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Convergent relaxations of polynomial matrix inequalities and static output feedback
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Modelchecking Markov chains in the presence of uncertainties
 Tools and Algorithms for the Construction and Analysis of Systems (TACAS), volume 3920 of LNCS
, 2006
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Model Reduction in Physical Domain
 Proceedings of American Control Conference 1999
, 1999
"... Modeling is an essential part of the analysis and the design of dynamic systems. Contemporary computer algorithms can produce very detailed models for complex systems with little time and effort. However, over complicated models may not be efficient. Therefore, reducing a model to a more manageable ..."
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Modeling is an essential part of the analysis and the design of dynamic systems. Contemporary computer algorithms can produce very detailed models for complex systems with little time and effort. However, over complicated models may not be efficient. Therefore, reducing a model to a more manageable size has become an attractive research topic. A very useful type of reduced models is obtained by removing as many physical components as possible from the original model. Such approach is known as model reduction in the physical domain. Many results have been achieved in model reduction in the physical domain during past decades. Nonetheless, the newest developments in engineering practice as well as in theoretical research have brought about further challenges and opportunities. In this thesis, the criteria and the scope of model reduction in the physical domain are reinvestigated. As a result, a criterion based on the H,, norm of certain error model is proposed. Furthermore, the scope of model reduction is also extended. In this thesis, a mathematical framework is constructed for model reduction in physical domain. Specifically, model reduction
GPCLPV: a predictive LPV controller based on BMIs
, 2005
"... In this paper the authors present a predictive linear parameter varying (LPV) controller based on the GPC controller [1][3], for nonlinear systems. The resulting controller is denoted as GPCLPV. This one has the same structure as a general LPV controller [4][7], which has a lineal fractional de ..."
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In this paper the authors present a predictive linear parameter varying (LPV) controller based on the GPC controller [1][3], for nonlinear systems. The resulting controller is denoted as GPCLPV. This one has the same structure as a general LPV controller [4][7], which has a lineal fractional dependence on the process signal measurements. Therefore, this controller has the ability of modifying its dynamics depending on measurements leading to a possibly nonlinear controller. That controller is designed in two steps. First, for a given steady state point is obtained a linear GPC using a local model of the nonlinear system around that operating point. And second, using bilinear matrix inequalities (BMIs) the remaining matrices of GPCLPV are selected in order to achieve some closed loop properties: stability in some operation zone, norm bounding of some input/output channels, maximum settling time, maximum overshoot, etc. This methodology of design can be applied to nonlinear systems which can be embedded in a LPV system using differential inclusion techniques. Finally, the GPCLPV is applied to the nonlinear model of a liquidgas separation process.
Solutions of Polynomial Systems derived from the Steady Cavity Flow Problem
, 2008
"... We propose a general algorithm to enumerate all solutions of a zerodimensional polynomial system with respect to a given cost function. The algorithm is developed and is used to study a polynomial system obtained by discretizing the steady cavity flow problem in two dimensions. The key technique ..."
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We propose a general algorithm to enumerate all solutions of a zerodimensional polynomial system with respect to a given cost function. The algorithm is developed and is used to study a polynomial system obtained by discretizing the steady cavity flow problem in two dimensions. The key technique on which our algorithm is based is to solve polynomial optimization problems via sparse semidefinite programming relaxations (SDPR) [20], which has been adopted successfully to solve reactiondiffusion boundary value problems in [13]. The cost function to be minimized is derived from discretizing the fluid’s kinetic energy. The enumeration algorithm’s solutions are shown to converge to the minimal kinetic energy solutions for SDPR of increasing order. We demonstrate the algorithm with SDPR of first and second order on polynomial systems for different scenarios of the cavity flow problem and succeed in deriving the k smallest kinetic energy solutions. The question whether these solutions converge to solutions of the steady cavity flow problem is discussed, and we pose a conjecture for the minimal energy solution for increasing Reynolds number.
Quasiconvex SumofSquares Programming
"... Abstract — A sumofsquares program is an optimization problem with polynomial sumofsquares constraints. The constraints and the objective function are affine in the decision variables. This paper introduces a generalized sumofsquares programming problem. This generalization allows one decision ..."
