We develop a realizable circuit reduction to generate the interconnect macro-model for parasitic estimation in wideband applications. The inductance is represented by VPEC (vector potential equivalent circuit) model, ...
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ISBN:
(纸本)0780387368
We develop a realizable circuit reduction to generate the interconnect macro-model for parasitic estimation in wideband applications. The inductance is represented by VPEC (vector potential equivalent circuit) model, which not only enables the passive sparsification but also gives correct low-frequency response, whereas the recent Y - Delta circuit reduction intrinsically has inaccurate dc value and low-frequency response due to nodal-susceptance formulation. Applying hierarchical circuit-reduction enhanced by multi-point expansions, we can obtain an accurate high-order impedance function to capture the high-frequency response. The impedance function is further enforced passivity by convex programming realized by a Foster's synthesis. Experiments show that our method is as accurate as PRIMA in high frequency range, but leads to a realized circuit model with up to 10X times less complexity and up to 8X smaller simulation time. In addition, under the same reduction ratio, its error margin is less than that for the time-constant based reduction in both time-domain and frequency-domain simulations.
The problem of minimax estimation is considered for the linear multivariate statistically indeterminate observation model with mixed uncertainty. It is shown that in the regular case the minimax estimate is defined ex...
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The problem of minimax estimation is considered for the linear multivariate statistically indeterminate observation model with mixed uncertainty. It is shown that in the regular case the minimax estimate is defined explicitly via the solution of the dual optimization problem. For the singular models, the method of dual optimization is developed by means of using the technique of Tikhonov regularization. Several particular cases which are widely used in practice are also examined.
A whole variety of robust analysis and synthesis problems can be formulated as robust Semi-Definite Programs (SDPs), i.e. SDPs with data matrices that are functions of an uncertain parameter which is only known to be ...
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A whole variety of robust analysis and synthesis problems can be formulated as robust Semi-Definite Programs (SDPs), i.e. SDPs with data matrices that are functions of an uncertain parameter which is only known to be contained in some set. We consider uncertainty sets described by general polynomial semi-definite constraints, which allows to represent norm-bounded and structured uncertainties as encountered in μ-analysis, polytopes and various other possibly non-convex compact uncertainty sets. As the main novel result we present a family of Linear Matrix Inequalities (LMI) relaxations based on sum-of-squares (sos) decompositions of polynomial matrices whose optimal values converge to the optimal value of the robust SDP. The number of variables and constraints in the LMI relaxations grow only quadratically in the dimension of the underlying data matrices. We demonstrate the benefit of this a priori complexity bound by an example and apply the method in order to asses the stability of a fourth order LPV model of the longitudinal dynamics of a helicopter.
An output feedback constrained MPC control scheme for uncertain LFR/Norm-Bounded discrete-time linear systems is discussed. The design procedure consists of an off-line step in which a state-feedback and an asymptotic...
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An output feedback constrained MPC control scheme for uncertain LFR/Norm-Bounded discrete-time linear systems is discussed. The design procedure consists of an off-line step in which a state-feedback and an asymptotic observer (dynamic primal controller) are designed via BMI optimization and used to robustly stabilize a suitably augmented system. The on-line moving horizon procedure adds N free control moves to the action of the primal controller and its computation consists of solving an online LMI optimization problem whose numerical complexity grows up only linearly with the control horizon N. The effectiveness is illustrated by a numerical example.
An active set based algorithm for calculating the coefficients of univariate cubic L-1 splines is developed. It decomposes the original problem in a geometric-programming setting into independent optimization problems...
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An active set based algorithm for calculating the coefficients of univariate cubic L-1 splines is developed. It decomposes the original problem in a geometric-programming setting into independent optimization problems of smaller sizes. This algorithm requires only simple algebraic operations to obtain an exact optimal solution in a finite number of iterations. In stability and computational efficiency, the algorithm outperforms a currently widely used discretization-based primal affine algorithm.
In this paper, we present an algorithm to solve a particular convex model explicitly. The model may massively arise when, for example, Benders decomposition or Lagrangean relaxation-decomposition is applied to solve l...
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In this paper, we present an algorithm to solve a particular convex model explicitly. The model may massively arise when, for example, Benders decomposition or Lagrangean relaxation-decomposition is applied to solve large design problems in facility location and capacity expansion. To attain the optimal solution of the model, we analyze its Karush-Kuhn-Tucker optimality conditions and develop a constructive algorithm that provides the optimal primal and dual solutions. This approach yields better performance than other convex optimization techniques.
The paper is concerned with the basic optimization problem of projecting a point onto the intersection of several ellipsoids. We present a class of methods where the problem is reduced to a sequence of projections ont...
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The paper is concerned with the basic optimization problem of projecting a point onto the intersection of several ellipsoids. We present a class of methods where the problem is reduced to a sequence of projections onto the intersection of several balls. The subproblems are simpler and more tractable, but the main advantage is that, in so doing, we can avoid solving linear systems completely, and thus the methods are very suitable for large scale problems. The methods have been shown to have nice convergence properties under Slater's constraint qualification and to be very reliable and efficient in our testing.
A novel robust predictive control algorithm is presented for uncertain discrete-time input-saturated linear systems described by structured norm-bounded model uncertainties. The solution is based on the minimization, ...
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A novel robust predictive control algorithm is presented for uncertain discrete-time input-saturated linear systems described by structured norm-bounded model uncertainties. The solution is based on the minimization, at each time instant, of a semi-definite convex optimization problem subject to a number of LMI feasibility constraints which grows up only linearly with the control horizon length N. The general case of arbitrary N is considered. Closed-loop stability and feasibility retention over the time are proved and comparisons with robust multi-model (polytopic) MPC algorithms are reported. (C) 2004 Elsevier Ltd. All rights reserved.
We consider nonlinear stochastic optimization problems with probabilistic constraints. The concept of a p-efficient point of a probability distribution is used to derive equivalent problem formulations, and necessary ...
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We consider nonlinear stochastic optimization problems with probabilistic constraints. The concept of a p-efficient point of a probability distribution is used to derive equivalent problem formulations, and necessary and sufficient optimality conditions. We analyze the dual functional and its subdifferential. Two numerical methods are developed based on approximations of the p-efficient frontier. The algorithms yield an optimal solution for problems involving r-concave probability distributions. For arbitrary distributions, the algorithms provide upper and lower bounds for the optimal value and nearly optimal solutions. The operation of the methods is illustrated on a cash matching problem with a probabilistic liquidity constraint.
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