Necessary and sufficient conditions are established for the existence of positive solutions to polynomial diophatine equations. A method for computation of the set of positive solutions to polynomial diophatine equati...
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Necessary and sufficient conditions are established for the existence of positive solutions to polynomial diophatine equations. A method for computation of the set of positive solutions to polynomial diophatine equation based on extreme points and extreme directions is proposed. The effectiveness of the method is demonstrated on a numerical example.
In this paper the regularized variants of barrier function methods are discussed. These variants are related to the following regularization methods: Tichonov-function method, method of residuals and method of quasiso...
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In this paper the regularized variants of barrier function methods are discussed. These variants are related to the following regularization methods: Tichonov-function method, method of residuals and method of quasisolutions. .A convergence rate estimation is given for each method if both the original minimization problem and the connected problem of finding R-normal sohlion posses The feature of strong compatibility.
The goal of this work it is to reformulate a conceptually meaningful optimal sensor placement problem (as outlined by Bagajewicz, 1997). This reformulation converts the original mixed integer nonlinear program (MINLP)...
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The goal of this work it is to reformulate a conceptually meaningful optimal sensor placement problem (as outlined by Bagajewicz, 1997). This reformulation converts the original mixed integer nonlinear program (MINLP) with dimensions dependent upon the value of the integer decision variables into a mixed integer convex program (MICP) with fixed matrix dimensions. This reformulation allows for the problem to be solved globally and efficiently using standard interior point and branch and bound search algorithms. Additionally, the traditional sensor placement problem, based on static process conditions, is extended to linear dynamic processes.
This study investigates the filter design problem for two-dimensional (2D) discrete-time non-linear systems in Takagi–Sugeno (T–S) fuzzy model. The frequency of the exogenous disturbances is assumed to belong to a k...
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This study investigates the filter design problem for two-dimensional (2D) discrete-time non-linear systems in Takagi–Sugeno (T–S) fuzzy model. The frequency of the exogenous disturbances is assumed to belong to a known finite frequency (FF) domain. An FF performance is defined for 2D discrete-time systems, which generalises the standard one and makes use of the frequency-domain characteristics of practical signals. By virtue of the defined FF performance, sufficient conditions are proposed for analysing the disturbance attenuation performance of the filtering error system. Efficient conditions are obtained to guarantee the existence of a filter and such that the error system is asymptotically stable with an FF performance index. A systematic filter design scheme is developed by converting the corresponding fuzzy filter design into a convex optimisation problem. Finally, a gas absorption system is employed to illustrate the validity of the proposed methods.
In this paper identification of mixed parametric/nonparametric linear models is considered. A set membership setting is adopted. Disturbances are assumed to be bounded according to the 2-norm, while estimation errors ...
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In this paper identification of mixed parametric/nonparametric linear models is considered. A set membership setting is adopted. Disturbances are assumed to be bounded according to the 2-norm, while estimation errors are measured according to an H norm. Worst case optimal and suboptimal algorithms are analyzed, minimizing the H norm of the unstructured perturbation. The behavior of estimation errors for different model orders is discussed on application examples.
作者：
Claudio De PersisPietro TesiENTEG
University of Groningen Nijenborgh 4 9747AG Groningen The Netherlands DINFO
University of Florence 50139 Florence Italy
In a recent paper we have shown that data collected from linear systems excited by persistently exciting inputs during low-complexity experiments, can be used to design state- and output-feedback controllers, includin...
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In a recent paper we have shown that data collected from linear systems excited by persistently exciting inputs during low-complexity experiments, can be used to design state- and output-feedback controllers, including optimal Linear Quadratic Regulators (LQR), by solving linear matrix inequalities (LMI) and semidefinite programs. We have also shown how to stabilize in the first approximation unknown nonlinear systems using data. In contrast to the case of linear systems, however, in the case of nonlinear systems the conditions for learning a controller directly from data may not be fulfilled even when the data are collected in experiments performed using persistently exciting inputs. In this paper we show how to design experiments that lead to the fulfilment of these conditions.
