Anisotropy-based performance analysis of linear discrete time invariant control systems

The anisotropic norm of a linear discrete-time-invariant system measures system output sensitivity to stationary Gaussian input disturbances of bounded mean anisotropy. Mean anisotropy characterizes the degree of predictability (or colouredness) and spatial non-roundness of the noise. The anisotropic norm falls between the H-2 and H-infinity norms and accommodates their loss of performance when the probability structure of input disturbances is not exactly known. This paper develops a method for numerical computation of the anisotropic norm which involves linked Riccati and Lyapunov equations and an associated special type equation.

Optimal control, geometry, and quantum computing

We prove upper and lower bounds relating the quantum gate complexity of a unitary operation, U, to the optimal control cost associated to the synthesis of U. These bounds apply for any optimal control problem, and can be used to show that the quantum gate complexity is essentially equivalent to the optimal control cost for a wide range of problems, including time-optimal control and finding minimal distances on certain Riemannian, sub-Riemannian, and Finslerian manifolds. These results generalize the results of [Nielsen, Dowling, Gu, and Doherty, Science 311, 1133 (2006)], which showed that the gate complexity can be related to distances on a Riemannian manifold.

Practicality of time-optimal two-qubit Hamiltonian simulation

What is the time-optimal way of using a set of control Hamiltonians to obtain a desired interaction? Vidal, Hammerer, and Cirac [Phys. Rev. Lett. 88, 237902 (2002)] have obtained a set of powerful results characterizing the time-optimal simulation of a two-qubit quantum gate using a fixed interaction Hamiltonian and fast local control over the individual qubits. How practically useful are these results? We prove that there are two-qubit Hamiltonians such that time-optimal simulation requires infinitely many steps of evolution, each infinitesimally small, and thus is physically impractical. A procedure is given to determine which two-qubit Hamiltonians have this property, and we show that almost all Hamiltonians do. Finally, we determine some bounds on the penalty that must be paid in the simulation time if the number of steps is fixed at a finite number, and show that the cost in simulation time is not too great.

Optimal control and operation of drum granulation processes

Process optimisation and optimal control of batch and continuous drum granulation processes are studied in this paper. The main focus of the current research has been: (i) construction of optimisation and control relevant, population balance models through the incorporation of moisture content, drum rotation rate and bed depth into the coalescence kernels; (ii) investigation of optimal operational conditions using constrained optimisation techniques; (iii) development of optimal control algorithms based on discretized population balance equations; and (iv) comprehensive simulation studies on optimal control of both batch and continuous granulation processes. The objective of steady state optimisation is to minimise the recycle rate with minimum cost for continuous processes. It has been identified that the drum rotation-rate, bed depth (material charge), and moisture content of solids are practical decision (design) parameters for system optimisation. The objective for the optimal control of batch granulation processes is to maximize the mass of product-sized particles with minimum time and binder consumption. The objective for the optimal control of the continuous process is to drive the process from one steady state to another in a minimum time with minimum binder consumption, which is also known as the state-driving problem. It has been known for some time that the binder spray-rate is the most effective control (manipulative) variable. Although other possible manipulative variables, such as feed flow-rate and additional powder flow-rate have been investigated in the complete research project, only the single input problem with the binder spray rate as the manipulative variable is addressed in the paper to demonstrate the methodology. It can be shown from simulation results that the proposed models are suitable for control and optimisation studies, and the optimisation algorithms connected with either steady state or dynamic models are successful for the determination of optimal operational conditions and dynamic trajectories with good convergence properties. (c) 2005 Elsevier Ltd. All rights reserved.

Anisotropy-based robust performance analysis of finite horizon linear discrete time varying systems

We consider a problem of robust performance analysis of linear discrete time varying systems on a bounded time interval. The system is represented in the state-space form. It is driven by a random input disturbance with imprecisely known probability distribution; this distributional uncertainty is described in terms of entropy. The worst-case performance of the system is quantified by its a-anisotropic norm. Computing the anisotropic norm is reduced to solving a set of difference Riccati and Lyapunov equations and a special form equation.

Saving, productivity and national income: a discrete-time geometric framework

This paper proposes an alternative geometric framework for analysing the inter-relationship between domestic saving, productivity and income determination in discrete time. The framework provides a means of understanding how low saving economies like the United States sustained high growth rates in the 1990s whereas high saving Japan did not. It also illustrates how the causality between saving and economic activity runs both ways and that discrete changes in national output and income depend on both current and previous accumulation behaviour. The open economy analogue reveals how international capital movements can create external account imbalances that enhance income growth for both borrower and lender economies. (C) 2002 Elsevier Science B.V. All rights reserved.

Convergence analysis of a discrete-time single-unit gradient ICA algorithm

We revisit the one-unit gradient ICA algorithm derived from the kurtosis function. By carefully studying properties of the stationary points of the discrete-time one-unit gradient ICA algorithm, with suitable condition on the learning rate, convergence can be proved. The condition on the learning rate helps alleviate the guesswork that accompanies the problem of choosing suitable learning rate in practical computation. These results may be useful to extract independent source signals on-line.

Experimental control of single-mode laser chaos by using continuous, time-delayed feedback

Control of chaos in the single-mode optically pumped far-infrared (NH3)-N-15 laser is experimentally demonstrated using continuous time-delay control. Both the Lorenz spiral chaos and the detuned period-doubling chaos exhibited by the laser have been controlled. While the laser is in the Lorenz spiral chaos regime the chaos has been controlled both such that the laser output is cw, with corrections of only a fraction of a percent necessary to keep it there, and to period one. The laser has also been controlled while in the period-doubling chaos regime, to both the period-one and -two states.

Economic and environmental impacts of pollution control in a system of environment and economic interdependence

The importance of the rate of change of the pollution stock in determining the damage to the environment has been an issue of increasing concern in the literature. This paper uses a three-sector (economy, population and environment), non-linear, discrete time, calibrated model to examine pollution control. The model explicitly links economic growth to the health of the environment. The stock of natural resources is affected by the rate of pollution flows, through their impact on the regenerative capacity of the natural resource stock. This can shed useful insights into pollution control strategies, particularly in developing countries where environmental resources are crucial for production in many sectors of the economy. Simulation exercises suggested that, under plausible assumptions, it is possible to reverse undesirable transient dynamics through pollution control expenditure, but this is dependent upon the strategies used for control. The best strategy is to spend money fostering the development of production technologies that reduce pollution rather than spending money dealing with the effects of the pollution flow into the environment. (C) 2001 Elsevier Science Ltd. All rights reserved.

Analysis of small signal stability margins using genetic optimization

Power system small signal stability analysis aims to explore different small signal stability conditions and controls, namely: (1) exploring the power system security domains and boundaries in the space of power system parameters of interest, including load flow feasibility, saddle node and Hopf bifurcation ones; (2) finding the maximum and minimum damping conditions; and (3) determining control actions to provide and increase small signal stability. These problems are presented in this paper as different modifications of a general optimization to a minimum/maximum, depending on the initial guesses of variables and numerical methods used. In the considered problems, all the extreme points are of interest. Additionally, there are difficulties with finding the derivatives of the objective functions with respect to parameters. Numerical computations of derivatives in traditional optimization procedures are time consuming. In this paper, we propose a new black-box genetic optimization technique for comprehensive small signal stability analysis, which can effectively cope with highly nonlinear objective functions with multiple minima and maxima, and derivatives that can not be expressed analytically. The optimization result can then be used to provide such important information such as system optimal control decision making, assessment of the maximum network's transmission capacity, etc. (C) 1998 Elsevier Science S.A. All rights reserved.