1979 — 1981 |
Brockett, Roger Byrnes, Christopher |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Linear Dynamical Systems |
0.915 |
1982 — 1986 |
Brockett, Roger Byrnes, Christopher |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
High Gain Linear and Nonlinear Feedback |
0.915 |
1984 — 1985 |
Brockett, Roger |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Equipment Grant For a Vision/Robotics System |
0.915 |
1984 — 1988 |
Brockett, Roger |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
The Mechanics of Robotic Manipulation |
0.915 |
2002 — 2006 |
Brockett, Roger Khaneja, Navin [⬀] |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Time Optimal Control of Quantum Information Processing Systems
EIA-0218441 Navin Khaneja Harvard University
Time Optimal Control of Quantum Information Processing Systems
Time optimal control of quantum mechanical systems can significantly minimize decoherence effects in coherent manipulation of quantum pheonomenon. The central theme of the project is to develop a mathematical theory for optimal unitary control of quantum networks. Network of coupled two level quantum systems form the benchmark for a quantum computer. Finding the minimum time it takes to produce a desired unitary evolution in a network of coupled quantum systems is of fundamental practical importance not just in the field of quantum information processing but the whole field of coherent spectroscopy. In particular, focus is on optimal control of network of coupled spin half particles (acting as qubits in liquid and solid state NMR quantum conputing with fixed interaction Hamiltonian and ability to selectively excite some of the qubits. One of the goals of this project is to develop geometric methods for computing fundamental bounds on the minimum time it takes to produce unitary evolution in a network of coupled quantum systems and find time optimal control laws which achieve these bounds.
These methods are based on variational ideas as captured by the theory of optimal control. Finding optimal strategies to control the dynamics of quantum networks can be reduced to problems in Riemannian geometry of computing subriemannian geodesics in certain homogeneous spaces. Using these geometric techniques time optimal control strategies for quantum networks are being computed.
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0.915 |
2003 — 2004 |
Brockett, Roger |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Small Grant For Exploratory Research
This proposal describes a new more comprehensive approach to the design of feedback controls for a wide variety of systems. The basic idea is to replace the usual differential equation description of the system being controlled by a corresponding Louiville equation and to formulate an optimization problem that takes into account a range of initial conditions and the way in which the control depends on time and state. The mathematical problems that arise do not seem to have been explored up until now and so an important intellectual challenge to be overcome in this research will be to develop methods for solving the type of variational problems involving partial differential equations that arise in these problems.
The potential for this work to benefit society rests on two main lines of thought. First of all, control systems are now found in almost all durable goods, including dishwashers, heaters, toasters, automobiles, etc. and are becoming common in building management involving lighting, heating and security. The use of conventional optimal control often defines a control law that is too expensive to implement and so that ad hoc schemes are used that yield a performance level that is not all that it could be. The ideas discussed here are directed toward developing a methodology for finding less expensive, higher performance solutions. Secondly, although biological systems are replete with feedback control mechanisms, conventional control theory has had only limited success in predicting and explaining the structures identified so far. Arguing that living systems, through evolution, are attempting to optimize a trade-off between the performance of the system and its complexity, we make the case that better success will be had in explaining biological phenomena using theories of the type proposed here.
The proposer has a long history of educating students at both the graduate and undergraduate level. For example, this spring one of his undergraduate students received one of only three ``Fay" prizes given to graduating seniors for research work. The student designed and fabricated a VLSI chip implementing a very sophisticated motor controller. This is the second undergraduate student of his in the last two years that has received University wide recognition for undergraduate research. The funds requested are absolutely essential if he is to make these kinds of opportunities available to tomorrow's students, both at the graduate and undergraduate level.
