P. Khargonekar
University of Florida, Electrical and Computer Engineering, Faculty Member
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In general terms, the robust stabilization problem may be formulated as follows: Let Pk(s) be a family of linear tine-invariant SISO plants, where the index k takes valiles in some set K. Then the robust stabilization problem is to find a... more
In general terms, the robust stabilization problem may be formulated as follows: Let Pk(s) be a family of linear tine-invariant SISO plants, where the index k takes valiles in some set K. Then the robust stabilization problem is to find a (realizable) controller C(s) such that the above closed loop system is internally asynptotizall? stable for each k in K. If this problerr. is solvable, then C(s) is a robust controller in the sense that as long as the plant belongs to the set I:Pk(s) : k in K3, the closed loop system is internally asymptotizally stable.
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H∞ control problems for digital control systems are investigated in both finite and infinite horizon cases. Necessary and sufficient conditions are obtained for the existence of controllers that satisfy a specified H∞ performance bound.... more
H∞ control problems for digital control systems are investigated in both finite and infinite horizon cases. Necessary and sufficient conditions are obtained for the existence of controllers that satisfy a specified H∞ performance bound. These conditions are stated in terms of Riccati differential equations with jumps. When these conditions hold, explicit formulas for a controller satisfying the H∞ performance bound are given
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Introduction and Overview - Khargonekar l Virtual Control and Design of Plasma Equipment - Kushner l Toward Growing Films with Total Texture Control - Srolovitz l Optical Sensing - In-Situ Ellipsometry - Terry l Optimal DoE for Modeling... more
Introduction and Overview - Khargonekar l Virtual Control and Design of Plasma Equipment - Kushner l Toward Growing Films with Total Texture Control - Srolovitz l Optical Sensing - In-Situ Ellipsometry - Terry l Optimal DoE for Modeling Feedback Control Variables - Nair l Estimation and Control in Plasma Processing - Khargonekar l Conclusions and Wrap Up - Khargonekar Michigan/Illinois MURI - Modeling & Control of Plasma Processing RESEARCH OBJECTIVES l Research Goal: Significant improvements in the robustness and performance of processes used in the manufacture of integrated circuits and flat panel displays l Focus on plasma deposition and etching l Approach - Synergistic Combination of Modeling and Simulation - First Principles, Phenomenological, Response Surface and System Ide
ABSTRACT This paper describe application of the recent work on "identification in H ¿ " to the data for a JPL flexible space structure.
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This paper presents the results of a controller design exercise on the turret test fixture using the H∞ synthesis method. The controller is required to provide good step and ramp tracking performance in the presence of firing... more
This paper presents the results of a controller design exercise on the turret test fixture using the H∞ synthesis method. The controller is required to provide good step and ramp tracking performance in the presence of firing disturbances. An important step in this design exercise has been the formulation of an appropriate synthesis model. We describe this process in great detail. Results of the linear analysis and simulation of the closed-loop response (with both linear and non-linear plant models) are presented.
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Motivated by climate change and sustainability, and the resulting need to decarbonize the electricity sector, there is a major global movement toward large-scale integration of renewable energy, i.e., wind and solar, into the existing... more
Motivated by climate change and sustainability, and the resulting need to decarbonize the electricity sector, there is a major global movement toward large-scale integration of renewable energy, i.e., wind and solar, into the existing power grid. The inherent variability of wind and solar energy production poses a major challenge in achieving these goals. The problem becomes more challenging as we consider issues of competitive markets, low cost and high reliability. In the last few years, we have been working on new systems and control problems that arise from these considerations. In this paper, we will present some highlights of our work on developing demand response methods using distributed control and bounding the loss of efficiency in these methods.
