Mustafa Khammash - US grants

This project concerns the development of new theory and techniques dealing with the analysis and synthesis of control systems in the presence of uncertainty. The main outcome of this project is a theory that provides a systematic means for designing controllers which lead to systems possessing optimal stability and performance properties despite the presence of plant and signal uncertainty. This theory is based on the structured uncertainty model which allows the inclusion of information about the sources of modelling uncertainty thus minimizing conservatism in the analysis and design procedures. In addition, by adopting the l-infinity signal norm, time domain objectives can be included in the design in a natural way. The use of this norm distinguishes this approach from other approaches and provides a novel way for addressing the issues involved in controlling uncertain systems. The methods employed in the project will take advantage of recently developed theory which makes possible the analysis of system stability and performance robustness. Numerical algorithms implementing the developed controller synthesis techniques will also be developed and applied to practical examples. In addition, the theory for robustness analysis will be extended to incorporate a larger class of systems and to allow a better representation of disturbances and uncertainty.

This project focuses on control strategies for power systems when they are operating near their limits. I is attempting to extend the L infinity robustness results to include complex signals. This of specific interest to the robustness analysis of power systems, were load changes and network admittance changes result in uncertainty dealing with complex admittances. In addition, the HVDC and SVC control will be incorporated in the robustness control procedure. A systematic procedure to design HVDC and SVC control parameters is also proposed. The analytical methods proposed and the algorithms developed will be tested on a realistic power network and the results obtained will be compared with those obtained by conventional analysis.

9457485 Khammash The research plan involves the creation and development of new analytical and computational tools for the analysis and synthesis of control systems in the presence of modeling uncertainty. Another goal is to develop new robustness tools suitable for handling more refined models of uncertainty and disparate performance objectives. The research will address the robustness issues specific to particular application areas such as power systems and compressor control systems. The design of power systems stabilizers, high voltage direct current modulation, and static VAR compensators will be investigated. ***

The principal goal of this project is to develop a novel and unique undergraduate laboratory in control system. The laboratory provides hands-on experience in the various steps of control systems design, aids students in visualizing the abstract concepts covered in a control system course, introduces students to the practical aspects of design, and provides an avenue to synthesize theoretical materials developed in a lecture. This project is setting up a computer-controlled control system design laboratory to support undergraduate courses and design efforts. The laboratory includes four novel design experiments, specifically designed to stimulate the students and to demonstrate the practical and analytical issues in control system design and development. The project is using this "hands-on" integrated capability to provide a complete design and analysis experience. This includes model development and verification, model simulation, control design, system implementation, and verification of performance objectives. Modifications to original designs can be included and parameters can be fine tuned. Students are confronted with design and analysis activities similar to those faced by engineers in industry.

ECS-9810081 Khammash In recent years, the North American Electric Interconnection has undergone major changes with the advent of a competitive market place, and deregulation. These changes will impose new requirements on system operation and planning. It is likely that the emergence of open access, and wheeling of power in a competitive market place will drive the need to operate and plan the system at higher levels of loading, leading to further stress on the system. To a large extent, adequate system dynamic performance will depend on the proper operation and performance of critical controls. Proper design and robust performance of these controls are essential for the reliable operation of the interconnected power system. This proposal deal with development of techniques to apply modern robust control methods to design and analyze controls for large scale power systems. We propose to extend existing methods of robust stability analysis to deal with large scale power system problems. Specifically we intend to use the Structured Singular Value approach, and develop analytical and numerical techniques to exploit the structural characteristics of large power systems. We will investigate and develop numerical techniques which are suitable for large scale problems. The developments would involve issues related to uncertainty characterization and parameter selection, frequency sweeps, state space methods utilizing branch and bound techniques, and efficient techniques for control synthesis. The methods developed will be applied to realistic test systems obtained from two North American Electric Utilities.

