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590
Supervisory Control of Families of Linear SetPoint Controllers  Part 2: Robustness
 IEEE Trans. Automat. Contr
, 1998
"... A simplystructured highlevel controller called a `supervisor' has recently been proposed in [1] for the purpose of orchestrating the switching of a sequence of candidate setpoint controllers into feedback with an imprecisely modeled siso process so as to cause the output of the process to ap ..."
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Cited by 234 (26 self)
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A simplystructured highlevel controller called a `supervisor' has recently been proposed in [1] for the purpose of orchestrating the switching of a sequence of candidate setpoint controllers into feedback with an imprecisely modeled siso process so as to cause the output of the process to approach and track a constant reference input. The process is assumed to be modeled by a siso linear system whose transfer function is in the union of a number of subclasses, each subclass being small enough so that one of the candidate controllers would solve the setpoint tracking problem, were the process's transfer function to be one of the subclass's members. In [1] it is shown that in the absence of unmodelled process dynamics the proposed supervisor can successfully perform its function fi.e., achieve a zero steady state tracking errorg even if process disturbances are present, provided they are constant. This paper proves that without any further modification, the same supervisor can also perform this function in the face of normbounded unmodelled dynamics and moreover that none of the signals within the overall system can grow without bound in response to bounded disturbance and noise inputs, be they constant or not.
Krylov Projection Methods For Model Reduction
, 1997
"... This dissertation focuses on efficiently forming reducedorder models for large, linear dynamic systems. Projections onto unions of Krylov subspaces lead to a class of reducedorder models known as rational interpolants. The cornerstone of this dissertation is a collection of theory relating Krylov p ..."
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Cited by 213 (3 self)
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This dissertation focuses on efficiently forming reducedorder models for large, linear dynamic systems. Projections onto unions of Krylov subspaces lead to a class of reducedorder models known as rational interpolants. The cornerstone of this dissertation is a collection of theory relating Krylov projection to rational interpolation. Based on this theoretical framework, three algorithms for model reduction are proposed. The first algorithm, dual rational Arnoldi, is a numerically reliable approach involving orthogonal projection matrices. The second, rational Lanczos, is an efficient generalization of existing Lanczosbased methods. The third, rational power Krylov, avoids orthogonalization and is suited for parallel or approximate computations. The performance of the three algorithms is compared via a combination of theory and examples. Independent of the precise algorithm, a host of supporting tools are also developed to form a complete modelreduction package. Techniques for choosing the matching frequencies, estimating the modeling error, insuring the model's stability, treating multipleinput multipleoutput systems, implementing parallelism, and avoiding a need for exact factors of large matrix pencils are all examined to various degrees.
A Convex Characterization of GainScheduled Hâˆž Controllers
"... An important class of linear timevarying systems consists of plants where the statespace matrices are fixed functions of some timevarying physical parameters `. Small Gain techniques can be applied to such systems to derive robust timeinvariant controllers. Yet, this approach is often overly ..."
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Cited by 104 (5 self)
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An important class of linear timevarying systems consists of plants where the statespace matrices are fixed functions of some timevarying physical parameters `. Small Gain techniques can be applied to such systems to derive robust timeinvariant controllers. Yet, this approach is often overly conservative when the parameters ` undergo large variations during system operation. In general, much higher performance can be achieved by control laws that incorporate available measurements of ` and therefore "adjust" to the current plant dynamics. This paper discusses extensions of Hâˆž synthesis techniques to allow for controller dependence on timevarying but measured parameters. When this dependence is linear fractional, the existence of such gainscheduled H1 controllers is fully characterized in terms of linear matrix inequalities (LMIs). The underlying synthesis problem is therefore a convex program for which efficient optimization techniques are available. The formalism and...
The periodic Schur decomposition. Algorithms and applications
 In Proc. SPIE Conference
, 1992
"... . In this paper we derive a unitary eigendecomposition for a sequence of matrices which we call the periodic Schur decomposition. We prove its existence and discuss its application to the solution of periodic difference equations arising in control. We show how the classical QR algorithm can be ext ..."
