On the minimum exit rate for a diffusion process pertaining to a chain of distributed control systems with random perturbations

In this paper, we consider the problem of minimizing the exit rate with which a diffusion process pertaining to a chain of distributed control systems, with random perturbations, exits from a given bounded open domain. In particular, we consider a chain of distributed control systems that are formed by $n$ subsystems (with $n \ge 2$), where the random perturbation enters only in the first subsystem and is then subsequently transmitted to the other subsystems. Furthermore, we assume that, for any $\ell \in \{2, \ldots, n\}$, the distributed control systems, which is formed by the first $\ell$ subsystems, satisfies an appropriate H\"ormander condition. As a result of this, the diffusion process is degenerate, in the sense that the infinitesimal generator associated with it is a degenerate parabolic equation. Our interest is to establish a connection between the minimum exit rate with which the diffusion process exits from the given domain and the principal eigenvalue for the infinitesimal generator with zero boundary conditions. Such a connection allows us to derive a family of Hamilton-Jacobi-Bellman equations for which we provide a verification theorem that shows the validity of the corresponding optimal control problems. Finally, we provide an estimate on the attainable exit probability of the diffusion process with respect to a set of admissible (optimal) Markov controls for the optimal control problems.Comment: 12 Pages. (Additional Note: This work is, in some sense, a continuation of our previous paper arXiv:1408.6260.

Space-Time-Domain Decomposition for Optimal Control Problems Governed by Linear Hyperbolic Systems

In this article, we combine a domain decomposition method in space and time for optimal control problems with PDE-constraints described in [2] to a simultaneous space-time decomposition applied to optimal control problems for systems of linear hyperbolic equations with distributed control. We thereby extend the recent work [31, 32] and answer a long standing open question as to whether the combination of time- and space-domain decomposition for the method under consideration can be put into one single convergent iteration procedure. The algorithm is designed for a semi-elliptic system of equations obtained from the hyperbolic optimality system by the way of reduction to the adjoint state. The focus is on the relation to the classical procedure introduced by P. L. Lions [25] for elliptic problems.In this article, we combine a domain decomposition method in space and time for optimal control problems with PDE-constraints described in [2] to a simultaneous space-time decomposition applied to optimal control problems for systems of linear hyperbolic equations with distributed control. We thereby extend the recent work [31, 32] and answer a long standing open question as to whether the combination of time- and space-domain decomposition for the method under consideration can be put into one single convergent iteration procedure. The algorithm is designed for a semi-elliptic system of equations obtained from the hyperbolic optimality system by the way of reduction to the adjoint state. The focus is on the relation to the classical procedure introduced by P. L. Lions [25] for elliptic problems

Thermal Therapy: Stabilization and Identification

44 pages, In "Heat Transfer - Mathematical Modelling, Numerical Methods and Information Technology", A. Belmiloudi (Ed.), InTech (Open Access Publisher), Vienna, 2011 - ISBN 978-953-307-550-1International audienceMotivated by topics and issues critical to human health and safety of treatment, the problem studied in this chapter derives from the modeling and stabilizing control of the transport of thermal energy in biological systems with porous structures. First, the modeling of thermal transport by perfusion within the framework of the theory of porous media is presented and the governing equations are established. The thermal processes within the tissues are predicted by using some generalized uncertain evolutive nonlinear bioheat transfer type models with nonlinear Robin boundary conditions, by taking into account porous structures and directional blood flow. Afterwards the existence, the uniqueness and the regularity of the solution of the state equation are presented as well as stability and maximum principle under extra assumptions. Second, we introduce the initial perturbation problem and give the existence and uniqueness of the perturbation solution and obtain a stability result. Third, the real-time identification and robust stabilization problems are formulated, in different situations, in order to reconstitute simultaneously the blood perfusion rate, the porosity parameter, the heat transfer parameter, the distributed energy source terms and the heat flux due to the evaporation, which affect the effects of thermal physical properties on the transient temperature of biological tissues, and to control and stabilize the desired online temperature and thermal damage provided by MRI measurements. Because, it is now well-known that a controlled and stabilized temperature field does not necessarily imply a controlled and stabilized tissue damage. This work includes results concerning the existence of the optimal solutions, the sensitivity problems, adjoint problems, necessary optimality conditions and optimization problems. Next, we analyse the case when data are measured in only some points in space-time domain, and the case where the body Ω is constituted by different tissue types which occupy finitely many disjointed subdomains. Some numerical strategies, based on adjoint control optimization , in order to perform the robust control, are also discussed. Finally, control and stabilization problems for a coupled thermal, radiation transport and coagulation processes modeling the laser-induced thermotherapy in biological tissues, during cancer treatment, are analyzed