The effective operation of power systems in the present and the future depends to a large extent on how well several emerging challenges are met today. Power systems continue to be stressed as they are operated in many instances at or near their full capacities. Addition of new transmission lines to relieve this stress is often very difficult and is mired in regulatory procedure. The new deregulated environment has the potential of exacerbating this stress as more power is shipped from longer distances. At the same time, new flexible ac transmission system (FACTS) devices are being commissioned in various locations. While these devices can offer significant performance improvements and may help alleviate some of the problems alluded to; they do have unique dynamic properties that are less familiar than those of existing devices. In addition proper design and analysis of control systems for FACTS is crucial for efficient operation. The resulting dynamic behavior of the overall system that incorporates these FACTS devices is not well understood. Consequently, the potential benefits of these devices may not be fully realized. The market mechanisms in the future will have a bearing on the operating conditions and the transaction contracts that are established. Since the market would be geared to fully utilizing efficient generation, additional stress would be imposed on the transmission grid in certain locations. New technology involving distributed generation is being rapidly introduced in the system to meet growing demand. As a result several important technical issues related to system interconnection, reliability, and location need to be addressed. These important issues call for work in the areas of real time control, sensing, communication, economics, modeling, and analysis of large scale systems.

We propose to conduct a workshop that will bring together researchers, scientist, and federal agency participants in the areas described above. Selected participants will present position papers and discussions that address key research issues will be conducted. The workshop will focus on identifying emerging problem in power systems that can benefit from the system and control theoretic developments as well as presenting new research ideas in the control, operation, and economics of large networks and their application to power systems. The outcomes of the presentations and discussions will be used as the basis to identify future research needs in the area of large-scale power systems and the means by which such needs can be met. The presentations, discussions, and recommendations for future research will be published in the workshop proceedings.

0123496
Khammash

The objective of the proposed research is to study examples of biological feedback regulation mechanisms using the tools of dynamical systems and feedback control theory, and to use the results to shed new understanding on the operation of these systems in health and disease. In achieving this objective, The PI seeks to identify functional modules that serve specific feedback control roles, to determine the physiological basis of these modules, and to understand the extent to which such modules generalize to other regulatory systems and across hierarchical scales. These questions are key in addressing the long-term objective to develop a unified framework for analyzing homeostatic mechanisms--one that is centered on feedback control theory concepts and language, and takes into account known physiology. It is believed that such a framework will make it possible to make new progress in the understanding of those complex biological and chemical processes involved in homeostasis and the functional modules that these processes constitute, based on the functional constraints that are imposed on these modules by the necessities of feedback and robustness.

This symposium will encourage the participation of researchers from a broad range of disciplines, while maintaining a core representation from the areas of Dynamics and Controls. Many of the presentations will focus on new emerging research areas of key significance. These new areas share in common the fact the dynamics and control theory and methods provide the appropriate framework for the understanding of the corresponding phenomena, while at the same time providing many of the tools necessary for their application to relevant technologies. Examples of these opportunities include the areas of systems biology, quantum feedback and control, fluid dynamics, and control applications in nanotechnology. The importance of these emerging areas in the current research agenda in science and technology means that a unique opportunity exists to drastically extend the scope and impact of dynamics and control methods far beyond their traditional areas of application in engineering.