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Sufficient conditions are given under which an adaptive control system is robustly stable and achieves a guaranteed robust asymptotic performance level equal to that of the robust controller given perfect parameter information. The... more
Sufficient conditions are given under which an adaptive control system is robustly stable and achieves a guaranteed robust asymptotic performance level equal to that of the robust controller given perfect parameter information. The conditions are general in several respects. For example, structured nonparametric uncertainty (e.g., block diagonal) is allowed as well as exogenous noise inputs. In addition, the structure of the parametric uncertainty is very general and allows for parameters which scale the uncertainty magnitudes. This allows one to identify the size of the nonparametric uncertainty and to schedule the controller based on this size. The robust gain scheduled controller is largely unrestricted. For this general problem, concrete robust identification mechanisms have not yet been found
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ABSTRACT It is shown that a finite-dimensional linear time-varying continuous-time system admits normalized coprime factorizations if and only it admits a stabilizable and detectable realization, or equivalently, if and only if it is... more
ABSTRACT It is shown that a finite-dimensional linear time-varying continuous-time system admits normalized coprime factorizations if and only it admits a stabilizable and detectable realization, or equivalently, if and only if it is internally stabilizable via dynamic output feedback. In the process, a simple proof that stabilizability and detectability are sufficient to ensure the existence of stabilizing solutions to standard continuous-time control and filter Riccati equations is given. State-space formulas for normalized coprime factorizations are given. These are used to define the graph metric for the set of internally stabilizable finite-dimensional linear time-varying plants. As an application a robustness estimate is derived for feedback stability of linear time-varying plants using nonlinear time-varying controllers
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In this paper, the problem of "system identification in H1 " is investigated in the case when the given frequency response data is not necessarily on a uniformly spaced grid of frequencies. A large class of robustly convergent... more
In this paper, the problem of "system identification in H1 " is investigated in the case when the given frequency response data is not necessarily on a uniformly spaced grid of frequencies. A large class of robustly convergent identification algorithms are derived. A particular algorithm is further examined and explicit worst case error bounds (in the H1 norm) are derived for both discrete-time and continuous-time systems. Examples are provided to illustrate the application of the algorithms. 1 Introduction System identification is a well established field of research with a large body of literature, see for example, the book by Ljung [17]. System identification research has been and continues to be dominated by stochastic problem formulations. In some recent papers, results on the resulting identification error have been obtained, see for example, [3, 4, 18]. For deterministic worst case modeling error bounds as used in robust control, a deterministic system identificatio...
... James 34. Krause i* and Pramod P. Khargonekar *f f Honeywell Systems and Research Center 3660 Technology Drive Minneapolis, MN 5541 8 * Dept. ... THEOREM 1: (A) For A and W as above, with d = Av, v = Wu, u finite and piecewise... more
... James 34. Krause i* and Pramod P. Khargonekar *f f Honeywell Systems and Research Center 3660 Technology Drive Minneapolis, MN 5541 8 * Dept. ... THEOREM 1: (A) For A and W as above, with d = Av, v = Wu, u finite and piecewise continuous, ...
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ABSTRACT In this paper, we pose a new sequential variant of the famous Colonel Blotto game in which two players, Player A and Player B, must allocate finite resources among N regions of a battlefield. A key new feature of our problem... more
ABSTRACT In this paper, we pose a new sequential variant of the famous Colonel Blotto game in which two players, Player A and Player B, must allocate finite resources among N regions of a battlefield. A key new feature of our problem formulation is the introduction of a deterministic sensor network employed by Player B to gain an informational advantage over Player A. The existence of the sensor network and its properties are common knowledge in the game. We pose the resulting resource allocation game and obtain necessary conditions for Nash equilibrium optimal mixed strategies for the two players in terms of each player's available resources and the sensor network characteristics. These conditions apply to the marginal probability distribution functions of each player's strategy. The optimality conditions are developed using a novel case of the associated first-price all pay auctions with upper or lower bounds on the players' allocations. A numerical example is included to show the tractability of our solution.
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ABSTRACT A coordinated e#ort to satisfy the modelling requirements for robust design, real-time feedbackvariable selection and run-to-run control, for reactive ion etching of a self-aligned gate, is presented. These techniques may be used... more
ABSTRACT A coordinated e#ort to satisfy the modelling requirements for robust design, real-time feedbackvariable selection and run-to-run control, for reactive ion etching of a self-aligned gate, is presented. These techniques may be used in a complementary fashion to reduce process variance. Advanced sensors considered for real-time process control include an RF probe, mass spectroscopy and optical emission spectroscopy. The e#ectiveness of these sensors for feedback control is compared. Introduction Reduction of variance in the output characteristics of semiconductor manufacturing processes is critical in order to continue decreasing the dimensions of integrated circuits. Variance reduction to date has relied on design improvements to the processing equipment, the use of robust design techniques and application of statistical process control #SPC#. During the last decade, anumber of e#orts to reduce process variance for certain semiconductor manufacturing processes via in-run feedback...
ABSTRACT Some further results on possible root locations of two-dimensional (2-D) polynomials are presented. It is established that the distinguished boundary of the unit bidisc being free of zeros is a nongeneric property of 2-D... more
ABSTRACT Some further results on possible root locations of two-dimensional (2-D) polynomials are presented. It is established that the distinguished boundary of the unit bidisc being free of zeros is a nongeneric property of 2-D polynomials. The result is illustrated by a simple example.
