Reduced order output feedback control design for PDE systems using proper orthogonal decomposition and nonlinear semidefinite programming

AbstractThe design of an optimal (output feedback) reduced order control (ROC) law for a dynamic control system is an important example of a difficult and in general non-convex (nonlinear) optimal control problem. In this paper we present a novel numerical strategy to the solution of the ROC design problem if the control system is described by partial differential equations (PDE). The discretization of the ROC problem with PDE constraints leads to a large scale (non-convex) nonlinear semidefinite program (NSDP). For reducing the size of the high dimensional control system, first, we apply a proper orthogonal decomposition (POD) method to the discretized PDE. The POD approach leads to a low dimensional model of the control system. Thereafter, we solve the corresponding small-sized NSDP by a fully iterative interior point constraint trust region (IPCTR) algorithm. IPCTR is designed to take advantage of the special structure of the NSDP. Finally, the solution is a ROC for the low dimensional approximation of the control system. In our numerical examples we demonstrate that the reduced order controller computed from the small scaled problem can be used to control the large scale approximation of the PDE system

A geometric theory for 2-D systems including notions of stabilisability

In this paper we consider the problem of internally and externally stabilising controlled invariant and output-nulling subspaces for two-dimensional (2-D) Fornasini–Marchesini models, via static feedback. A numerically tractable procedure for computing a stabilising feedback matrix is developed via linear matrix inequality techniques. This is subsequently applied to solve, for the first time, various 2-D disturbance decoupling problems subject to a closed-loop stability constraint

Ageing and Financial Stability

Abstract: Although the precise details are subject to major uncertainty, it seems likely that the process of population ageing will involve major shifts in financing, which may give rise to financial turbulence and systemic risk. The locus and scale of these effects will also depend on the predominant approach to retirement income provision. It is argued that the financial-stability risks arising from continuing with unsustainable pay-as-you-go systems would be more threatening than those arising from funding. Fiscal crises can have incalculable consequences for private financial markets, while pension funding involves more an adaptation by regulatory authorities to a more securitised and institutionalised financial system, that is likely to develop in any case. Concerning policy, for social security, the key issue is reform, so that the fiscal difficulties and their consequences for financial stability foreshadowed above do not arise. For institutional investors involved in funding, policy issues arising include the need for prudent person asset regulation, absence of guarantees generating moral hazard and international diversification of institutional portfolios, so that they are less dependent on the performance of the domestic economy than would otherwise be the case. Banks would not be immune to the side-effects of the various patterns ageing will generate, and an awareness of such risks as well a

Argonne National Laboratory Reports

One aspect of Argonne research in parallel computing involves the speed and other properties of parallel SDI algorithms. Various algorithms under study have exhibited speedups resulting from parallelization on shared-memory machines. A weapon-target accessibility algorithm called ACCESS exhibited a high degree of inherent parallelism and has been studied on a wide variety of sequential and parallel multiple instruction multiple data (MIMD) machines. To study ACCESS on a massively parallel single instruction multiple data (SIMD) machine architecture, ANL researchers developed a version of ACCESS on a Thinking Machines Corporation 16K processor Connection Machine-2 (CM-2) located at the ACRF. ANL researchers wrote the Connection Machine version of ACCESS in C(*), a version of C by Thinking Machines Corporation with extensions to accommodate SIMD parallelism. Because of the large number of available physical processors and the ability to create virtual processors on the CM-2, the Connection Machine version of ACCESS was able to process an array of 128 x 1024 tasks in parallel. For the data tested, the CM-2 implementation of ACCESS was faster than both the parallel version run on the Alliant FX/8, the Encore Multimax, and the Sequent Balance and the sequential version run on the ANL Cray X-MP/14. For the benchmark ACCESS problem, the CM-2 at ANL with 16K processors achieved a sustained performance of 400 Mflops. On other larger CM-2 machines, the same problem achieved even higher performance: nearly 1600 Mflops on the Los Alamos National Laboratory 64K processor CM-2. %boratory 64K processor CM-2. The investigation has demonstrated that achieving optimal performance requires structuring the code carefully to keep all available processors busy and to reduce disruptive communication on the front-end processor

A successive SDP-NSDP approach to a robust optimization problem in finance

Robust optimization, Nonlinear semidefinite programming, Static hedging, Barrier options, Eigenvalue minimization,

A comparison of software- and hardware-gating techniques applied to near-field antenna measurements

It is well-known that antenna measurements are error prone with respect to reflections within an antenna measurements test facility. The influence on near-field (NF) measurements with subsequent NF to far-field (FF) transformation can be significantly reduced applying soft- or hard-gating techniques. Hard-gating systems are often used in compact range facilities employing fast PIN-diode switches (Hartmann, 2000) whereas soft-gating systems utilize a network analyzer to gather frequency samples and eliminate objectionable distortions in the time-domain by means of Fourier-transformation techniques. Near-field (NF) antenna measurements are known to be sensitive to various errors concerning the measurement setup as there have to be mentioned the accuracy of the positioner, the measurement instruments or the quality of the anechoic chamber itself. Two different approaches employing soft- and hard-gating techniques are discussed with respect to practical applications. Signal generation for the antenna under test (AUT) is implemented using a newly developed hard-gating system based on digital signal synthesis allowing gate-widths of 250 ps to 10 ns. Measurement results obtained from a Yagi-Uda antenna under test (AUT) and a dual polarized open-ended waveguide used as probe antenna are presented for the GSM 1800 frequency range