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Ian R. Petersen

Bio: Ian R. Petersen is an academic researcher from Australian National University. The author has contributed to research in topics: Robust control & Quantum. The author has an hindex of 67, co-authored 959 publications receiving 22649 citations. Previous affiliations of Ian R. Petersen include University of Cambridge & University of Manchester.


Papers
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Journal ArticleDOI
TL;DR: A robust control method based on sliding mode design for two-level quantum systems with bounded uncertainties and the conditions for designing such a control law are given, which can guarantee the desired robustness in the presence of the uncertainties.

139 citations

Journal ArticleDOI
TL;DR: In this article, a feedback control technique, known as integral resonant control (IRC), is proposed for damping vibrations in collocated flexible structures, and conditions for the stability of the proposed controller are derived, and shown that the set of stabilizing IRCs is convex.
Abstract: A transfer-function is said to be negative imaginary if the corresponding frequency response function has a negative definite imaginary part (on the positively increasing imaginary axis). Negative imaginary transfer-functions can be stabilized using negative imaginary feedback controllers. Flexible structures with compatible collocated sensor/actuator pairs have transfer-functions that are negative imaginary. In this paper a model structure that typically represents a collocated structure is considered. An identification algorithm which enforces the negative imaginary constraint is proposed for estimating the model parameters. A feedback control technique, known as integral resonant control (IRC), is proposed for damping vibrations in collocated flexible structures. Conditions for the stability of the proposed controller are derived, and shown that the set of stabilizing IRCs is convex. Finally, a flexible beam with two pairs of collocated piezoelectric actuators/sensors is considered. The proposed identification scheme is used determining the transfer-function and an IRC is designed for damping the vibrations. The experimental results obtained are reported.

136 citations

Journal ArticleDOI
01 Mar 1997
TL;DR: In this article, robust state feedback controllers for a class of uncertain linear time-delay systems with norm-bounded uncertainty are presented, where the state feedback controller can be constructed via the solution of a parameter dependent Riccati equation.
Abstract: The design of robust state feedback controllers for a class of uncertain linear time-delay systems with norm-bounded uncertainty is presented. The state feedback results extend previous results on quadratic guaranteed cost control to the case of uncertain time-delay systems. This is done by the authors' definition of quadratic stability for uncertain time-delay systems with norm bounded uncertainty. It is shown that the state feedback controller can be constructed via the solution of a parameter dependent Riccati equation.

134 citations

Journal ArticleDOI
TL;DR: It is demonstrated that the Gaussian process machine learner is able to discover a ramp that produces high quality BECs in 10 times fewer iterations than a previously used online optimization technique.
Abstract: Machine-designed control of complex devices or experiments can discover strategies superior to those developed via simplified models. We describe an online optimization algorithm based on Gaussian processes and apply it to optimization of the production of Bose-Einstein condensates (BEC). BEC is typically created with an exponential evaporation ramp that is approximately optimal for s-wave, ergodic dynamics with two-body interactions and no other loss rates, but likely sub-optimal for many real experiments. Machine learning using a Gaussian process, in contrast, develops a statistical model of the relationship between the parameters it controls and the quality of the BEC produced. This is an online process, and an active one, as the Gaussian process model updates on the basis of each subsequent experiment and proposes a new set of parameters as a result. We demonstrate that the Gaussian process machine learner is able to discover a ramp that produces high quality BECs in 10 times fewer iterations than a previously used online optimization technique. Furthermore, we show the internal model developed can be used to determine which parameters are essential in BEC creation and which are unimportant, providing insight into the optimization process.

133 citations

Journal ArticleDOI
TL;DR: In this article, the authors present a procedure for designing a full state observer and feedback control law which will stabilize a given uncertain linear system, where the uncertain linear systems under consideration are described by state equations which depend on uncertain parameters.
Abstract: This paper presents a procedure for designing a full state observer and feedback control law which will stabilize a given uncertain linear system. The uncertain linear systems under consideration are described by state equations which depend on uncertain parameters. These uncertain parameters may be time varying. Their values, however, are constrained to lie within known compact bounding sets. The design procedure involves solving two algebraic Riccati equations. A feature of the design procedure presented is the fact that it reduces to the standard LQG design procedure if the system contains no uncertain parameters.