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The authors present the results of a design exercise in which recent developments in H∞ synthesis theory were applied to the design of a controller for an autonomous underwater vehicle (AUV). The problem statement requires the design of a... more
The authors present the results of a design exercise in which recent developments in H∞ synthesis theory were applied to the design of a controller for an autonomous underwater vehicle (AUV). The problem statement requires the design of a position and attitude control system for the vehicle to achieve precise trajectory following. The major steps in the synthesis procedure were
Research Interests: Geology, Optimal Control, Control Engineering, Nonlinear dynamics, Vehicle Dynamics, and 13 moreRobust control, Autonomous Underwater Vehicle, Trajectory, Mobile Robots, Sliding mode control, Remotely Operated Vehicles, Satellite Attitude Control System, Linearization, Nonlinear system, Underwater vehicles, Nonlinear Model, Attitude Control, and Multivariable Calculus
ABSTRACT In this note we present a constructive technique for obtaining polynomial matrix fraction representations for reachable linear systems over a principal ideal domain. An example is given to illustrate the algorithm.
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A robust stabilization problem in a state-space setting is treated. It is assumed that the states are available for feedback. Using a fixed Lyapunov function approach (quadratic stability) it is shown that an open loop stabilizability... more
A robust stabilization problem in a state-space setting is treated. It is assumed that the states are available for feedback. Using a fixed Lyapunov function approach (quadratic stability) it is shown that an open loop stabilizability condition is equivalent to the existence of a ...
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ABSTRACT This paper considers a continuous-time linear system with finite jumps at discrete instants of time. An iterative method to compute the ${\cal L}_2$-induced norm of a linear system with jumps is presented. Each iteration requires... more
ABSTRACT This paper considers a continuous-time linear system with finite jumps at discrete instants of time. An iterative method to compute the ${\cal L}_2$-induced norm of a linear system with jumps is presented. Each iteration requires solving an algebraic Riccati equation. It is also shown that a linear feedback interconnection of a continuous-time finite-dimensional linear time-invariant (FDLTI) plant and a discrete-time finite-dimensional linear shift-invariant (FDLSI) controller can be represented as a linear system with jumps. This leads to an iterative method to compute the ${\cal L}_2$-induced norm of a sampled-data system.
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ABSTRACT This paper deals with the existence and construction of proper stable Bezout factorizations of transfer function matrices of linear time-invariant systems with commensurate time delays. Existence of factorizations is... more
ABSTRACT This paper deals with the existence and construction of proper stable Bezout factorizations of transfer function matrices of linear time-invariant systems with commensurate time delays. Existence of factorizations is characterized in terms of spectral controllability (or spectral observability)of the co-canonical (or canonical) realization of the transfer function matrix. An explicit procedure for computing proper stable Bezout factorizations is given in terms of a specialized ring of pure and distributed time delays. This procedure is utilized to construct finite-dimensional stabilizing compensators and to construct feedback systems which assign the characteristic polynomial of the closed-loop system.
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... 95 1 A Time-Domain Approach to Model Validation Kameshwar Poolla, Pramod Khargonekar, Fellow, ZEEE, Ashok Tikku, James Krause, Member, IEEE, and Krishan Nagpal Abstruct-In this paper we offer a novel approach to control-oriented model... more
... 95 1 A Time-Domain Approach to Model Validation Kameshwar Poolla, Pramod Khargonekar, Fellow, ZEEE, Ashok Tikku, James Krause, Member, IEEE, and Krishan Nagpal Abstruct-In this paper we offer a novel approach to control-oriented model validation problems. ...
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Abstract. In this paper, we consider the problem of persistent bounded disturbance rejec-tion for uncertain Lurie systems with delay. We mainly focus on the problems of absolute stability (delay-independent stability and delay-dependent... more
Abstract. In this paper, we consider the problem of persistent bounded disturbance rejec-tion for uncertain Lurie systems with delay. We mainly focus on the problems of absolute stability (delay-independent stability and delay-dependent stability) and performance of bounded ...
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ABSTRACT We consider the multiobjective problem of ℋ ∞ suboptimal control with the controller constrained to achieve robust closed-loop regulation with respect to step inputs. Computable necessary and sufficient conditions under which the... more
ABSTRACT We consider the multiobjective problem of ℋ ∞ suboptimal control with the controller constrained to achieve robust closed-loop regulation with respect to step inputs. Computable necessary and sufficient conditions under which the problem admits a solution are derived. When these conditions are met, explicit state-space formulae for a controller that solves the problem are given. In particular, if robust regulation of ℓ outputs is desired, the controller we exhibit is of McMillan degree ℓ in the state feedback case. In the output feedback case, the controller we exhibit is of McMillan degree no greater than (n+ℓ), where n is the order of the plant.
