Valery Ugrinovskii

Bio: Valery Ugrinovskii is an academic researcher from University of New South Wales. The author has contributed to research in topics: Robust control & Control theory. The author has an hindex of 30, co-authored 220 publications receiving 3896 citations. Previous affiliations of Valery Ugrinovskii include University of Haifa & Australian Defence Force Academy.

Robust control design using H-∞ methods

Abstract: 1. Introduction.- 1.1 The concept of an uncertain system.- 1.2 Overview of the book.- 2. Uncertain systems.- 2.1 Introduction.- 2.2 Uncertain systems with norm-bounded uncertainty.- 2.2.1 Special case: sector-bounded nonlinearities.- 2.3 Uncertain systems with integral quadratic constraints.- 2.3.1 Integral quadratic constraints.- 2.3.2 Integral quadratic constraints with weighting coefficients.- 2.3.3 Integral uncertainty constraints for nonlinear uncertain systems.- 2.3.4 Averaged integral uncertainty constraints.- 2.4 Stochastic uncertain systems.- 2.4.1 Stochastic uncertain systems with multiplicative noise.- 2.4.2 Stochastic uncertain systems with additive noise: Finitehorizon relative entropy constraints.- 2.4.3 Stochastic uncertain systems with additive noise: Infinite-horizon relative entropy constraints.- 3. H? control and related preliminary results.- 3.1 Riccati equations.- 3.2 H? control.- 3.2.1 The standard H? control problem.- 3.2.2 H? control with transients.- 3.2.3 H? control of time-varying systems.- 3.3 Risk-sensitive control.- 3.3.1 Exponential-of-integral cost analysis.- 3.3.2 Finite-horizon risk-sensitive control.- 3.3.3 Infinite-horizon risk-sensitive control.- 3.4 Quadratic stability.- 3.5 A connection between H? control and the absolute stabilizability of uncertain systems.- 3.5.1 Definitions.- 3.5.2 The equivalence between absolute stabilization and H? control.- 4. The S-procedure.- 4.1 Introduction.- 4.2 An S-procedure result for a quadratic functional and one quadratic constraint.- 4.2.1 Proof of Theorem 4.2.1.- 4.3 An S-procedure result for a quadratic functional and k quadratic constraints.- 4.4 An S-procedure result for nonlinear functionals.- 4.5 An S-procedure result for averaged sequences.- 4.6 An S-procedure result for probability measures with constrained relative entropies.- 5. Guaranteed cost control of time-invariant uncertain systems.- 5.1 Introduction.- 5.2 Optimal guaranteed cost control for uncertain linear systems with norm-bounded uncertainty.- 5.2.1 Quadratic guaranteed cost control.- 5.2.2 Optimal controller design.- 5.2.3 Illustrative example.- 5.3 State-feedback minimax optimal control of uncertain systems with structured uncertainty.- 5.3.1 Definitions.- 5.3.2 Construction of a guaranteed cost controller.- 5.3.3 Illustrative example.- 5.4 Output-feedback minimax optimal control of uncertain systems with unstructured uncertainty.- 5.4.1 Definitions.- 5.4.2 A necessary and sufficient condition for guaranteed cost stabilizability.- 5.4.3 Optimizing the guaranteed cost bound.- 5.4.4 Illustrative example.- 5.5 Guaranteed cost control via a Lyapunov function of the Lur'e-Postnikov form.- 5.5.1 Problem formulation.- 5.5.2 Controller synthesis via a Lyapunov function of the Lur'e-Postnikov form.- 5.5.3 Illustrative Example.- 5.6 Conclusions.- 6. Finite-horizon guaranteed cost control.- 6.1 Introduction.- 6.2 The uncertainty averaging approach to state-feedback minimax optimal control.- 6.2.1 Problem Statement.- 6.2.2 A necessary and sufficient condition for the existence of a state-feedback guaranteed cost controller.- 6.3 The uncertainty averaging approach to output-feedback optimal guaranteed cost control.- 6.3.1 Problem statement.- 6.3.2 A necessary and sufficient condition for the existence of a guaranteed cost controller.- 6.4 Robust control with a terminal state constraint.- 6.4.1 Problem Statement.- 6.4.2 A criterion for robust controllability with respect to a terminal state constraint.- 6.4.3 Illustrative example.- 6.5 Robust control with rejection of harmonic disturbances.- 6.5.1 Problem Statement.- 6.5.2 Design of a robust controller with harmonic disturbance rejection.- 6.6 Conclusions.- 7. Absolute stability, absolute stabilization and structured dissipativity.