``A complete stability analysis of planar linear systems under saturation,''
IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, Vol.47, No.4,
pp.498-512, 2000.
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