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- Journal:
- D. Chatterjee, A. Patra, and H. K. Joglekar, Swing-up and
stabilization of a cart-pendulum system under restricted cart track
length Systems & Control Letters, Vol. 47, No. 4,
pp 353-362, Nov, 2002.
[Abstract: This paper describes the swing-up
and stabilization of a cart pendulum system with a restricted cart
track length and restricted control force using generalized energy
control methods. Starting from a pendant position, the pendulum is
swung up to the upright unstable equilibrium configuration using energy
control principles. An ``energy well'' is built within the cart track
to prevent the cart from going outside the limited length. When
sufficient energy is acquired by the pendulum, it goes into a
``cruise'' mode when the acquired energy is maintained. Finally, when
the pendulum is close to the upright configuration, a stabilizing
controller is activated around a linear zone about the upright
configuration. The proposed scheme has worked well both in simulation
and a practical setup and the conditions for stability have been
derived using the multiple Lyapunov functions approach.]
- D. Chatterjee and D. Liberzon, Stability analysis of
deterministic and stochastic switched systems via a comparison
principle and multiple Lyapunov functions, SIAM Journal on Control
and Optimization, vol. 45, no. 1, pp. 174-206, 2006.
[This article may be found here. Typos
]
[Abstract: This paper presents a general
framework for analyzing stability of nonlinear switched systems, by
combining the method of multiple Lyapunov functions with a suitably
adapted comparison principle in the context of stability in terms of
two measures. For deterministic switched systems, this leads to a
unification of representative existing results and an improvement upon
the current scope of the method of multiple Lyapunov functions. For
switched systems perturbed by white noise, we develop new results which
may be viewed as natural stochastic counterparts of the deterministic
ones. In particular, we study stability of deterministic and stochastic
switched systems under average dwell-time switching.]
- L. Vu, D. Chatterjee, and D. Liberzon, Input-to-state
stability of switched systems and switching adaptive control. (
Automatica, vol. 43, pp. 639-646, April 2007) [This article may be found here.]
[Abstract: In this paper we prove that a
switched nonlinear system has several useful ISS-type properties under
average dwell-time switching signals if each constituent dynamical
system is ISS. This extends available results for switched linear
systems. We apply our result to stabilization of uncertain nonlinear
systems via switching supervisory control, and show that the plant
states can be kept bounded in the presence of bounded disturbances when
the candidate controllers provide ISS properties with respect to the
estimation errors. Detailed illustrative examples are included.]
- D. Chatterjee and D. Liberzon, Stability of Randomly
Switched Systems. (To appear in IEEE Transactions on Automatic
Control) [Preprint may be found here.]
[Abstract: This article is concerned with
stability analysis and stabilization of randomly switched systems.
These systems may be regarded as piecewise deterministic stochastic
systems; the discrete switchings are triggered by a stochastic process
which is independent of the state of the system, and between two
consecutive switching instants the dynamics are deterministic. Our
results provide sufficient conditions for almost sure and mean
stability using Lyapunov-based methods when individual subsystems are
stable and a certain ``slow switching'' condition holds. This slow
switching condition takes the form of an asymptotic upper bound on the
probability mass function of the number of switches that occur between
the initial and current time instants. This condition is shown to hold
for switching signals coming from the states of finite-dimensional
continuous-time Markov chains; our results therefore hold for Markovian
jump systems in particular. For systems with control inputs we provide
explicit control schemes for stabilization.]
- D. Chatterjee and D.
Liberzon, Stabilizing Randomly Switched Systems. (To be submitted to SICON)
[Abstract:
This article is concerned with stability analysis and stabilization of
randomly switched systems with control inputs. The switching signal is
modeled as a jump stochastic semi-Markov process independent of the system state;
it selects, at each instant of time, the active subsystem from a family
of systems. We first establish sufficient conditions for stochastic
stability of the switched system when the subsystems
do not possess control inputs; not every subsystem is required to be
stable. Thereafter we design feedback controllers when the
subsystems are affine in control, the control space being general
subsets of
. Our analysis results and universal
formulae for
feedback stabilization of nonlinear systems for the corresponding
control spaces constitute the primary tools for control design.]
- D. Chatterjee and D.
