831 research outputs found
Time-Varying Input and State Delay Compensation for Uncertain Nonlinear Systems
A robust controller is developed for uncertain, second-order nonlinear
systems subject to simultaneous unknown, time-varying state delays and known,
time-varying input delays in addition to additive, sufficiently smooth
disturbances. An integral term composed of previous control values facilitates
a delay-free open-loop error system and the development of the feedback control
structure. A stability analysis based on Lyapunov-Krasovskii (LK) functionals
guarantees uniformly ultimately bounded tracking under the assumption that the
delays are bounded and slowly varying
Minimal data rate stabilization of nonlinear systems over networks with large delays
Control systems over networks with a finite data rate can be conveniently
modeled as hybrid (impulsive) systems. For the class of nonlinear systems in
feedfoward form, we design a hybrid controller which guarantees stability, in
spite of the measurement noise due to the quantization, and of an arbitrarily
large delay which affects the communication channel. The rate at which feedback
packets are transmitted from the sensors to the actuators is shown to be
arbitrarily close to the infimal one.Comment: 16 pages; references have now been adde
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Attitude dynamics stabilization with unknown delay in feedback control implementation
textThis work addresses the problem of stabilizing attitude dynamics with
an unknown delay in feedback. Two cases are considered: 1) constant time-delay 2) time-varying time-delay. This is to our best knowledge the first result
that provides asymptotically stable closed-loop control design for the attitude dynamics problem with an unknown delay in feedback. Strict upper bounds on the unknown delay are assumed to be known. The time-varying delay is assumed to be made of the constant unknown delay with a time-varying
perturbation. Upper bounds on the magnitude and rate of the time-varying part of the delay are assumed to be known. A novel modification to the concept
of the complete type Lyapunov-Krasovskii (L-K) functional plays a crucial
role in this analysis towards ensuring stability robustness to time-delay in the control design. The governing attitude dynamic equations are partitioned to
form a nominal system with a perturbation term. Frequency domain analysis is employed in order to construct necessary and sufficient stability conditions
for the nominal system. Consequently, a complete type L-K functional is constructed for stability analysis that includes the perturbation term. As an
intermediate step, an analytical solution for the underlying Lyapunov matrix is obtained. Departing from previous approaches, where controller parameter values are arbitrarily chosen to satisfy the sufficient conditions obtained from
robustness analysis, a systematic numerical optimization process is employed here to choose control parameters so that the region of attraction is maximized. The estimate of the region of attraction is directly related to the initial angular velocity norm and the closed-loop system is shown to be stable for a large set
of initial attitude orientations.Aerospace Engineering and Engineering Mechanic
Backstepping and Sequential Predictors for Control Systems
We provide new methods in mathematical control theory for two significant classes of control systems with time delays, based on backstepping and sequential prediction. Our bounded backstepping results ensure global asymptotic stability for partially linear systems with an arbitrarily large number of integrators. We also build sequential predictors for time-varying linear systems with time-varying delays in the control, sampling in the control, and time-varying measurement delays. Our bounded backstepping results are novel because of their use of converging-input-converging-state conditions, which make it possible to solve feedback stabilization problems under input delays and under boundedness conditions on the feedback control. Our sequential predictors work is novel in its ability to cover time-varying measurement delays and sampling which were beyond the scope of existing sequential predictor methods for time-varying linear systems, and in the fact that the feedback controls that we obtain from our sequential predictors do not contain any distributed terms
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