12 research outputs found
Output error minimizing back and forth nudging method for initial state recovery
We show that for linear dynamical systems with skew-adjoint generators, the
initial state estimate given by the back and forth nudging method with
colocated feedback, converges to the minimizer of the discrepancy between the
measured and simulated outputs - given that the observer gains are chosen
suitably and the system is exactly observable. If the system's generator A is
essentially skew-adjoint and dissipative (with not too much dissipation), the
colocated feedback has to be corrected by the operator e^{At}e^{A*t} in order
to obtain such convergence. In some special cases, a feasible approximation for
this operator can be found analytically. The case with wave equation with
constant dissipation will be demonstrated.Comment: This is the preprint version of the article. The final, published
version is available on the journal's websit
Approximate robust output regulation of boundary control systems
We extend the internal model principle for systems with boundary control and
boundary observation, and construct a robust controller for this class of
systems. However, as a consequence of the internal model principle, any robust
controller for a plant with infinite-dimensional output space necessarily has
infinite-dimensional state space. We proceed to formulate the approximate
robust output regulation problem and present a finite-dimensional controller
structure to solve it. Our main motivating example is a wave equation on a
bounded multidimensional spatial domain with force control and velocity
observation at the boundary. In order to illustrate the theoretical results, we
construct an approximate robust controller for the wave equation on an annular
domain and demonstrate its performance with numerical simulations.Comment: 29 pages, 4 figure
On the dynamic behavior and stability of controlled connected Rayleigh beams under pointwise output feedback
We study the dynamic behavior and stability of two connected Rayleigh beams that are subject to, in addition to two sensors and two actuators applied at the joint point, one of the actuators also specially distributed along the beams. We show that with the distributed control employed, there is a set of generalized eigenfunctions of the closed-loop system, which forms a Riesz basis with parenthesis for the state space. Then both the spectrum-determined growth condition and exponential stability are concluded for the system. Moreover, we show that the exponential stability is independent of the location of the joint. The range of the feedback gains that guarantee the system to be exponentially stable is identified
Recovering the observable part of the initial data of an infinite-dimensional linear system with skew-adjoint generator
We consider the problem of recovering the initial data (or initial state) of infinite-dimensional linear systems with unitary semigroups. It is well-known that this inverse problem is well posed if the system is exactly observable, but this assumption may be very restrictive in some applications. In this paper we are interested in systems which are not exactly observable, and in particular, where we cannot expect a full reconstruction. We propose to use the algorithm studied by Ramdani et al. in (Automatica 46:1616–1625, 2010) and prove that it always converges towards the observable part of the initial state. We give necessary and sufficient condition to have an exponential rate of convergence. Numerical simulations are presented to illustratethe theoretical results
Robust Controllers for Regular Linear Systems with Infinite-Dimensional Exosystems
We construct two error feedback controllers for robust output tracking and
disturbance rejection of a regular linear system with nonsmooth reference and
disturbance signals. We show that for sufficiently smooth signals the output
converges to the reference at a rate that depends on the behaviour of the
transfer function of the plant on the imaginary axis. In addition, we construct
a controller that can be designed to achieve robustness with respect to a given
class of uncertainties in the system, and present a novel controller structure
for output tracking and disturbance rejection without the robustness
requirement. We also generalize the internal model principle for regular linear
systems with boundary disturbance and for controllers with unbounded input and
output operators. The construction of controllers is illustrated with an
example where we consider output tracking of a nonsmooth periodic reference
signal for a two-dimensional heat equation with boundary control and
observation, and with periodic disturbances on the boundary.Comment: 30 pages, 3 figures, to appear in SIAM Journal on Control &
Optimizatio