Project Summary
Motivated by design problems i anotechnology and by key theoretical problems of interest,
we consider a paradigm whereby the plant description depends on one or several parameters that
are subject to design.We propose a general framework for I tegrated Parameter and Controller
(IPC)design that allows multiple performance requirements.We propose to address the problem
of designing these parameters in conjunction with the feedback controller i order to achieve one or
more objectives.We then propose to address and solve the underlying optimization problem.The
theoretical underpinnings will rely o ew results in the non-convex optimization literature that
utilize convex relaxation i order to get global optimal solutions.The potential of our approach
to yield e .ective solutions to the resulting problems is demonstrated by our recent work that
applies the proposed methods to the robust synthesis problem in 1 giving the only global optimal
solution to this important problem.Aside from its contribution to the theory of control design,
the IPC design tools to be developed will be used to address several practical problems where the
simultaneous parameter and controller design can have a large and measurable impact.Speci .cally,
we will address a signi .cant nanotechnology design problem i volving ultra-high resolution micro-
cantilevers.This problem will take adva tage of existing expertise i the laboratory of the PIs and
will be conducted i close collaboration with the relevant industry.Based o the interdisciplinary
tools eeded for IPC design theory,we also address educational goals that are made possible by
the proposed research.
The intellectual merit of this proposal stems from the novel approach for a well recognized
unsolved problem of integrated parameter and controller (IPC)design.The proposal will contribute
signi .cantly to optimization based methodologies in control theory solving hitherto unaddressed
problems that are of importance for practical control design.The proposal lays particular emphasis
on applying the theory developed to micro-cantilever based technologies in the context of IPC
design.The theoretical paradigm is well suited and timely for furthering this technology.
Apart from the theoretical impact the related technology to be developed will be applicable
to practical problems i the two hundred million dollar scanning probe industry.The PIs have
signi .cant collaboration with industry and the technical knowhow developed will be guided and
transferred e .ectively to the industry.E .ort will be placed on integrating the software developed
on a typical Matlab platform.This will enable wide use of the tools developed by the related
communities.The main topic of the proposal provides a unique opportunity to expose the student
to the importance of plant structure that facilitates good overall plant-controller performance.A
novel course that builds o the ideas and results of this project to motivate the general philosophy
and techniques of integrated parameter and control design will be developed.
1

The now well-known vision and challenge in post-genomics biology is to make the entire process of research
scalable to large networks using high-throughput techniques and large-scale computation. Computational biology and bioinformatics have focused attention on the need for sophisticated methods for handling large databases and tools for modeling and simulating complex networks. Not as widely recognized is that the scalability of the more subtle processes of drawing meaningful and reliable scientific, medical, and biological inferences from the wealth of data and computation is equally important and requires the development of fundamentally new theory and software.
The research objective of this project is to develop the theoretical foundation and information technology in-frastructure necessary to accelerate progress in systems biology, with concrete demonstrations on a variety of bi-ological experiments. This ambitious goal requires augmenting bioinformatics and current modeling and simula-tion approaches with greater understanding of the organizational principles underlying network complexity, including connections with molecular details, and exploiting this understanding to advance mainstream experimental biology.
Building on recent breakthroughs in theory and scalable algorithms for systematic robustness analysis and model (in)validation of nonlinear network models with uncertain rate constants, the project maps out a research path that will (1) develop the necessary rigorous and practical mathematical theory; (2) embody it in a software environment that supports the complex iterative processes involved in going from raw data to modeling, analysis, and inference, with tight feedback to experimentation and modeling throughout; and (3) apply the theory and software to specific experimental studies in biology as a way of grounding the entire endeavor.
The intellectual merit combines immediate practical impact and conceptual depth. Automating and computation-ally augmenting scientific and mathematical inference from noisy and incomplete data for uncertain models has long been an elusive goal. Achieving it in the context of complex biological systems is for the first time both a necessity and an achievable goal. To do this, data and modeling assertions and questions must be described in a common framework that is biologically natural, yet can be stored, manipulated, shared, and ultimately turned over to powerful algorithms for resolution. Our objective is to create tools which make it possible to systematically answer questions such as: Is a proposed model consistent with experimental data? If so, is it robust to additional perturbations that are plausible but untested? Are different models at multiple scales of resolution consistent? What is the most promising experiment to refute or confirm a model? Traditionally, such network-level questions that arise naturally in biology have been
considered computationally intractable, since they are typically stochastic, nonlinear, nonequilibrium, ncertain, in-volve multiple scales, and hybrid (mixing continuous and discrete mathematics), limiting approaches to heuristic and brute-force methods, or to extreme simplification. Recently this situation changed profoundly, based on new methods developed by the research team and their collaborators. A crucial insight is that evolution favors high robustness to uncertain environments and components, yet allows severe fragility to novel perturbations, and this robust yet fragile feature must be exploited explicitly in scalable algorithmic approaches.
The broader impact lies in the synergistic links this work forges with similar challenges that exist throughout science and technology, such as the Internet, aerospace systems design, materials science, multiscale physics, stochas-tic multiscale chemistry, and disturbance ecology. The theoretical foundations build broadly on robust control theory, dynamical systems, numerical analysis, operator theory, real algebraic geometry, computational complexity theory, duality and optimization, and semi-definite programming. The results will be made accessible to the broadest possible audience, both with representative and challenging experimental biology and the connections with other examples of complex systems. The preliminary progress already made by this team is striking and has been applied to under-standing,
for example, the robustness of complex control systems, the performance of internet protocols, and bacterial
chemotaxis and stress response. The work is creating new mathematics and algorithms, beginning to appear in the highest-impact journals, and concretely demonstrating that this research can help experimental biologists.
Diversity and breadth appear at every level. In the research group of the lead PI (Doyle), 6 of 11 graduate
students and 2 of 4 postdoctoral scholars are women, and include a broad racial and ethnic diversity. The other 5 co-PIs are from a broad spectrum of disciplines and diverse but elite academic institutions, 3 are women, and all PIs have strong and very concrete commitments to integrative, multidisciplinary research, diversity, educational innovation, and outreach at every level including K-12. The team members are frequent featured speakers at integrative conferences and in interdisciplinary colloquia at premier universities, and speakers and organizers of workshops and short courses in systems biology. This program both directly involves leading mainstream biology, and has broad contact with it through additional collaborations, creating conduits to broad dissemination of the research results in biology. The team's algorithms and software infrastructure are becoming de facto standard tools empowering research in multiple disciplines, and forming a solid foundation upon which this program builds.

