https://www.control.utoronto.ca/people/profs/francis/dft.pdf

Feedback Control Theory

The problem of finding an internally stabilizing controller that minimizes a mixed H/sub 2//H/sub infinity / performance measure subject to an inequality constraint on the H/sub infinity / norm of another closed-loop transfer function is considered. This problem can be interpreted and motivated as a problem of optimal nominal performance subject to a robust stability constraint. Both the state-feedback and output-feedback problems are considered. It is shown that in the state-feedback case one can come arbitrarily close to the optimal (even over full information controllers) mixed H/sub 2//H/sub infinity / performance measure using constant gain state feedback. Moreover, the state-feedback problem can be converted into a convex optimization problem over a bounded subset of (n*n and n*q, where n and q are, respectively, the state and input dimensions) real matrices. Using the central H/sub infinity / estimator, it is shown that the output feedback problem can be reduced to a state-feedback problem. In this case, the dimension of the resulting controller does not exceed the dimension of the generalized plant. >

Mixed H/sub 2//H/sub infinity / control: a convex optimization approach

This paper presents a new procedure for continuous and discrete-time linear control systems design. It consists of the definition of a convex programming problem in the parameter space that, when solved, provides the feedback gain. One of the most important features of the procedure is that additional design constraints are easily incorporated in the original formulation, yielding solutions to problems that have raised a great deal of interest within the last few years. This is precisely the case of the decentralized control problem and the quadratic stabilizability problem of uncertain systems with both dynamic and input uncertain matrices. In this last case, necessary and sufficient conditions for the existence of a linear stabilizing gain are provided and, to the authors’ knowledge, this is one of the first numerical procedures able to handle and solve this interesting design problem for high-order, continuous-time or discrete-time linear models. The theory is illustrated by examples.

On a convex parameter space method for linear control design of uncertain systems

The results obtained in studies of robust stability and stabilizability of control systems with parametric (structured) uncertainties are reviewed. Both the algebraic methods based upon characteristic equations and the methods using Lyapunov functions and Riccati equations are discussed and compared. In the context of algebraic methods, most promising are the Kharitonov-type approach and the optimization procedure of embedding a geometric figure of some kind inside the stability regions of the parameter space, maximizing its size using minimax or some other mathematical programming technique. In the framework of Lyapunov's direct method, the dominant approach has been a quadratic function estimation of stability regions in the parameter space. In large-sale systems, the concept of vector Lyapunov functions has been used with the possibility of choosing quadratic forms, norm-like functions, and their combinations. >

Parameter space methods for robust control design: a guided tour

Method and apparatus for predicting properties of a target object comprise application of a search manager for analyzing parameters of a plurality of databases for a plurality of objects, the databases comprising an electrical, electromagnetic, acoustic spectral database (ESD), a micro-body assemblage database (MAD) and a database of image data whereby the databases store data objects containing identifying features, source information and information on site properties and context including time and frequency varying data. The method comprises application of multivariate statistical analysis and principal component analysis in combination with content-based image retrieval for providing two-dimensional attributes of three dimensional objects, for example, via preferential image segmentation using a tree of shapes and to predict further properties of objects by means of k-means clustering and related methods. By way of example, one of a criminal activity and a fraudulent activity event, an intrusion event and a fire event and residual objects may be predicted and located and qualified such that, for example, properties of the residual objects may be qualified, for example, via black body radiation and micro-body databases including charcoal assemblages.

Method and apparatus for predicting object properties and events using similarity-based information retrieval and modeling

A computer-aided design (CAD) method and associated architectures are proposed for linear controllers. The design method and architecture are based on recent results that parameterize all controllers that stabilize a given plant. With this architecture, the design of controllers is a convex programming problem that can be solved numerically. Constraints on the closed-loop system, such as asymptotic tracking, decoupling, limits on peak excursions of variables, step response, settling time, and overshoot, as well as frequency-domain inequalities, are readily incorporated in the design. The minimization objective is quite general, with LQG (linear quadratic Gaussian) H/sub infinity / and new l/sub 1/ types as special cases. The constraints and objective are specified in a control specification language which is natural for the control engineer, referring directly to step responses, noise powers, transfer functions, and so on. >

A new CAD method and associated architectures for linear controllers

A new CAD method and associated architectures are proposed for linear controllers. The design method and architecture are based on recent results which parametrize all controllers which stabilize a given plant. With this architecture, the design of controllers is a convex programming problem which can be solved numerically. Constraints on the closed-loop system such as asymptotic tracking, decoupling, limits on peak excursions of variables, step response settling time and overshoot, as well as frequency domain inequalities are readily incorporated in the design. The minimization objective is quite general, with LQG, H ? , and new l 1 types as special cases. The constraints and objective are specified in a control specification language which is natural for the control engineer, referring directly to step responses, noise powers, transfer functions, and so on. This control specification language will be the input to a compiler which will translate the specifications into a standard convex program in RL, which is then solved by some numerical convex program solver. A small but powerful subset of the language has been specified and its associated compiler implemented. The architecture proposed not only makes design of the controller simple but also its implementation. These controllers can be built right now from off the shelf components or integrated using standard VLSI cells.

N. M. Khraishi

Papers

A new CAD method and associated architectures for linear controllers

A New CAD Method and Associated Architectures for Linear Controllers