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Cited by 91 (13 self)
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. In this paper we derive a unitary eigendecomposition for a sequence of matrices which we call the periodic Schur decomposition. We prove its existence and discuss its application to the solution of periodic difference equations arising in control. We show how the classical QR algorithm can be extended to provide a stable algorithm for computing this generalized decomposition. We apply the decomposition also to cyclic matrices and two point boundary value problems. Key words. Numerical algorithms, linear algebra, periodic systems, Kcyclic matrices, twopoint boundary value problems 1 Introduction In the study of timevarying control systems in (generalized) state space form : ( E k \Delta z k+1 = F k \Delta z k +G k \Delta u k y k = H k \Delta z k + J k \Delta u k (1) the periodic coefficients case has always been considered the simplest extension of the timeinvariant case. Here the coefficients satisfy, for some K ? 0 the periodicity conditions E k = E k+K , F k = F k+K , G k...
A characterization of integral inputtostate stability
 IEEE Trans. Autom. Control
, 2000
"... AbstractThe notion of inputtostate stability (ISS) is now recognized as a central concept in nonlinear systems analysis. It provides a nonlinear generalization of finite gains with respect to supremum norms and also of finite 2 gains. It plays a central role in recursive design, coprime factoriz ..."
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Cited by 87 (10 self)
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AbstractThe notion of inputtostate stability (ISS) is now recognized as a central concept in nonlinear systems analysis. It provides a nonlinear generalization of finite gains with respect to supremum norms and also of finite 2 gains. It plays a central role in recursive design, coprime factorizations, controllers for nonminimum phase systems, and many other areas. In this paper, a newer notion, that of integral inputtostate stability (iISS), is studied. The notion of iISS generalizes the concept of finite gain when using an integral norm on inputs but supremum norms of states, in that sense generalizing the linear " 2 " theory. It allows one to quantify sensitivity even in the presence of certain forms of nonlinear resonance. We obtain here several necessary and sufficient characterizations of the iISS property, expressed in terms of dissipation inequalities and other alternative and nontrivial characterizations. These characterizations serve to show that integral inputtostate stability is a most natural concept, one that might eventually play a role at least comparable to, if not even more important than, ISS.
A Generalized Entropy Criterion for NevanlinnaPick Interpolation with Degree Constraint
 IEEE Trans. Automat. Control
, 2001
"... In this paper, we present a generalized entropy criterion for solving the rational NevanlinnaPick problem for +1 interpolating conditions and the degree of interpolants bounded by . The primal problem of maximizing this entropy gain has a very wellbehaved dual problem. This dual is a convex opti ..."
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Cited by 73 (30 self)
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In this paper, we present a generalized entropy criterion for solving the rational NevanlinnaPick problem for +1 interpolating conditions and the degree of interpolants bounded by . The primal problem of maximizing this entropy gain has a very wellbehaved dual problem. This dual is a convex optimization problem in a finitedimensional space and gives rise to an algorithm for finding all interpolants which are positive real and rational of degree at most . The criterion requires a selection of a monic Schur polynomial of degree . It follows that this class of monic polynomials completely parameterizes all such rational interpolants, and it therefore provides a set of design parameters for specifying such interpolants. The algorithm is implemented in statespace form and applied to several illustrative problems in systems and control, namely sensitivity minimization, maximal power transfer and spectral estimation.
Computational techniques for the verification of hybrid systems
 Proceedings of the IEEE
, 2003
"... Hybrid system theory lies at the intersection of the fields of engineering control theory and computer science verification. It is defined as the modeling, analysis, and control of systems that involve the interaction of both discrete state systems, represented by finite automata, and continuous sta ..."
