Optimal control theory for a unitary operation under dissipative evolution

We show that optimizing a quantum gate for an open quantum system requires the time evolution of only three states irrespective of the dimension of Hilbert space. This represents a significant reduction in computational resources compared to the complete basis of Liouville space that is commonly believed necessary for this task. The reduction is based on two observations: the target is not a general dynamical map but a unitary operation; and the time evolution of two properly chosen states is sufficient to distinguish any two unitaries. We illustrate gate optimization employing a reduced set of states for a controlled phasegate with trapped atoms as qubit carriers and a iSWAP gate with superconducting qubits.

Modeling, Estimation, and Control of Robot-Soil Interactions

This thesis presents the development of hardware, theory, and experimental methods to enable a robotic manipulator arm to interact with soils and estimate soil properties from interaction forces. Unlike the majority of robotic systems interacting with soil, our objective is parameter estimation, not excavation. To this end, we design our manipulator with a flat plate for easy modeling of interactions. By using a flat plate, we take advantage of the wealth of research on the similar problem of earth pressure on retaining walls. There are a number of existing earth pressure models. These models typically provide estimates of force which are in uncertain relation to the true force. A recent technique, known as numerical limit analysis, provides upper and lower bounds on the true force. Predictions from the numerical limit analysis technique are shown to be in good agreement with other accepted models. Experimental methods for plate insertion, soil-tool interface friction estimation, and control of applied forces on the soil are presented. In addition, a novel graphical technique for inverting the soil models is developed, which is an improvement over standard nonlinear optimization. This graphical technique utilizes the uncertainties associated with each set of force measurements to obtain all possible parameters which could have produced the measured forces. The system is tested on three cohesionless soils, two in a loose state and one in a loose and dense state. The results are compared with friction angles obtained from direct shear tests. The results highlight a number of key points. Common assumptions are made in soil modeling. Most notably, the Mohr-Coulomb failure law and perfectly plastic behavior. In the direct shear tests, a marked dependence of friction angle on the normal stress at low stresses is found. This has ramifications for any study of friction done at low stresses. In addition, gradual failures are often observed for vertical tools and tools inclined away from the direction of motion. After accounting for the change in friction angle at low stresses, the results show good agreement with the direct shear values.

Experimental Modeling and Control Strategies on an Open Mobile Robot Platform PRIM

This research work deals with the problem of modeling and design of low level speed controller for the mobile robot PRIM. The main objective is to develop an effective educational tool. On one hand, the interests in using the open mobile platform PRIM consist in integrating several highly related subjects to the automatic control theory in an educational context, by embracing the subjects of communications, signal processing, sensor fusion and hardware design, amongst others. On the other hand, the idea is to implement useful navigation strategies such that the robot can be served as a mobile multimedia information point. It is in this context, when navigation strategies are oriented to goal achievement, that a local model predictive control is attained. Hence, such studies are presented as a very interesting control strategy in order to develop the future capabilities of the system

Operation and control of SBR processes for enhanced biological nutrient removal from wastewater

In the last decades, the awareness of environmental issues has increased in society considerably. There is an increasing need to improve the effluent quality of domestic wastewater treatment processes. This thesis describes the application of the Sequencing Batch Reactor (SBR) technology for Biological Nutrient Removal (BNR) from the wastewater. In particular, the work presented evolves from the nitrogen removal to the biological nutrient removal (i.e. nitrogen plus phosphorous removal) with special attention to the operational strategy design, the identification of possible reactor cycle controls or the influent composition related to the process efficiency. In such sense, also the use of ethanol as an external carbon (when low influent Carbon:Phosphorus (C:P) or Carbon:Nitrogen (C:N) ratios are presented) are studied as an alternative to maintain the BNR efficiency.

Modelling disease spread and control in networks: implications for plant sciences

Networks are ubiquitous in natural, technological and social systems. They are of increasing relevance for improved understanding and control of infectious diseases of plants, animals and humans, given the interconnectedness of today's world. Recent modelling work on disease development in complex networks shows: the relative rapidity of pathogen spread in scale-free compared with random networks, unless there is high local clustering; the theoretical absence of an epidemic threshold in scale-free networks of infinite size, which implies that diseases with low infection rates can spread in them, but the emergence of a threshold when realistic features are added to networks (e.g. finite size, household structure or deactivation of links); and the influence on epidemic dynamics of asymmetrical interactions. Models suggest that control of pathogens spreading in scale-free networks should focus on highly connected individuals rather than on mass random immunization. A growing number of empirical applications of network theory in human medicine and animal disease ecology confirm the potential of the approach, and suggest that network thinking could also benefit plant epidemiology and forest pathology, particularly in human-modified pathosystems linked by commercial transport of plant and disease propagules. Potential consequences for the study and management of plant and tree diseases are discussed.

