Karolos M. Grigoriadis

Survey paper: Static output feedback-A survey

This paper reviews the static output feedback problem in the control of linear, time-invariant (LTI) systems. It includes analytical and computational methods and presents in a unified fashion the knowledge gained in the decades of research into this important open problem. The paper shows that although many approaches and techniques exist to approach different versions of the problem, no efficient algorithmic solutions are available.

Actuator Saturation Control

Uniting local and global controllers for anti-windup design LQR/LQG theory for systems with saturated actuators - a stochastic linearization approach LPV-based control of systems with amplitude and rate actuator saturation constraints analysis and control of linear systems with saturation using convex optimization an LPV approach for disturbance attentuation of systems with bounded inputs regional H2 performance analysis and synthesis with saturating control control of discrete-time systems with actuator amplitude and rate nonlinearities null controllability and stabilization of linear systems subject to asymmetric actuator saturation internal stabilization and Lp(1p) performance for linear plants with actuators subject to amplitude and rate saturations optimal windup and directionality compensation in input-constrained nonlinear systems output feedback compensators for linear systems with position and rate bounded actuators.

Anti-windup controller design using linear parameter-varying control methods

In this paper, we seek to provide a systematic anti-windup control synthesis approach for systems with actuator saturation within a linear parameter-varying (LPV) design framework. The closed-loop induced L2 gain control problem is considered. Different from conventional two-step anti-windup design approaches, the proposed scheme directly utilizes saturation indicator parameters to schedule accordingly the parameter-varying controller. Hence, the synthesis conditions are formulated in terms of linear matrix inequalities (LMIs) that can be solved very efficiently. The resulting gain-scheduled controller is non-linear in general and would lead to graceful performance degradation in the presence of actuator saturation non-linearities and linear performance recovery. An aircraft longitudinal dynamics control problem with two input saturation non-linearities is used to demonstrate the effectiveness of the proposed LPV anti-windup scheme.

Optimal H ∞ model reduction via linear matrix inequalities: continuous- and discrete-time cases

Necessary and sufficient conditions are derived for the existence of a solution to the continuous-time and discrete-time H∞ model reduction problems. These conditions are expressed in terms of linear matrix inequalities (LMIs) and a coupling non-convex rank constraint set. In addition, an explicit parametrization of all reduced-order models that correspond to a feasible solution is provided in terms of a contractive matrix. These results follow from the recent solution of the H∞ control design problem using LMIs. Particularly simple conditions and a simple parametrization of all solutions are obtained for the zeroth-order H∞ approximation problem, and the convexity of this problem is demonstrated. Computational issues are discussed and an iterative procedure is proposed to solve the H∞ model reduction problem using alternating projections, although global convergence of the algorithm is not guaranteed.

Optimal Redesign of Linear Systems

This paper proposes a redesign procedure for linear systems. We suppose that an initial satisfactory controller which yields the desired performance is given. Then both the plant and the controller are redesigned to minimize the required active control effort. Either the closed-loop system matrix or the closed-loop covariance matrix of the initial design can be preserved under the redesign. Convex quadratic programming solves this problem. In addition, an iterative approach for integrated plant and controller design is proposed, which uses the above optimal plant/controller redesign in each iterative step. The algorithm has guaranteed convergence and provides a sequence of designs with monotonically decreasing active control effort. Examples are included to illustrate the procedure.

Optimal controllers for finite wordlength implementation

When a controller is implemented by a digital computer with A/D and D/A conversion, numerical errors can severely affect the performance of the control system. There exist realizations of a given controller transfer function exhibiting arbitrarily large effects from computational errors. Assuming sufficient excitation of the system, the problem of designing an optimal controller in the presence of both external disturbances and internal roundoff errors is solved. The results reduce to the standard LQG controller when infinite-precision computation is used. For finite precision, however, the separation principle does not hold. A penalty is also added to the cost function to penalize the sum of the wordlengths used to compute the fractional part of each state variable of the controller. This sum can be used to represent the lower bound on computer memory needed for controller synthesis. It measures controller complexity and is minimized (penalized) here. >

LMI-based filter design for fault detection and isolation

A linear matrix inequality (LMI) based filter design approach for fixed-order robust fault detection and isolation (FDI) is examined. The proposed filter design provides necessary and sufficient conditions for the existence of a solution to the detection and isolation of faults using an H/sub /spl infin// formulation. These conditions are expressed in terms of LMIs with matrix rank constraints, and a parameterization of all admissible filters is provided, which corresponds to a feasible solution. A convex LMI problem is obtained for the full-order FDI filter design. Finally, the proposed methods are demonstrated using a structural system simulation example, which include faulty actuators, sensors and external disturbances.

Optimal unbiased filtering via linear matrix inequalities

Abstract Solutions to the optimal H∞ and L2−L∞ unbiased reduced-order filtering problems are obtained in terms of linear matrix inequalities (LMIs). The order of the optimal filter is equal to the number of measurements. Both continuous- and discrete-time results are presented. An explicit parametrization of all optimal unbiased filters is provided in terms of a free contractive matrix.

Alternating convex projection methods for covariance control design

The problem of designing a static state feedback or full order dynamic controller is formulated as a problem of designing an appropriate plant state covariance matrix. We show that closed loop stability and multiple output norm constraints imply that the plant state covariance matrix lies at the intersection of some specified closed convex sets in the space of symmetric matrices. We address the covariance feasibility problem to determine the existence and compute a covariance matrix to satisfy assignability and output norm performance constraints. We address the covariance optimization problem to construct an assignable covariance matrix which satisfies output performance constraints and is as close as possible to a given desired covariance. We also treat inconsistent constraints where we look for an assignable covariance matrix which ‘best’ approximates desired but non-achievable output performance objectives (we call this the infeasible covariance optimization problem). All these problems are of a conve...

Covariance controllers: a new parametrization of the class of all stabilizing controllers

The class of all stabilizing controllers is parameterized in terms of the covariance matrix and an arbitrary skew symmetric matrix. The new parameterization is in closed form for any specified controller order.