- 7.1 Introduction.- 7.2 Robust stabilization with a Lyapunov function of the Lur'e-Postnikov form.- 7.2.1 Problem statement.- 7.2.2 Design of a robustly stabilizing controller.- 7.3 Structured dissipativity and absolute stability for nonlinear uncertain systems.- 7.3.1 Preliminary remarks.- 7.3.2 Definitions.- 7.3.3 A connection between dissipativity and structured dissipativity.- 7.3.4 Absolute stability for nonlinear uncertain systems.- 7.4 Conclusions.- 8. Robust control of stochastic uncertain systems.- 8.1 Introduction.- 8.2 H? control of stochastic systems with multiplicative noise.- 8.2.1 A stochastic differential game.- 8.2.2 Stochastic H? control with complete state measurements.- 8.2.3 Illustrative example.- 8.3 Absolute stabilization and minimax optimal control of stochastic uncertain systems with multiplicative noise.- 8.3.1 The stochastic guaranteed cost control problem.- 8.3.2 Stochastic absolute stabilization.- 8.3.3 State-feedback minimax optimal control.- 8.4 Output-feedback finite-horizon minimax optimal control of stochastic uncertain systems with additive noise.- 8.4.1 Definitions.- 8.4.2 Finite-horizon minimax optimal control with stochastic uncertainty constraints.- 8.4.3 Design of a finite-horizon minimax optimal controller.- 8.5 Output-feedback infinite-horizon minimax optimal control of stochastic uncertain systems with additive noise.- 8.5.1 Definitions.- 8.5.2 Absolute stability and absolute stabilizability.- 8.5.3 A connection between risk-sensitive optimal control and minimax optimal control.- 8.5.4 Design of the infinite-horizon minimax optimal controller.- 8.5.5 Connection to H? control.- 8.5.6 Illustrative example.- 8.6 Conclusions.- 9. Nonlinear versus linear control.- 9.1 Introduction.- 9.2 Nonlinear versus linear control in the absolute stabilizability of uncertain systems with structured uncertainty.- 9.2.1 Problem statement.- 9.2.2 Output-feedback nonlinear versus linear control.- 9.2.3 State-feedback nonlinear versus linear control.- 9.3 Decentralized robust state-feedback H? control for uncertain large-scale systems.- 9.3.1 Preliminary remarks.- 9.3.2 Uncertain large-scale systems.- 9.3.3 Decentralized controller design.- 9.4 Nonlinear versus linear control in the robust stabilizability of linear uncertain systems via a fixed-order output-feedback controller.- 9.4.1 Definitions.- 9.4.2 Design of a fixed-order output-feedback controller.- 9.5 Simultaneous H? control of a finite collection of linear plants with a single nonlinear digital controller.- 9.5.1 Problem statement.- 9.5.2 The design of a digital output-feedback controller.- 9.6 Conclusions.- 10. Missile autopilot design via minimax optimal control of stochastic uncertain systems.- 10.1 Introduction.- 10.2 Missile autopilot model.- 10.2.1 Uncertain system model.- 10.3 Robust controller design.- 10.3.1 State-feedback controller design.- 10.3.2 Output-feedback controller design.- 10.4 Conclusions.- 11. Robust control of acoustic noise in a duct via minimax optimal LQG control.- 11.1 Introduction.- 11.2 Experimental setup and modeling.- 11.2.1 Experimental setup.- 11.2.2 System identification and nominal modelling.- 11.2.3 Uncertainty modelling.- 11.3 Controller design.- 11.4 Experimental results.- 11.5 Conclusions.- A. Basic duality relationships for relative entropy.- B. Metrically transitive transformations.- References.

Robust H∞ infinity control in the presence of stochastic uncertainty

Abstract: This paper considers a robust H infinity state feedback control problem for linear uncertain systems with stochastic uncertainty. The uncertainty class considered in the paper involves uncertain multiplicative white noise perturbations which satisfy a certain variance constraint. A state feedback controller is presented which guarantees a prescribed level of disturbance attenuation for all admissible stochastic uncertainties.

I and i

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 …

Linear systems

Abstract: Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

Energy function analysis for power system stability

Abstract: (1990). ENERGY FUNCTION ANALYSIS FOR POWER SYSTEM STABILITY. Electric Machines & Power Systems: Vol. 18, No. 2, pp. 209-210.