<i>H</i>₂ and mixed <i>H</i>₂/<i>H</i>_∞ Stabilization and Disturbance Attenuation for Differential Linear Repetitive Processes

Repetitive processes are a distinct class of two-dimensional systems (i.e., information propagation in two independent directions) of both systems theoretic and applications interest. A systems theory for them cannot be obtained by direct extension of existing techniques from standard (termed 1-D here) or, in many cases, two-dimensional (2-D) systems theory. Here, we give new results towards the development of such a theory in H2 and mixed H2/H∞ settings. These results are for the sub-class of so-called differential linear repetitive processes and focus on the fundamental problems of stabilization and disturbance attenuation

Control and Filtering for Discrete Linear Repetitive Processes with H infty and ell 2--ell infty Performance

Repetitive processes are characterized by a series of sweeps, termed passes, through a set of dynamics defined over a finite duration known as the pass length. On each pass an output, termed the pass profile, is produced which acts as a forcing function on, and hence contributes to, the dynamics of the next pass profile. This can lead to oscillations which increase in amplitude in the pass to pass direction and cannot be controlled by standard control laws. Here we give new results on the design of physically based control laws for the sub-class of so-called discrete linear repetitive processes which arise in applications areas such as iterative learning control. The main contribution is to show how control law design can be undertaken within the framework of a general robust filtering problem with guaranteed levels of performance. In particular, we develop algorithms for the design of an H? and $\ell_{2}–\ell_{\infty}$ dynamic output feedback controller and filter which guarantees that the resulting controlled (filtering error) process, respectively, is stable along the pass and has prescribed disturbance attenuation performance as measured by $H_{\infty}$ and $\ell_{2}$–$\ell_{\infty}$ norms

Dissipative stability theory for linear repetitive processes with application in iterative learning control

This paper develops a new set of necessary and sufficient conditionsfor the stability of linear repetitiveprocesses, based on a dissipative setting for analysis. Theseconditions reduce the problem of determining whether a linearrepetitive process is stable or not to that of checking for theexistence of a solution to a set of linear matrixinequalities (LMIs). Testing the resulting conditions only requirescomputations with matrices whose entries are constant in comparison toalternatives where frequency response computations are required

Stability and stabilisation of 2D discrete linear systems with multiple delays

In this paper, we study the stability and the stabilisation of 2D discrete linear systems with multiple state delays. All of the new results obtained are based on analysis of the Fornasini-Marchesini state space model with delays and the resulting conditions are given in terms of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the overall approach.published_or_final_versio

LMI based stability analysis and controller design for a class of 2D continuous-discrete linear systems

Differential linear repetitive processes are a distinct class of 2D continuous-discrete linear systems of both applications and systems theoretic interest. In the latter area, they arise, for example, in the analysis of both iterative learning control schemes and iterative algorithms for computing the solutions of nonlinear dynamic optimal control algorithms based on the maximum principle. Repetitive processes cannot be analysed/controlled by direct application of existing systems theory and to date there are few results on the specification and design of control schemes for them. The paper uses an LMI setting to develop the first really significant results in this problem domain.published_or_final_versio

Dissipative stability theory for linear repetitive processes with application in iterative learning control

Abstract-This paper develops a new set of necessary and sufficient conditions for the stability of linear repetitive processes, based on a dissipative setting for analysis. These conditions reduce the problem of determining whether a linear repetitive process is stable or not to that of checking for the existence of a solution to a set of linear matrix inequalities (LMIs). Testing the resulting conditions only requires computations with matrices whose entries are constant in comparison to alternatives where frequency response computations are required

Measurements, Models, Systems and Design

531 s.

Predicting the Propagation of Acoustic Waves using Deep Convolutional Neural Networks

A novel approach for numerically propagating acoustic waves in two-dimensional quiescent media has been developed through a fully convolutional multi-scale neural network. This data-driven method managed to produce accurate results for long simulation times with a database of Lattice Boltzmann temporal simulations of propagating Gaussian Pulses, even in the case of initial conditions unseen during training time, such as the plane wave configuration or the two initial Gaussian pulses of opposed amplitudes. Two different choices of optimization objectives are compared, resulting in an improved prediction accuracy when adding the spatial gradient difference error to the traditional mean squared error loss function. Further accuracy gains are observed when performing an a posteriori correction on the neural network prediction based on the conservation of acoustic energy, indicating the benefit of including physical information in data-driven methods