133 citations


Cited by
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Journal ArticleDOI

[...]

08 Dec 2001-BMJ
TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

33,785 citations

Book
01 Jan 1994
TL;DR: In this paper, the authors present a brief history of LMIs in control theory and discuss some of the standard problems involved in LMIs, such as linear matrix inequalities, linear differential inequalities, and matrix problems with analytic solutions.
Abstract: Preface 1. Introduction Overview A Brief History of LMIs in Control Theory Notes on the Style of the Book Origin of the Book 2. Some Standard Problems Involving LMIs. Linear Matrix Inequalities Some Standard Problems Ellipsoid Algorithm Interior-Point Methods Strict and Nonstrict LMIs Miscellaneous Results on Matrix Inequalities Some LMI Problems with Analytic Solutions 3. Some Matrix Problems. Minimizing Condition Number by Scaling Minimizing Condition Number of a Positive-Definite Matrix Minimizing Norm by Scaling Rescaling a Matrix Positive-Definite Matrix Completion Problems Quadratic Approximation of a Polytopic Norm Ellipsoidal Approximation 4. Linear Differential Inclusions. Differential Inclusions Some Specific LDIs Nonlinear System Analysis via LDIs 5. Analysis of LDIs: State Properties. Quadratic Stability Invariant Ellipsoids 6. Analysis of LDIs: Input/Output Properties. Input-to-State Properties State-to-Output Properties Input-to-Output Properties 7. State-Feedback Synthesis for LDIs. Static State-Feedback Controllers State Properties Input-to-State Properties State-to-Output Properties Input-to-Output Properties Observer-Based Controllers for Nonlinear Systems 8. Lure and Multiplier Methods. Analysis of Lure Systems Integral Quadratic Constraints Multipliers for Systems with Unknown Parameters 9. Systems with Multiplicative Noise. Analysis of Systems with Multiplicative Noise State-Feedback Synthesis 10. Miscellaneous Problems. Optimization over an Affine Family of Linear Systems Analysis of Systems with LTI Perturbations Positive Orthant Stabilizability Linear Systems with Delays Interpolation Problems The Inverse Problem of Optimal Control System Realization Problems Multi-Criterion LQG Nonconvex Multi-Criterion Quadratic Problems Notation List of Acronyms Bibliography Index.

11,085 citations

Book
17 Aug 1995
TL;DR: This paper reviewed the history of the relationship between robust control and optimal control and H-infinity theory and concluded that robust control has become thoroughly mainstream, and robust control methods permeate robust control theory.
Abstract: This paper will very briefly review the history of the relationship between modern optimal control and robust control. The latter is commonly viewed as having arisen in reaction to certain perceived inadequacies of the former. More recently, the distinction has effectively disappeared. Once-controversial notions of robust control have become thoroughly mainstream, and optimal control methods permeate robust control theory. This has been especially true in H-infinity theory, the primary focus of this paper.

6,945 citations

Journal ArticleDOI
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Abstract: Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

5,689 citations

Journal ArticleDOI
TL;DR: In this article, simple state-space formulas are derived for all controllers solving the following standard H/sub infinity / problem: for a given number gamma > 0, find all controllers such that the H/ sub infinity / norm of the closed-loop transfer function is (strictly) less than gamma.
Abstract: Simple state-space formulas are derived for all controllers solving the following standard H/sub infinity / problem: For a given number gamma >0, find all controllers such that the H/sub infinity / norm of the closed-loop transfer function is (strictly) less than gamma . It is known that a controller exists if and only if the unique stabilizing solutions to two algebraic Riccati equations are positive definite and the spectral radius of their product is less than gamma /sup 2/. Under these conditions, a parameterization of all controllers solving the problem is given as a linear fractional transformation (LFT) on a contractive, stable, free parameter. The state dimension of the coefficient matrix for the LFT, constructed using the two Riccati solutions, equals that of the plant and has a separation structure reminiscent of classical LQG (i.e. H/sub 2/) theory. This paper is intended to be of tutorial value, so a standard H/sub 2/ solution is developed in parallel. >

5,272 citations