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184
Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization
, 2000
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System analysis via integral quadratic constraints

, 1997
"... This paper introduces a unified approach to robustness analysis with respect to nonlinearities, time variations, and uncertain parameters. From an original idea by Yakubovich, the approach has been developed under a combination of influences from the Western and Russian traditions of control theor ..."
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Cited by 231 (13 self)
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This paper introduces a unified approach to robustness analysis with respect to nonlinearities, time variations, and uncertain parameters. From an original idea by Yakubovich, the approach has been developed under a combination of influences from the Western and Russian traditions of control theory. It is shown how a complex system can be described, using integral quadratic constraints (IQC’s) for its elementary components. A stability theorem for systems described by IQC’s is presented that covers classical passivity/dissipativity arguments but simplifies the use of multipliers and the treatment of causality. A systematic computational approach is described, and relations to other methods of stability analysis are discussed. Last, but not least, the paper contains a summarizing list of IQC’s for important types of system components.
Robust Constrained Model Predictive Control using Linear Matrix Inequalities
, 1996
"... The primary disadvantage of current design techniques for model predictive control (MPC) is their inability to deal explicitly with plant model uncertainty. In this paper, we present a new approach for robust MPC synthesis which allows explicit incorporation of the description of plant uncertainty i ..."
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Cited by 140 (5 self)
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The primary disadvantage of current design techniques for model predictive control (MPC) is their inability to deal explicitly with plant model uncertainty. In this paper, we present a new approach for robust MPC synthesis which allows explicit incorporation of the description of plant uncertainty in the problem formulation. The uncertainty is expressed both in the time domain and the frequency domain. The goal is to design, at each time step, a statefeedback control law which minimizes a "worstcase" infinite horizon objective function, subject to constraints on the control input and plant output. Using standard techniques, the problem of minimizing an upper bound on the "worstcase" objective function, subject to input and output constraints, is reduced to a convex optimization involving linear matrix inequalities (LMIs). It is shown that the feasible receding horizon statefeedback control design robustly stabilizes the set of uncertain plants under consideration. Several extensions...
Distributed control of spatially invariant systems
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 2002
"... We consider distributed parameter systems where the underlying dynamics are spatially invariant, and where the controls and measurements are spatially distributed. These systems arise in many applications such as the control of vehicular platoons, flow control, microelectromechanical systems (MEMS), ..."
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Cited by 96 (2 self)
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We consider distributed parameter systems where the underlying dynamics are spatially invariant, and where the controls and measurements are spatially distributed. These systems arise in many applications such as the control of vehicular platoons, flow control, microelectromechanical systems (MEMS), smart structures, and systems described by partial differential equations with constant coefficients and distributed controls and measurements. For fully actuated distributed control problems involving quadratic criteria such as linear quadratic regulator (LQR), P and, optimal controllers can be obtained by solving a parameterized family of standard finitedimensional problems. We show that optimal controllers have an inherent degree of decentralization, and this provides a practical distributed controller architecture. We also prove a general result that applies to partially distributed control and a variety of performance criteria, stating that optimal controllers inherit the spatial invariance structure of the plant. Connections of this work to that on systems over rings, and systems with dynamical symmetries are discussed.
Chromatographic Methods
 In International
, 1992
"... Still the doctor — by a country mile! Preferences for health services in two country towns in northwest New South Wales he relative importance people place on particular healthcare services is a significant factor in meeting their healthcare needs and influencing their health behaviour. ..."
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Cited by 76 (1 self)
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Still the doctor — by a country mile! Preferences for health services in two country towns in northwest New South Wales he relative importance people place on particular healthcare services is a significant factor in meeting their healthcare needs and influencing their health behaviour.