Liberzon, Randomly Switched Systems:
External Stability and Stabilization. (Preprint)
[Abstract:
This article is concerned with stability analysis and stabilization of
randomly switched systems with control inputs in the presence of
disturbances. The switching signal is
modeled as a jump stochastic process independent of the system state;
it selects, at each instant of time, the active subsystem from a family
of systems. A class of switching signals whose holding times and values
at jump instants are mutually independent i.i.d sequences is
considered. We first establish sufficient conditions for stochastic
versions of input to state stability (ISS) of the switched system when
the subsystems
do not possess control inputs; not every subsystem is required to be
stable. Thereafter we design feedback controllers when the
subsystems are affine in control, the control space being general
subsets of
. Our analysis results and universal
formulae for ISS-disturbance attenuation of nonlinear systems for the
corresponding
control spaces constitute the primary tools for control design.]
- Conference:
- H. K. Joglekar, D. Chatterjee, A. Patra, Swing-up
and stabilization of a cart-pendulum system using energy control in
Proceedings of International Conference on Energy, Automation and
Information Technology, Department of Electrical Engineering, IIT
Kharagpur, Dec 10-12, 2001, pp 33-37.
[Abstract: This paper describes the swing-up
and stabilization of a cart-pendulum system with restricted cart-length
and restricted control force using energy methods. The pendulum starts
from the inverted position which is the stable equilibrium position and
swing-up is achieved using energy-control. After the pendulum acquires
sufficient energy to reach the upright position the control is switched
to a throwing strategy. The pendulum then swings freely until it
reaches the upright equilibrium position which is the unstable
equilibrium position. Here control is switched to the stabilizing
strategy which then stabilizes it in the upright position. It is
observed that ``throwing'' plays a very significant role in the
ultimate stabilization of the system because throwing has to be done at
the moment the total pendulum energy reaches the value at the upright
position.]
- D. Chatterjee and D. Liberzon, On stability of
stochastic switched systems, in Proceedings of the 43rd Conference
on Decision and Control, Paradise Island, Bahamas, Dec 2004,
pp. 4125-4127. [The article may be found here.]
[Abstract: This paper proposes a method for
stability analysis of switched systems perturbed by a Wiener process.
It utilizes multiple Lyapunov-like functions and is analogous to an
existing result for deterministic switched systems.]
- L. Vu, D. Chatterjee, and D. Liberzon, ISS
of switched systems and applications to switching adaptive control
in Proceedings of the 44th Conference on Decision and Control, Seville,
Spain, Dec 2005, pp. 120-125. [The article may be found here.]
[Abstract: In this paper we prove that a
switched nonlinear system has several useful ISS-type properties under
average dwell-time switching signals if each constituent dynamical
system is ISS. This extends available results for switched linear
systems. We apply our result to stabilization of uncertain nonlinear
systems via switching supervisory control, and show that the plant
states can be kept bounded in the presence of bounded disturbances when
the candidate controllers provide ISS properties with respect to the
estimation errors. Detailed illustrative examples are included.]
- D. Chatterjee, and D. Liberzon, Stability and
stabilization of randomly switched systems, (Submitted to CDC'06)
[Preprint may be found here,
together with a more complete version.]
[Abstract: This article is concerned with
stability analysis and stabilization of randomly switched systems with
control inputs. The switching signal is modeled as a jump stochastic
process independent of the system state; it selects, at each instant of
time, the active subsystem from a family of deterministic systems.
Three different types of switching signals are considered: the first is
a jump stochastic process that satisfies a statistically slow switching
condition; the second and the third are characterized by exponential
and uniform holding times, respectively, together with a stationary
temporal probability distribution over the family of subsystems. For
each of the three cases we first establish sufficient conditions for
stochastic stability of the switched system when the subsystems do not
possess control inputs; not every subsystem is required to be stable.
Thereafter we design feedback controllers when the subsystems are
affine in control and are not all zero-input stable, with the control
space being general subsets of
. Our analysis
results and universal
formulae for feedback stabilization of nonlinear systems for the
corresponding control spaces constitute the primary tools for control
design.]
- Book Review:
- Stochastic Switching Systems: Analysis
and Design, by El-Kébir Boukas, Boston: Birkhäuser,
2006. AMS
Math Reviews.
[I have NO idea why the pdf document obtainable via AMS MathSciNet shows H1 in place of H_\infty everywhere.]
Next: Courses Taken Up: Homepage of
Debasish Chatterjee Previous: Education
Debasish Chatterjee
2006-04-09