The objective of this research is to develop the theory and advanced computational tools for a modular decomposition and analysis of complex gene networks. The key challenge to overcome is that biological networks are high-dimensional coupled stochastic nonlinear systems with uncertain components. The approach is to employ tools and expertise from computational and experimental systems biology, stochastic dynamic nonlinear networks, and control theory to systematically decompose the network into simple modules whose dynamic properties can be understood in isolation and then related to the behavior of the network.

The research has the potential to provide a framework that (a) enables the decomposition of complex biological networks into modules; (b) identifies the essential characteristics of each module necessary to account for its role in the network's behavior; and (c) provides the analytical and computational foundation for the analysis and synthetic construction of networks of modules. The systematic approach explicitly accounts for network dynamics, the stochastic nature, and uncertainty of biological networks. Development of the framework is guided by and validated through carefully selected biological experiments.

The research has the potential to provide new tools to help scientists reverse-engineer complex biological networks, leading to a deeper understanding of biological function. Such understanding is a key step in the rational design of therapies. Research and educational activities are tightly integrated to train a diverse cadre of scientists and engineers who are adept at employing computational thinking in multi-disciplinary research. Recruitment of women and students from under-represented groups through summer internships, campus programs, and special institutional partnerships is central to the investigators' strategy for achieving diversity.

Eccs-0802008
Bamieh


Objective

One of the central problems in the emerging field of Systems Biology is the analysis and functional classification of large complex biochemical reaction networks. Such networks are increasingly being scrutinized and their individual components painstakingly investigated in detail. However, a general methodology for inferring dynamical and functional behavior from the detailed network description is still sorely lacking. We propose methodologies by which large components of such networks can be replaced by components of much smaller state dimension that have similar functionality. We term this problem Functional Model Reduction to emphasize distinctions with traditional model reduction techniques. The enabling ideas behind this methodology consist of understanding how dynamical systems that are designed for prescribed functions (such as logical or hybrid operations) can be implemented with dynamical networks constrained to have specific types of building blocks. We investigate it in the specific context of building blocks that are available from basic biochemical kinetics. Enabled with this analysis, we pose the problem of carrying out this analysis in reverse, that is, given networks with specific types of building blocks, we ask what type of functional behavior they represent, and whether it is possible to mirror that behavior with dynamical system of much lower dimension. Our goal is not to develop a general nonlinear model reduction technique, but rather one that is particularly tailored to the differential equations that result from biochemical kinetics. Some novel aspects of systems theory will need to be developed such as realizations with prespecified network components as well as functional objectives for model reduction.