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Cited by 72 (9 self)
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Hybrid system theory lies at the intersection of the fields of engineering control theory and computer science verification. It is defined as the modeling, analysis, and control of systems that involve the interaction of both discrete state systems, represented by finite automata, and continuous state dynamics, represented by differential equations. The embedded autopilot of a modern commercial jet is a prime example of a hybrid system: the autopilot modes correspond to the application of different control laws, and the logic of mode switching is determined by the continuous state dynamics of the aircraft, as well as through interaction with the pilot. To understand the behavior of hybrid systems, to simulate, and to control these systems, theoretical advances, analyses, and numerical tools are needed. In this paper, we first present a general model for a hybrid system along with an overview of methods for verifying continuous and hybrid systems. We describe a particular verification
Imprecision in Engineering Design
 ASME JOURNAL OF MECHANICAL DESIGN
, 1995
"... Methods for incorporating imprecision in engineering design decisionmaking are briefly reviewed and compared. A tutorial is presented on the Method of Imprecision (MoI), a formal method, based on the mathematics of fuzzy sets, for representing and manipulating imprecision in engineering design. The ..."
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Cited by 66 (6 self)
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Methods for incorporating imprecision in engineering design decisionmaking are briefly reviewed and compared. A tutorial is presented on the Method of Imprecision (MoI), a formal method, based on the mathematics of fuzzy sets, for representing and manipulating imprecision in engineering design. The results of a design cost estimation example, utilizing a new informal cost specification, are presented. The MoI can provide formal information upon which to base decisions during preliminary engineering design and can facilitate setbased concurrent design.
A Rational Lanczos Algorithm for Model Reduction II: Interpolation Point Selection
 Numerical Algorithms
, 1998
"... In part I of this work [10], a rational Lanczos algorithm was developed which led to rational interpolants of dynamical systems. In this sequel, the important implementational issue of interpolation point selection is analyzed in detail. A residual expression is derived for the rational Lanczos al ..."
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Cited by 65 (1 self)
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In part I of this work [10], a rational Lanczos algorithm was developed which led to rational interpolants of dynamical systems. In this sequel, the important implementational issue of interpolation point selection is analyzed in detail. A residual expression is derived for the rational Lanczos algorithm and is used to govern the placement and type of the interpolation points. Algorithms are developed and applied to a problem arising from circuit interconnect modeling. AMS classification: Primary 65F15; Secondary 65G05. Key Words : State space systems, rational Lanczos algorithm, preconditioning, rational interpolation, model reduction. 1 Introduction A variety of Lanczosbased methods are now available for acquiring a reducedorder model for a stable, linear, timeinvariant system. Many of these Lanczosbased methods interpolate the value and consecutive derivatives of the frequency response of the original system at one or more points, see [10] and references therein. Yet by...
Optimal and Robust Control and Estimation of Linear Paths to Transition
 J. Fluid Mech
, 1998
"... this paper is not valid. Iterative optimal control approaches over finite time intervals, which make use of full state information, may still be formulated (Abergel & Temam 1990) and performed (Moin & Bewley 1995) with impressive results. In order to make such schemes practical, one must und ..."
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Cited by 63 (10 self)
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this paper is not valid. Iterative optimal control approaches over finite time intervals, which make use of full state information, may still be formulated (Abergel & Temam 1990) and performed (Moin & Bewley 1995) with impressive results. In order to make such schemes practical, one must understand how to account for disturbances in a rigorous fashion and how to estimate accurately the necessary components of the state (for instance, the location and strength of the nearwall coherent structures) based on limited flow measurements. The present paper makes these concepts clear in a fluidmechanical sense, albeit for a linear problem, and thus provides a step in this development. Techniques to extend the robust control concept, introduced for problems in fluid mechanics in the present work, to nonlinear problems (such as turbulence) are discussed in Bewley, Moin & Temam (1997) and Bewley, Temam & Ziane (1998). 1.1. Outline of paper The structure of the remainder of the paper is: Section 2: the governing equations for the flow stability problem are put in a standard notation which makes subsequent application of control theory straightforward. Two specific cases are identified to be examined in detail: one supercritical and one subcritical. Section 3: the control approach and numerical method used are briefly summarized. Section 4: the methods used to analyse the openloop and closedloop systems are reviewed. Section 5: the uncontrolled (`openloop') systems are studied in detail. Section 6: the controlled (`closedloop') systems are studied in detail. Root loci, which demonstrate the movement of the closedloop system eigenvalues with respect to control parameters, are shown to illuminate some general trends, but fail to provide a quantitative measure of system performa...