1,878 research outputs found
Control and State Estimation of the One-Phase Stefan Problem via Backstepping Design
This paper develops a control and estimation design for the one-phase Stefan
problem. The Stefan problem represents a liquid-solid phase transition as time
evolution of a temperature profile in a liquid-solid material and its moving
interface. This physical process is mathematically formulated as a diffusion
partial differential equation (PDE) evolving on a time-varying spatial domain
described by an ordinary differential equation (ODE). The state-dependency of
the moving interface makes the coupled PDE-ODE system a nonlinear and
challenging problem. We propose a full-state feedback control law, an observer
design, and the associated output-feedback control law via the backstepping
method. The designed observer allows estimation of the temperature profile
based on the available measurement of solid phase length. The associated
output-feedback controller ensures the global exponential stability of the
estimation errors, the H1- norm of the distributed temperature, and the moving
interface to the desired setpoint under some explicitly given restrictions on
the setpoint and observer gain. The exponential stability results are
established considering Neumann and Dirichlet boundary actuations.Comment: 16 pages, 11 figures, submitted to IEEE Transactions on Automatic
Contro
Nonlinear control of feedforward systems with bounded signals
Published versio
Mean-field equations for stochastic firing-rate neural fields with delays: Derivation and noise-induced transitions
In this manuscript we analyze the collective behavior of mean-field limits of
large-scale, spatially extended stochastic neuronal networks with delays.
Rigorously, the asymptotic regime of such systems is characterized by a very
intricate stochastic delayed integro-differential McKean-Vlasov equation that
remain impenetrable, leaving the stochastic collective dynamics of such
networks poorly understood. In order to study these macroscopic dynamics, we
analyze networks of firing-rate neurons, i.e. with linear intrinsic dynamics
and sigmoidal interactions. In that case, we prove that the solution of the
mean-field equation is Gaussian, hence characterized by its two first moments,
and that these two quantities satisfy a set of coupled delayed
integro-differential equations. These equations are similar to usual neural
field equations, and incorporate noise levels as a parameter, allowing analysis
of noise-induced transitions. We identify through bifurcation analysis several
qualitative transitions due to noise in the mean-field limit. In particular,
stabilization of spatially homogeneous solutions, synchronized oscillations,
bumps, chaotic dynamics, wave or bump splitting are exhibited and arise from
static or dynamic Turing-Hopf bifurcations. These surprising phenomena allow
further exploring the role of noise in the nervous system.Comment: Updated to the latest version published, and clarified the dependence
in space of Brownian motion
On the practical global uniform asymptotic stability of stochastic differential equations
The method of Lyapunov functions is one of the most effective ones for the
investigation of stability of dynamical systems, in particular, of stochastic
differential systems. The main purpose of the paper is the analysis of the
stability of stochastic differential equations by using Lyapunov functions when
the origin is not necessarily an equilibrium point. The global uniform
boundedness and the global practical uniform exponential stability of so-
lutions of stochastic differential equations based on Lyapunov techniques are
investigated. Furthermore, an example is given to illustrate the applicability
of the main result.Comment: To appear in Stochastic
Linear active disturbance rejection control of the hovercraft vessel model
A linearizing robust dynamic output feedback control scheme is proposed for earth coordinate position variables trajectory tracking tasks in a hovercraft vessel model. The controller design is carried out using only position and orientation measurements. A highly simplified model obtained from flatness considerations is proposed which vastly simplifies the controller design task. Only the order of integration of the input-to-flat output subsystems, along with the associated input matrix gain, is retained in the simplified model. All the unknown additive nonlinearities and exogenous perturbations are lumped into an absolutely bounded, unstructured, vector of time signals whose components may be locally on-line estimated by means of a high gain Generalized Proportional Integral (GPI) observer. GPI observers are the dual counterpart of GPI controllers providing accurate simultaneous estimation of each flat output associated phase variables and of the exogenous and endogenous perturbation inputs. These observers exhibit remarkably convenient self-updating internal models of the unknown disturbance input vector components. These two key pieces of on-line information are used in the proposed feedback controller to conform an active disturbance rejection, or disturbance accommodation, control scheme. Simulation results validate the effectiveness of the proposed design method
Deep Learning of Delay-Compensated Backstepping for Reaction-Diffusion PDEs
Deep neural networks that approximate nonlinear function-to-function
mappings, i.e., operators, which are called DeepONet, have been demonstrated in
recent articles to be capable of encoding entire PDE control methodologies,
such as backstepping, so that, for each new functional coefficient of a PDE
plant, the backstepping gains are obtained through a simple function
evaluation. These initial results have been limited to single PDEs from a given
class, approximating the solutions of only single-PDE operators for the gain
kernels. In this paper we expand this framework to the approximation of
multiple (cascaded) nonlinear operators. Multiple operators arise in the
control of PDE systems from distinct PDE classes, such as the system in this
paper: a reaction-diffusion plant, which is a parabolic PDE, with input delay,
which is a hyperbolic PDE. The DeepONet-approximated nonlinear operator is a
cascade/composition of the operators defined by one hyperbolic PDE of the
Goursat form and one parabolic PDE on a rectangle, both of which are bilinear
in their input functions and not explicitly solvable. For the delay-compensated
PDE backstepping controller, which employs the learned control operator,
namely, the approximated gain kernel, we guarantee exponential stability in the
norm of the plant state and the norm of the input delay state.
Simulations illustrate the contributed theory
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