Research Interests: Computer Science and CRC
ABSTRACT We analyze the problem of real-time thickness estimation for patterned wafers during an etching process using in situ spectroscopic ellipsometry. For that, a two-stage estimation algorithm is proposed. The first stage is an... more
ABSTRACT We analyze the problem of real-time thickness estimation for patterned wafers during an etching process using in situ spectroscopic ellipsometry. For that, a two-stage estimation algorithm is proposed. The first stage is an automatic model calibration algorithm that uses the data collected during an initial interval. The second stage is a nonlinear state estimation system designed for the tuned model. We study the sensitivity of this estimation strategy to variations in the wafer parameters and the process conditions
Research Interests: Materials Science, Microelectronics, Spectroscopy, Process Control, State Estimation, and 15 moreSystem Design, Parameter estimation, Ellipsometry, Nonlinear Systems, Calibration, Model Calibration, Real Time Systems, Data Collection, Real Time, Robustness, Etching, Sensitivity, Spectroscopic Ellipsometry, Nonlinear system, and Semiconductor device modeling
This paper presents some results on the stability and ℋ∞ performance of nonlinear feedback systems with gain scheduled controller implemented by 𝒟-implementation methodology: (1) For stability, provided the scheduling... more
This paper presents some results on the stability and ℋ∞ performance of nonlinear feedback systems with gain scheduled controller implemented by 𝒟-implementation methodology: (1) For stability, provided the scheduling variable is sufficiently slowly varying and the local linear closed loop systems satisfy a uniform stability constraint, the trajectory of the closed loop nonlinear system remains bounded; and (2) For ℋ∞ performance, if the local linear controllers are designed to satisfy an ℋ∞ norm constraint, then the closed loop nonlinear system also satisfies an ℋ∞ norm inequality. The results use properties of 𝒟-implementation methodology. An example is included to illustrate the ideas
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ABSTRACT This paper proposes a nonlinear filtering algorithm for unknown dynamics and high-complexity observations. We show that the algorithm yields bounded error under redundant observations and small bounded disturbances. The algorithm... more
ABSTRACT This paper proposes a nonlinear filtering algorithm for unknown dynamics and high-complexity observations. We show that the algorithm yields bounded error under redundant observations and small bounded disturbances. The algorithm is a generalization of what we have used to achieve the first reported real-time estimation of submicron patterned wafer geometries during a plasma etching process with spectral reflectometry
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We present experimental results validating a new technique that achieves accurate endpoint for a TFT backchannel recess etch. These results show a 90# reduction in the standard deviation of #nal channel thickness as compared to timed... more
We present experimental results validating a new technique that achieves accurate endpoint for a TFT backchannel recess etch. These results show a 90# reduction in the standard deviation of #nal channel thickness as compared to timed etches.
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ABSTRACT This paper focuses on the development and analysis of sub-optimal decision algorithms for a collection of robots that assist a remotely located operator in perimeter surveillance. The operator is tasked with the classification of... more
ABSTRACT This paper focuses on the development and analysis of sub-optimal decision algorithms for a collection of robots that assist a remotely located operator in perimeter surveillance. The operator is tasked with the classification of an incursion across the perimeter. Whenever there is an incursion into the perimeter, an Unattended Ground Sensor (UGS) in the vicinity, raises an alert. A robot services the alert by visiting the alert location, collecting evidence in the form of video and other imagery, and transmitting them to the operator. The accuracy of operator's classification depends on the volume and freshness of information gathered and provided by the robots at locations where incursions occur. There are two competing needs for a robot: it needs to spend adequate time at an alert location to collect evidence for aiding the operator in accurate classification but it also needs to service the alert as soon as possible, so that the evidence collected is relevant. The control problem is to determine the optimal amount of time a robot must spend servicing an alert. The incursions are stochastic and their statistics are assumed to be known a priori. This problem may be posed as a Markov Decision Problem. However, even for two robots and five UGS locations, the number of states is of the order of millions. Approximate Dynamic Programming (ADP) via Linear Programming (LP) provides a way to approximate the value function and provide bounds on its sub-optimality. The novel feature of this paper is to present a lower bound via LP based techniques and state partitioning and construct a sub-optimal policy whose performance betters the lower bound. An illustrative perimeter surveillance example corroborates the results presented in this paper.
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Page 1. Math. Control Signals Systems (1988) 1:107-122 Mathematics of Control, Signals, and Systems 9 1988 Springer-Verlag New York Inc. When Is a Controller Ho~ * Kathryn E. Lenz,t Pramod P. Khargonekar,, and John C. Doylew Abstract. ...