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Abstract — A sumofsquares program is an optimization problem with polynomial sumofsquares constraints. The constraints and the objective function are affine in the decision variables. This paper introduces a generalized sumofsquares programming problem. This generalization allows one decision variable to enter bilinearly in the constraints. The bilinear decision variable enters the constraints in a particular structured way. The objective function is the single bilinear decision variable. It is proved that this formulation is quasiconvex and hence the global optima can be computed via bisection. Many nonlinear analysis problems can be posed within this framework and two examples are provided. I.
A ROBUST OVERRIDE SCHEME ENFORCING STRICT OUTPUT CONSTRAINTS FOR A CLASS OF STRICTLY PROPER SYSTEMS
"... Abstract: This paper presents an override controller which ensures that constrained output variables retain certain prescribed strict bounds. The class of nominal closed loop systems considered for the constrained output regulation problem is strictly proper and minimum phase, assuming for each outp ..."
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Abstract: This paper presents an override controller which ensures that constrained output variables retain certain prescribed strict bounds. The class of nominal closed loop systems considered for the constrained output regulation problem is strictly proper and minimum phase, assuming for each output measurement constraint one available actuator and the first Markov parameter to be full rank. This necessitates the openloop plant to have the same inputtoconstrainedoutput characteristics. The advantage of the considered class of nominal systems is that an output constraint translates directly into a state constraint for which it is possible to use a particular nonsmooth Lyapunov function. The nonsmooth Lyapunov function is defined by the level of the output constraint creating an invariant set for which the strict output constraints are satisfied. The override strategy is designed to retain a minimal effect on the nominal control loop in case no output constraint is violated. Copyright 2005 IFAC
u.ac.jp
"... u.ac.jp We propose a general algorithm to approximately enumerate all solutions of a zerodimensional polynomial system with respect to a given cost function. The algorithm is developed and is used to study a polynomial system obtained by discretizing the steady cavity flow problem in two dimension ..."
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u.ac.jp We propose a general algorithm to approximately enumerate all solutions of a zerodimensional polynomial system with respect to a given cost function. The algorithm is developed and is used to study a polynomial system obtained by discretizing the steady cavity flow problem in two dimensions. The key technique on which our algorithm is based is to solve polynomial optimization problems via sparse semidefinite program relaxations (SDPR) [18], which has been adopted successfully to solve reactiondiffusion boundary value problems in [11]. The cost function to be minimized is derived from discretizing the kinetic energy of the fluid. The solutions of the enumeration algorithm are shown to converge to the minimal kinetic energy solutions for SDPR of increasing order. We take advantage of Gröbner basis method to tune the performance of the algorithm, demonstrate the algorithm with SDPR of first and second order on polynomial systems for different scenarios of the cavity flow problem and succeed in approximately deriving the k smallest kinetic energy solutions. The question of whether these solutions converge to solutions of the steady cavity flow problem is discussed, and we pose a conjecture for the minimal energy solution for increasing Reynolds number.
Wenping Xue Admissible FiniteTime Stability and Stabilization of Uncertain Discrete Singular Systems
"... The problems of admissible finitetime stability (AFTS) and admissible finitetime stabilization for a class of uncertain discrete singular systems are addressed in this study. The definition of AFTS is first given. Second, a sufficient condition for the AFTS of the nominal unforced system is estab ..."
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The problems of admissible finitetime stability (AFTS) and admissible finitetime stabilization for a class of uncertain discrete singular systems are addressed in this study. The definition of AFTS is first given. Second, a sufficient condition for the AFTS of the nominal unforced system is established, which is further extended to the uncertain case. Then, a sufficient condition is proposed for the design of a state feedback controller such that the closedloop system is admissibly finitetime stable for all admissible uncertainties. Both the AFTS and the controller design conditions are presented in terms of linear matrix inequalities (LMIs) with a fixed parameter. Finally, two numerical examples are provided to illustrate the effectiveness of the developed theory.
H ∞ Gain Scheduling for DiscreteTime Systems with Control Delays and TimeVarying Parameters: a BMI Approach
"... AbstractIn this paper, the problem of gain scheduling for timevarying systems with time delays is investigated. By using a memory at the feedback loop, a discrete gain scheduled controller which minimizes an upper bound to the H ∞ performance of the closed loop system is determined. ..."
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AbstractIn this paper, the problem of gain scheduling for timevarying systems with time delays is investigated. By using a memory at the feedback loop, a discrete gain scheduled controller which minimizes an upper bound to the H ∞ performance of the closed loop system is determined.