Dynamic recurrent neural network for system identification and control

A dynamic recurrent neural network (DRNN) that can be viewed as a generalisation of the Hopfield neural network is proposed to identify and control a class of control affine systems. In this approach, the identified network is used in the context of the differential geometric control to synthesise a state feedback that cancels the nonlinear terms of the plant yielding a linear plant which can then be controlled using a standard PID controller.

Autonomous ship collision free trajectory navigation and control algorithms

A new autonomous ship collision free (ASCF) trajectory navigation and control system has been introduced with a new recursive navigation algorithm based on analytic geometry and convex set theory for ship collision free guidance. The underlying assumption is that the geometric information of ship environment is available in the form of a polygon shaped free space, which may be easily generated from a 2D image or plots relating to physical hazards or other constraints such as collision avoidance regulations. The navigation command is given as a heading command sequence based on generating a way point which falls within a small neighborhood of the current position, and the sequence of the way points along the trajectory are guaranteed to lie within a bounded obstacle free region using convex set theory. A neurofuzzy network predictor which in practice uses only observed input/output data generated by on board sensors or external sensors (or a sensor fusion algorithm), based on using rudder deflection angle for the control of ship heading angle, is utilised in the simulation of an ESSO 190000 dwt tanker model to demonstrate the effectiveness of the system.

UK planning controls and the market responsiveness of housing supply

There is growing international interest in the impact of regulatory controls on the supply of housing The UK has a particularly restrictive planning regime and a detailed and uncertain process of development control linked to it. This paper presents the findings of empirical research on the time taken to gain planning permission for selected recent major housing projects from a sample of local authorities in southern England. The scale of delay found was far greater than is indicated by average official data measuring the extent to which local authorities meet planning delay targets. Hedonic analysis indicated that there is considerable variation in time it takes local authorities to process planning applications, with the worst being four times slower than the best. Smaller builders and housing association developments are processed more quickly than those of large developers and small sites appear to be particularly time intensive. These results suggest that delays in development control may be a significant contributory factor to the low responsiveness of UK housing supply to upturns in market activity.

The Mathematics of Control Theory

This text contains papers presented at the Institute of Mathematics and its Applications Conference on Control Theory, held at the University of Strathclyde in Glasgow. The contributions cover a wide range of topics of current interest to theoreticians and practitioners including algebraic systems theory, nonlinear control systems, adaptive control, robustness issues, infinite dimensional systems, applications studies and connections to mathematical aspects of information theory and data-fusion.

Applying robust control theory to solve problems in bio-medical sciences: study of an apoptotic model

Biological models of an apoptotic process are studied using models describing a system of differential equations derived from reaction kinetics information. The mathematical model is re-formulated in a state-space robust control theory framework where parametric and dynamic uncertainty can be modelled to account for variations naturally occurring in biological processes. We propose to handle the nonlinearities using neural networks.

On non-linear dynamics and control designs applied to the ideal and non-ideal variants of the Fitzhugh-Nagumo (FN) mathematical model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Mathematical modeling and control of population systems: Applications in biological pest control

The aim of this paper is to apply methods from optimal control theory, and from the theory of dynamic systems to the mathematical modeling of biological pest control. The linear feedback control problem for nonlinear systems has been formulated in order to obtain the optimal pest control strategy only through the introduction of natural enemies. Asymptotic stability of the closed-loop nonlinear Kolmogorov system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation, thus guaranteeing both stability and optimality. Numerical simulations for three possible scenarios of biological pest control based on the Lotka-Volterra models are provided to show the effectiveness of this method. (c) 2007 Elsevier B.V. All rights reserved.

Nonlinear Dynamics and Control of an Ideal/Nonideal Load Transportation System With Periodic Coefficients

In this paper, a loads transportation system in platforms or suspended by cables is considered. It is a monorail device and is modeled as an inverted pendulum built on a car driven by a dc motor the governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the dc motor and the dynamical system, that is, we have a so called nonideal periodic problem. The problem is analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, we also analyze the problem quantitatively using the Floquet multipliers technique. Finally, we devise a control for the studied nonideal problem. The method that was used for analysis and control of this nonideal periodic system is based on the Chebyshev polynomial exponsion, the Picard iterative method, and the Lyapunov-Floquet transformation (L-F transformation). We call it Sinha's theory.