Adaptive output feedback control for complex-valued reaction-advection-diffusion systems

Abstract

We study a problem of output feedback stabilization of complex-valued reaction-advection-diffusion systems with parametric uncertainties (these systems can also be viewed as coupled parabolic PDEs). Both sensing and actuation are performed at the boundary of the PDE domain and the unknown parameters are allowed to be spatially varying. First, we transform the original system into the form where unknown functional parameters multiply the output, which can be viewed as a PDE analog of observer canonical form. Input and output filters are then introduced to convert a dynamic parametrization of the problem into a static parametrization where a gradient estimation algorithm is used. The control gain is obtained by solving a simple complex-valued integral equation online. The solution of the closed-loop system is shown to be bounded and asymptotically stable around the zero equilibrium. The results are illustrated by simulations.

Output Feedback Stabilization of Unstable Heat Equations with Time Delay in Boundary Observation

“…where 􏽢 w 0 is the initial value of the observer (8), w 0 is the initial value of the original system (1), and M, ω and M 1 , ω 1 are constants in (13) and (23), respectively.…”

“…In the past decades, much effort has been made for the problems of unstable or antistable infinite-dimensional systems which can be applied to practical engineering (see [1][2][3][4][5][6][7][8][9][10][11][12][13]). For example, reference [14] relates the loss of the heat to the surrounding medium and the destabilizing heat generation inside the rod.…”

Fixed/Predefined-Time Synchronization of Complex-Valued Stochastic BAM Neural Networks with Stabilizing and Destabilizing Impulse

“…In addition, with the continuous development of neural network theory, it has been found that real-valued neural networks have some limitations when solving many practical application problems, for example XOR [20], reaction-convection-diffusion systems [21,22], etc. Thus, as a extension of real-valued neural network, the complex-valued neural network has been adopted and investigated in depth since they have a more complex structure and richer properties, which can solve the above problems more easily and effectively.…”