Introducing SOSTOOLS: A General Purpose Sum of Squares Programming Solver
 Proceedings of the IEEE Conference on Decision and Control (CDC), Las Vegas, NV
, 2002
"... SOSTOOLS is a MATLAB toolbox for constructing and solving sum of squares programs. It can be used in combination with semidefinite programming software, such as SeDuMi, to solve many continuous and combinatorial optimization problems, as well as various controlrelated problems. This paper provides ..."
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Cited by 74 (16 self)
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SOSTOOLS is a MATLAB toolbox for constructing and solving sum of squares programs. It can be used in combination with semidefinite programming software, such as SeDuMi, to solve many continuous and combinatorial optimization problems, as well as various controlrelated problems. This paper provides an overview on sum of squares programming, describes the primary features of SOSTOOLS, and shows how SOSTOOLS is used to solve sum of squares programs. Some applications from different areas are presented to show the wide applicability of sum of squares programming in general and SOSTOOLS in particular. 1
Distributed Control Design for Systems Interconnected Over an Arbitrary Graph
 IEEE Trans. Automatic Control
, 2004
"... Abstract—We consider the problem of synthesizing a distributed dynamic output feedback controller achieving performance for a system composed of different interconnected subunits, when the topology of the underlying graph is arbitrary. First, using tools inspired by dissipativity theory, we derive ..."
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Cited by 53 (0 self)
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Abstract—We consider the problem of synthesizing a distributed dynamic output feedback controller achieving performance for a system composed of different interconnected subunits, when the topology of the underlying graph is arbitrary. First, using tools inspired by dissipativity theory, we derive sufficient conditions in the form of finitedimensional linear matrix inequalities when the interconnections are assumed to be ideal. These inequalities are coupled in a way that reflects the spatial structure of the problem and can be exploited to design distributed synthesis algorithms. We then investigate the case of lossy interconnection links and derive similar results for systems whose interconnection relations can be captured by a class of integral quadratic constraints that includes constant delays. Index Terms—Dissipativity, distributed control, largescale systems, linear matrix inequalities (LMIs). I.
Matrix SumofSquares Relaxations for Robust SemiDefinite Programs
 Math. Program
, 2006
"... We consider robust semidefinite programs which depend polynomially or rationally on some uncertain parameter that is only known to be contained in a set with a polynomial matrix inequality description. On the basis of matrix sumofsquares decompositions, we suggest a systematic procedure to con ..."
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Cited by 33 (0 self)
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We consider robust semidefinite programs which depend polynomially or rationally on some uncertain parameter that is only known to be contained in a set with a polynomial matrix inequality description. On the basis of matrix sumofsquares decompositions, we suggest a systematic procedure to construct a family of linear matrix inequality relaxations for computing upper bounds on the optimal value of the corresponding robust counterpart. With a novel matrixversion of Putinar’s sumofsquares representation for positive polynomials on compact semialgebraic sets, we prove asymptotic exactness of the relaxation family under a suitable constraint qualification. If the uncertainty region is a compact polytope, we provide a new duality proof for the validity of Putinar’s constraint qualification with an a priori degree bound on the polynomial certificates. Finally, we point out the consequences of our results for constructing relaxations based on the socalled fullblock Sprocedure, which allows to apply recently developed tests in order to computationally verify the exactness of possibly smallsized relaxations.
Semidefinite Programming Relaxations and Algebraic Optimization in Control
 EUROPEAN JOURNAL OF CONTROL (2003)9:307321
, 2003
"... We present an overview of the essential elements of semidefinite programming as a computational tool for the analysis of systems and control problems. We make particular emphasis on general duality properties as providing suboptimality or infeasibility certificates. Our focus is on the exciting deve ..."
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Cited by 31 (5 self)
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We present an overview of the essential elements of semidefinite programming as a computational tool for the analysis of systems and control problems. We make particular emphasis on general duality properties as providing suboptimality or infeasibility certificates. Our focus is on the exciting developments which have occured in the last few years, including robust optimization, combinatorial optimization, and algebraic methods such as sumofsquares. These developments are illustrated with examples of applications to control systems.