Intellectual Merit

Uncovering and classification of function from the detailed description of biochemical reaction networks is a central problem in systems biology and dynamical systems theory. The proposed work will contribute techniques that are particularly tailored to the dynamical network that arise from biochemical kinetics. A new paradigm for model reduction based on network function will be developed.

Broader Impact

The broader impacts of this work include the application of the model reduction techniques developed in this project to a high order complex model of ischemic stroke that is being developed, which will make possible new understanding of this disease and new treatments for it. The multi-disciplinary nature of this work will ensure that graduate students from dynamical systems and control and those from the life sciences will develop new skill sets from the other disciplines and will help create graduates who are comfortable working at the boundary of their disciplines.

The overall objective of the workshop is to explore new methodologies and techniques for increasing the penetration of systems theory into other fields and for teaching systems theory and
control. The workshop will be open to all topics pertaining to the broad area of systems and control theory, but with especial emphasis on topics that are likely to have significant impact in
applications to engineering and the basic sciences.

Intellectual merit

The workshop will consist of four short tutorials, about a dozen technical talks, and two panel sections. The tutorials and technical talks will be delivered by a selected group
of researchers in academia and industry, internationally known for their interdisciplinary work and collaborations with researchers outside the systems and control area. A web site for the workshop
will be created to host all the talks along with related reference materials. A report will also be
written to summarize the discussion and key conclusions of the panels. All these materials will be
made publicly available.


Broader impacts

A key objective of this proposal is to seek the funds needed to ensure wide
participation in this event. We will actively seek participation by undergraduate and graduate
students in the areas of systems and control theory as well as other areas of engineering and the basic
sciences, where a systems perspective can have significant impact. To make the workshop especially
appealing for students, we will cover the expenses to a selected group of students and postdoctoral
researchers. By exposing these students to a vibrant research community, we expect to attract them
to research careers in Science, Technology, Engineering and Math (STEM). The student selection
plan will give priority and thus extend opportunities to students from underrepresented groups in
the STEM disciplines.

Cell polarity, whereby cellular components that were previously uniformly distributed become asymmetrically localized, is essential to the diverse specialized functions of eukaryotic cells. A hallmark of cell polarity is spatial localization. From a modeling point of view, spatial localization cannot be understood without proper modeling of the spatial dynamics governing its creation and time evolution. At the same time, spatial dynamics are profoundly influenced by stochastic events that manifest as cellular noise. Therefore, deep understanding of cell polarity inevitably requires the proper modeling, simulation, and analysis of stochastic spatial dynamics. The fundamental problem limiting work in this area in the past has been the computational complexity of stochastic spatial simulations. This project develops the experimental data and algorithms for modeling, simulation and analysis of spatial stochastic dynamics arising in cell polarity in the yeast pheromone response system. A novel algorithm is developed to address the computationally intensive task of spatial stochastic simulation. The algorithm is then further developed and then integrated into a powerful software infrastructure to enable its widespread use. Experiments capable of capturing stochastic variability inform model development and analysis.

Software developed as a result of this project enables routine simulation of highly complex spatial stochastic phenomena across the sciences and engineering. All software will be made widely available. Tutorial courses and presentations at meetings and workshops will be given to ensure the accessibility of the research. Graduate students involved in this project are provided with a unique, highly multidisciplinary research experience. Students at UCSB work as a tightly-knit team co-advised by Petzold and Khammash, with extended visits to UCI to work in Yi's experimental lab, learning about the possibilities and limitations of the experimental techniques. UCI students focused on experiment spend significant time at UCSB working with the modelers, learning first-hand what the systems-level approach can bring to biological research.