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0.915 |
2004 — 2007 |
Brockett, Roger |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Active Measurement and System Identification
The subject of active measurement is described here in the context of a type of measurement processes that has become common in engineering and physics, both at the macro scale and at the nano scale. Active measurement, or active sensing as it may also be called, is often used to extend the capabilities of sensors having limited dynamic range or the need for a sequence of preparatory steps. We focus on a class of problems of the type that arise in nuclear magnetic resonance (NMR) spectroscopy where the sample must be exposed to an excitation and the signal-to-noise ratios are very unfavorable. In this setting it often happens that the measurements must be repeated and averaged over long periods of time if one is to get a useful result. When these problems are conceptualized as problems of minimizing the error variance, an unusual range of diffculties present themselves reflecting the nonlinear nature of the problem. These are the subject of this proposal. Intellectual Merit: It is argued here that in a number of areas the basic insights and mathematical algorithms needed to obtain the most useful conclusions from an existing experimental apparatus are not yet available. In some cases we can conceptualize the problem by saying that in the case of stochastic processes, further improvements in the estimation process depend on determining how to best control the equation governing the error variance as it shows up in the Kalman-Bucy fiter equations. It is argued here, perhaps for the first time, that active control of this variance is akin to controlling a certain type of nonlinear systems in that non commutative effects are of critical importance. In this proposal we explore this idea in the context of NMR problems and find that when used in connection with a carefully designed mode selection process it is possible to increase the signal to noise ratio significantly. We also argue that these questions are best addressed in a somewhat broader context and the proposal seeks to place them in their natural generality. Broader Impact: The motivation for this work is firmly rooted in real world con- siderations. For example, for years it has been felt that the problem of determining the structure of individual proteins is of fundamental importance in understanding a wide range of diseases and the design of their treatments. NMR spectroscopy is the main tool for determining protein structure but the current methods are hampered by the fact that the evidence they provide is noisy and indirect. The current methods for designing the NMR pulses and processing the resulting data have been developed from experience and insight, backed up by an excellent understanding of the basic physics of nuclear spin. What is not well supported by theory is the subsequent signal processing and the interplay be- tween pulse design and signal processing. An important aspect of this work is to address this problem and thus make the process of protein structure determination faster and more accurate. We also point out that there is under development a new nanometer measure- ment tool that combines aspects of the atomic force microscope with NMR and which is may also provide a useful window on key questions in protein structure determination. 1
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0.915 |
2006 — 2007 |
Brockett, Roger Khaneja, Navin [⬀] |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Workshop Proposal: Control of Quantum Systems Conference, Harvard University; August 7-12, 2006
The proposal requests funds for a five day workshop on quantum control to be held at Harvard University in August of 2006. The goal of the workshop is to foster an understanding among control theorists of application-driven needs for methods to design control schemes and an appreciation of the practical constraints on their implementation. We also hope to build an appreciation among experimentalists and theoretical for the range and utility of analysis/design methods from control theory. Finally, we hope to begin the development conceptual and mathematical languages for quantum control. research presentations will be integrated with tutorial lectures. We are requesting funds from several sources with the expectation that we will be able to cover the travel and living expenses of about 55 attendees from outside Cambridge and about 20 local.
Intellectual Merit The workshop aims to bring researchers from diverse field of physics, chemistry, control theory, dynamical systems, stochastics, signal processing and information science to identify mathematical models and control problems whose study and solution will have significant bearing on technologies and experiments involving control and manipulation of quantum systems. Experience has shown that systematic use of methods of control theory that lead to significant improvement in the state of the art methods in fields ranging from magnetic resonance to quantum information processing. The workshop aims to build on these successes to create a unified language and system theory of quantum mechanical systems with potential impact on areas of atomic, molecular and optical physics, coherent spectroscopies in chemistry, magnetic resonance, quantum communication, information and computation.
Broader Impact Important component of this meeting are tutorial sessions that aim to educate students and researchers in areas of physics, chemistry and magnetic resonance, the analysis and design methods of control theory. There will also be tutorial session on basic models that arise in applications involving control and manipulation of quantum systems to researchers and students in engineering. There is a formidable gap between the types of models and analysis commonly utilized by application-oriented practitioners and those studied by control theorists. The workshop aims to bridge this gap.
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0.915 |
2015 — 2017 |
Tarokh, Vahid [⬀] Brockett, Roger Li, Na |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Eager: Limited Communications Demand Control in Power Grid
A major issue in future smart grid is how intelligent devices and independent producers can respectively change their power consumption/production to achieve near maximum efficiency for the power network. Limited communications between devices and producers necessitates a transformative approach where the elements of the network can act in an autonomous manner with limited information or communications, yet achieve near optimal performance. This is the main topic of the proposed project.
By combining the two-way power flow with the two-way information flow, demand response can be applied to reduce the peak demand, shift load for economic benefits, reduce operating reserves and improve the grid stability. An important obstacle has been the lack of supporting information, communication and computation infrastructures that can ensure quality of service (QoS) for various demand response applications and devices. This project goal is to develop transformative and applicable distributed algorithms and architectures with provable performance for demand control subject to communication constraints in power networks. Results from this project will be applied to achieve high-performance and high-confidence management of the smart buildings and cities, and further contributes to the goal of improving urban sustainability.
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0.915 |