Peter Dorato

Bio: Peter Dorato is an academic researcher from University of New Mexico. The author has contributed to research in topics: Robust control & Control theory. The author has an hindex of 16, co-authored 54 publications receiving 2590 citations.

Linear Quadratic Control: An Introduction

Abstract: From the Publisher: The purpose of this book is to provide an introduction to linear quadratic theory beyond the typical chapter on the subject found in texts on optimal or multivariable control. Of course, as an introductory text, the material here is not as detailed as that found in advanced books devoted exclusively to the subject.

Survey of robust control for rigid robots

Abstract: Current approaches to the robust control of the motion of rigid robots are surveyed, and the available literature is summarized. The five major design approaches discussed are the linear-multivariable approach, the passivity approach, the variable-structure approach, the saturation approach, and the robust-adaptive approach. Some guidelines for choosing a method are offered. >

Delayed Positive Feedback Can Stabilize Oscillatory Systems

Abstract: This paper expands on a method proposed in [1] for stabilizing oscillatory system with positive, delayed feedback. The closed-loop system obtained is shown (using the Nyquist criterion) to be stable for a range of delays.

A historical review of robust control

Abstract: A historical review of recent results in robust control is presented. The robust control problem, i.e., the problem of designing accurate control systems in the presence of significant plant uncertainties, is classical. However, over the past 15 years, significant new theory has been developed for the solution of this problem, especially with respect to linear multivariable systems characterized in the frequency domain, and the term robust control for this classical problem is only of recent vintage (1972). Some of the major contributions of modern robust control theory include the development of synthesis techniques for robust stabilization, and H2and H^{\infty} sensitivity optimization of multivariable systems. In this review, we confine the term robust control to the design of fixed controllers. Thus, only nonadaptive or nonself-tuning solutions to the problem of controlling uncertain systems are reviewed. Finally, it should be noted that the review is largely limited to the literature published in IEEE journals and conference proceedings, and some English-language journals. It is, of course, recognized that many significant related contributions have appeared elsewhere.

Stability of Time-Delay Systems

Abstract: Preface, Notations 1.Introduction to Time-Delay Systems I.Frequency-Domain Approach 2.Systems with Commensurate Delays 3.Systems withIncommensurate Delays 4.Robust Stability Analysis II.Time Domain Approach 5.Systems with Single Delay 6.Robust Stability Analysis 7.Systems with Multiple and Distributed Delays III.Input-Output Approach 8.Input-output stability A.Matrix Facts B.LMI and Quadratic Integral Inequalities Bibliography Index

Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization

Abstract: In the first part of this thesis, we introduce a specific class of Linear Matrix Inequalities (LMI) whose optimal solution can be characterized exactly. This family corresponds to the case where the associated linear operator maps the cone of positive semidefinite matrices onto itself. In this case, the optimal value equals the spectral radius of the operator. It is shown that some rank minimization problems, as well as generalizations of the structured singular value ($mu$) LMIs, have exactly this property. In the same spirit of exploiting structure to achieve computational efficiency, an algorithm for the numerical solution of a special class of frequency-dependent LMIs is presented. These optimization problems arise from robustness analysis questions, via the Kalman-Yakubovich-Popov lemma. The procedure is an outer approximation method based on the algorithms used in the computation of hinf norms for linear, time invariant systems. The result is especially useful for systems with large state dimension. The other main contribution in this thesis is the formulation of a convex optimization framework for semialgebraic problems, i.e., those that can be expressed by polynomial equalities and inequalities. The key element is the interaction of concepts in real algebraic geometry (Positivstellensatz) and semidefinite programming. To this end, an LMI formulation for the sums of squares decomposition for multivariable polynomials is presented. Based on this, it is shown how to construct sufficient Positivstellensatz-based convex tests to prove that certain sets are empty. Among other applications, this leads to a nonlinear extension of many LMI based results in uncertain linear system analysis. Within the same framework, we develop stronger criteria for matrix copositivity, and generalizations of the well-known standard semidefinite relaxations for quadratic programming. Some applications to new and previously studied problems are presented. A few examples are Lyapunov function computation, robust bifurcation analysis, structured singular values, etc. It is shown that the proposed methods allow for improved solutions for very diverse questions in continuous and combinatorial optimization.

Robot Manipulator Control: Theory and Practice

Abstract: Robot Manipulator Control offers a complete survey of control systems for serial-link robot arms and acknowledges how robotic device performance hinges upon a well-developed control system. Containing over 750 essential equations, this thoroughly up-to-date Second Edition, the book explicates theoretical and mathematical requisites for controls design and summarizes current techniques in computer simulation and implementation of controllers. It also addresses procedures and issues in computed-torque, robust, adaptive, neural network, and force control. New chapters relay practical information on commercial robot manipulators and devices and cutting-edge methods in neural network control.