174 research outputs found
Networked control systems in the presence of scheduling protocols and communication delays
This paper develops the time-delay approach to Networked Control Systems
(NCSs) in the presence of variable transmission delays, sampling intervals and
communication constraints. The system sensor nodes are supposed to be
distributed over a network. Due to communication constraints only one node
output is transmitted through the communication channel at once. The scheduling
of sensor information towards the controller is ruled by a weighted
Try-Once-Discard (TOD) or by Round-Robin (RR) protocols. Differently from the
existing results on NCSs in the presence of scheduling protocols (in the
frameworks of hybrid and discrete-time systems), we allow the communication
delays to be greater than the sampling intervals. A novel hybrid system model
for the closed-loop system is presented that contains {\it time-varying delays
in the continuous dynamics and in the reset conditions}. A new
Lyapunov-Krasovskii method, which is based on discontinuous in time Lyapunov
functionals is introduced for the stability analysis of the delayed hybrid
systems. Polytopic type uncertainties in the system model can be easily
included in the analysis. The efficiency of the time-delay approach is
illustrated on the examples of uncertain cart-pendulum and of batch reactor
Государственная молодежная политика Беларуси в преемственности и развитии
СОЦИАЛЬНОГО КОНТРОЛЯ ПОЛИТИКАПОЛИТИЧЕСКИЕ УСТАНОВКИПОЛИТИКИ ОСУЩЕСТВЛЕНИЕМОЛОДОЙ ВОЗРАСТ, 19-44 ЛЕТРЕСПУБЛИКА БЕЛАРУС
Predictor-based sampled-data exponential stabilization through continuous–discrete observers
International audienceThe problem of stabilizing a linear continuous-time system with discrete-time measurements and a sampled input with a pointwise constant delay is considered. In a first part, we design a continuous-discrete observer which converges when the maximum time interval between two consecutive measurements is sufficiently small. In a second part, we construct a dynamic output feedback by using a technique which is strongly reminiscent of the reduction model approach. It stabilizes the system when the maximal time between two consecutive sampling instants is sufficiently small. No limitation on the size of the delay is imposed and an ISS property with respect to additive disturbances is established
Delayed finite-dimensional observer-based control of 2D linear parabolic PDEs
Recently, a constructive method was suggested for finite-dimensional
observer-based control of 1D linear heat equation, which is robust to
input/output delays. In this paper, we aim to extend this method to the 2D case
with general time-varying input/output delays (known output delay and unknown
input delay) or sawtooth delays (that correspond to network-based control). We
use the modal decomposition approach and consider boundary or non-local sensing
together with non-local actuation, or Neumann actuation with non-local sensing.
To compensate the output delay that appears in the infinite-dimensional part of
the closed-loop system, for the first time for delayed PDEs we suggest a vector
Lyapunov functional combined with the recently introduced vector Halanay
inequality. We provide linear matrix inequality (LMI) conditions for finding
the observer dimension and upper bounds on delays that preserve the exponential
stability. We prove that the LMIs are always feasible for large enough observer
dimension and small enough upper bounds on delays. A numerical example
demonstrates the efficiency of our method and shows that the employment of
vector Halanay's inequality allows for larger delays than the classical scalar
Halanay inequality for comparatively large observer dimension
Stabilization of underactuated linear coupled reaction-diffusion PDEs via distributed or boundary actuation
This work concerns the exponential stabilization of underactuated linear
homogeneous systems of parabolic partial differential equations (PDEs) in
cascade (reaction-diffusion systems), where only the first state is controlled
either internally or from the right boundary and in which the diffusion
coefficients are distinct. For the distributed control case, a
proportional-type stabilizing control is given explicitly. After applying modal
decomposition, the stabilizing law is based on a transformation for the ODE
system corresponding to the comparatively unstable modes into a target one,
where the calculation of the stabilization law is independent of the
arbitrarily large number of these modes. This is achieved by solving
generalized Sylvester equations recursively. For the boundary control case, the
proposed controller is dynamic under appropriate sufficient conditions on the
coupling matrix (reaction term). A dynamic extension technique is first
performed via trigonometric change of variables that places the control
internally. Then, modal decomposition is applied followed by a state
transformation of the ODE system which must be stabilized in order to be
written in a form in which a dynamic law can be established. For both
distributed and boundary control systems, a constructive and scalable
stabilization algorithm is proposed, as the choice of the controller gains is
independent of the number of unstable modes and only relies on the
stabilization of the reaction term. The present approach solves the problem of
stabilization of underactuated systems when in the presence of distinct
diffusion coefficients. The problem is not directly solvable, similarly to the
scalar PDE case.Comment: arXiv admin note: substantial text overlap with arXiv:2202.0880
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