This article introduces a new approach to ℋ2robust filtering design for continuous and discrete-time LTI systems subjected to linear fractional parameter uncertainty representation. The novelty consists on the determi...
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This article introduces a new approach to ℋ2robust filtering design for continuous and discrete-time LTI systems subjected to linear fractional parameter uncertainty representation. The novelty consists on the determination of a performance certificate in terms of the gap between lower and upper bounds of a minimax programming problem which defines the optimal robust filter and the associated equilibrium cost. The calculations are performed through convex programming methods, applying slack variables, known as multipliers, to handle the fractional dependence of the plant transfer function with respect to the parameter uncertainty. The theory is illustrated by means of an example borrowed from the literature and a practical application involving the design of a robust filter for the load voltage estimation on a transmission line with a stub feeding an unknown resistive load.
In this paper, we focus on the primal-dual hybrid gradient (PDHG) method, which is being widely used to solve a broad spectrum of saddle-point problems. Despite of its wide applications in different areas, the study o...
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In this paper, we focus on the primal-dual hybrid gradient (PDHG) method, which is being widely used to solve a broad spectrum of saddle-point problems. Despite of its wide applications in different areas, the study of inexact versions of PDHG still seems to be in its infancy. We investigate how to design implementable inexactness criteria for solving the subproblems in PDHG scheme so that the convergence of an inexact PDHG can be guaranteed. We propose two specific inexactness criteria and accordingly some inexact PDHG methods for saddle-point problems. The convergence of both inexact PDHG methods is rigorously proved, and their convergence rates are estimated under different scenarios. Moreover, some numerical results on image restoration problems are reported to illustrate the efficiency of the proposed methods.
The design of high-precision sensing devises becomes ever more difficult and expensive. At the same time, the need for precise calibration of these devices (ranging from tiny sensors to space telescopes) manifests its...
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The design of high-precision sensing devises becomes ever more difficult and expensive. At the same time, the need for precise calibration of these devices (ranging from tiny sensors to space telescopes) manifests itself as a major roadblock in many scientific and technological endeavors. To achieve optimal performance of advanced high-performance sensors one must carefully calibrate them, which is often difficult or even impossible to do in practice. In this work we bring together three seemingly unrelated concepts, namely self-calibration, compressive sensing, and biconvex optimization. The idea behind self-calibration is to equip a hardware device with a smart algorithm that can compensate automatically for the lack of calibration. We show how several self-calibration problems can be treated efficiently within the framework of biconvex compressive sensing via a new method called SparseLift. More specifically, we consider a linear system of equations y = DAx, where both x and the diagonal matrix D (which models the calibration error) are unknown. By 'lifting' this biconvex inverse problem we arrive at a convex optimization problem. By exploiting sparsity in the signal model, we derive explicit theoretical guarantees under which both x and D can be recovered exactly, robustly, and numerically efficiently via linear programming. Applications in array calibration and wireless communications are discussed and numerical simulations are presented, confirming and complementing our theoretical analysis.
This paper analyzes array pattern tolerance against excitation errors. The nonprobabilistic interval analysis algorithm is used for tolerance analysis of the nonideal uniform linear array in this work. Toward this pur...
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This paper analyzes array pattern tolerance against excitation errors. The nonprobabilistic interval analysis algorithm is used for tolerance analysis of the nonideal uniform linear array in this work. Toward this purpose, corresponding interval models of the power pattern functions are established, respectively, with the consideration of the amplitude errors, phase errors, or both simultaneously, in antenna arrays. The tolerance for the amplitude-phase error of the main function parameters including the beamwidth, sidelobe level, and the directivity is simulated by computer according to the indicators and the actual requirements. Accordingly, the worst admissible performance of an array can be evaluated, which may provide theoretical reference for optimal antenna array design. As for the problem of array synthesis in the presence of various array errors, interval analysis-convex programming (IA-CP) is presented. Simulation results show that the proposed IA-CP based synthesis technique is robust for the amplitude and phase errors.
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