Memory Resilient Gain-scheduled State-Feedback Control of Uncertain LTI/LPV Systems with Time-Varying Delays

The stabilization of uncertain LTI/LPV time delay systems with time varying delays by state-feedback controllers is addressed. At the difference of other works in the literature, the proposed approach allows for the synthesis of resilient controllers with respect to uncertainties on the implemented delay. It is emphasized that such controllers unify memoryless and exact-memory controllers usually considered in the literature. The solutions to the stability and stabilization problems are expressed in terms of LMIs which allow to check the stability of the closed-loop system for a given bound on the knowledge error and even optimize the uncertainty radius under some performance constraints; in this paper, the $\mathcal{H}_\infty$ performance measure is considered. The interest of the approach is finally illustrated through several examples

Analysis of a new numerical approach to solutions of heat conduction equations arising from heat diffusion

In this work, a new numerical finite difference scheme with the aim of obtaining a new numerical scheme that will be used to solve for the solution of Partial Differential Equations (PDE) arising from heat conduction equation is developed. This is significant because in recent times there is a growing interest in literatures to obtain a continuous numerical method for solving PDE. The numerical accuracy of this new approach is also studied. Detailed numerical results have shown that the new method provides better results than the known explicit finite difference method by Schmidt. And in terms of stability, the new scheme has been able to clearly shown that it is more stable than the old Schmidt explicit method. There is no semi-discretization involved and no reduction of PDE to a system of ODEs in the new approach, but rather a system of algebraic equations is directly obtained. MATLAB software wasused to solve for the desired solutions and the results obtained has shown that the method is near exact solutions

Indirect stabilization of weakly coupled systems with hybrid boundary conditions

We investigate stability properties of indirectly damped systems of evolution equations in Hilbert spaces, under new compatibility assumptions. We prove polynomial decay for the energy of solutions and optimize our results by interpolation techniques, obtaining a full range of power-like decay rates. In particular, we give explicit estimates with respect to the initial data. We discuss several applications to hyperbolic systems with {\em hybrid} boundary conditions, including the coupling of two wave equations subject to Dirichlet and Robin type boundary conditions, respectively

A spatiotemporal framework for the analytical study of optimal growth under transboundary pollution

We construct a spatiotemporal frame for the study of optimal growth under transboundary pollution. Space is continuous and polluting emissions originate in the intensity of use of the production input. Pollution flows across locations following a diffusion process. The objective functional of the economy is to set the optimal production policy over time and space to maximize welfare from consumption, taking into account a negative local pollution externality and the diffusive nature of pollution. Our framework allows for space and time dependent preferences and productivity, and does not restrict diffusion speed to be space-independent. This provides a comprehensive setting to analyze pollution diffusion with a close account of geographic heterogeneity. The involved optimization problem is infinite-dimensional. We propose an alternative method for an analytical characterization of the optimal paths and the asymptotic spatial distributions. The method builds on a deep economic concept of pollution spatiotemporal welfare effect, which makes it definitely useful for economic analysis

A theory of the infinite horizon LQ-problem for composite systems of PDEs with boundary control

We study the infinite horizon Linear-Quadratic problem and the associated algebraic Riccati equations for systems with unbounded control actions. The operator-theoretic context is motivated by composite systems of Partial Differential Equations (PDE) with boundary or point control. Specific focus is placed on systems of coupled hyperbolic/parabolic PDE with an overall `predominant' hyperbolic character, such as, e.g., some models for thermoelastic or fluid-structure interactions. While unbounded control actions lead to Riccati equations with unbounded (operator) coefficients, unlike the parabolic case solvability of these equations becomes a major issue, owing to the lack of sufficient regularity of the solutions to the composite dynamics. In the present case, even the more general theory appealing to estimates of the singularity displayed by the kernel which occurs in the integral representation of the solution to the control system fails. A novel framework which embodies possible hyperbolic components of the dynamics has been introduced by the authors in 2005, and a full theory of the LQ-problem on a finite time horizon has been developed. The present paper provides the infinite time horizon theory, culminating in well-posedness of the corresponding (algebraic) Riccati equations. New technical challenges are encountered and new tools are needed, especially in order to pinpoint the differentiability of the optimal solution. The theory is illustrated by means of a boundary control problem arising in thermoelasticity.Comment: 50 pages, submitte