Using Problem Frames and projections to analyze requirements for distributed systems

Subproblems in a problem frames decomposition frequently make use of projections of the complete problem context. One specific use of projec-tions occurs when an eventual implementation will be distributed, in which case a subproblem must interact with (use) the machine in a projection that represents another subproblem. We refer to subproblems used in this way as services, and propose an extension to projections to represent services as a spe-cial connection domain between subproblems. The extension provides signifi-cant benefits: verification of the symmetry of the interfaces, exposure of the machine-to-machine interactions, and prevention of accidental introduction of shared state. The extension’s usefulness is validated using a case study

Experiences in Integrated Multi-Domain Service Management

Increased competition, complex service provision chains and integrated service offerings require effective techniques for the rapid integration of telecommunications services and management systems over multiple organisational domains. This paper presents some of the results of practical development work in this area, detailing the technologies and standards used, the architectural approach taken and the application of this approach to specific services. This work covers the integration of multimedia services, broadband networks, service management and network management, though the detailed examples given focus specifically on the integration of services and service management

Frequency-Domain Control Design in Power Systems

The scope of this thesis encompasses two main subjects: fixed-structure data-driven control design on one side, and control design in power systems on the other. The overall goal is to identify challenging and relevant problems in power systems, to express them as rigorous specifications from the viewpoint of control systems, and to solve them by developing and applying advanced methods in robust control. This work aims to combine expertise from both fields to open up a holistic perspective and bridge the gap between control and power systems. First, the derivation of a novel fixed-structure, data-driven frequency-domain control design method for multivariable systems is described. A key feature of the method is that only the frequency response of the plant is required for the design, and no parametric model is required. The designed controllers are fully parametrized in terms of matrix polynomial functions and can take a centralized, decentralized or distributed structure. The controller performance is formulated as H_2 and H_infinity constraints on any loop transfer function. A convex formulation of the optimization problem is derived, and it is shown that the solution converges to a locally optimal solution of the original problem. The versatility of the design method is demonstrated in various simulation examples, as well as in experiments on two electromechanical setups. Next, a frequency-domain modeling approach for power grids is discussed. A model based on dynamic phasors is developed that represents the electromagnetic and electromechanic dynamics of lines, inverters, synchronous machines and constant power loads. It also offers a modular structure that makes it straightforward to combine white-, grey- and blackbox models in a single framework. Then, the control design method and dynamic phasor model are applied in two relevant power systems case studies. First, the design of a decentralized current controller for parallel, grid-connected voltage source inverters in a typical distribution grid is considered. It is shown how performance specifications can be formulated as frequency-domain constraints in order to attenuate the resonances introduced by the output filters and coupling effects, and to provide robustness against model uncertainties and grid topology changes. The controllers for all VSIs are designed in a single step, and stability and performance is guaranteed by design. Furthermore, an approach for plug-and-play control design is presented. The results are validated in numerical simulation as well as in power-hardware-in-the-loop experiments. The second study concerns the design of a distributed controller that combines primary and secondary frequency and voltage control for an islanded, meshed low-voltage grid with any number of voltage source inverters and synchronous generators in a single framework. No assumption on the R/X-ratio of the lines is made, and it is shown how advanced control specifications such as proportional active power sharing, zero frequency steady-state error and decoupling can be formulated as constraints on the norm of weighted sensitivity functions. Furthermore, the communication delays of the distributed controller are considered exactly during the design. The controller is implemented in numerical simulation, and results show significantly improved performance as compared to the classical hierarchical structure