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In this paper we consider some extensions of the Linear Complementarity Problem, which is one of the fundamental problems in mathematical programming. More specifically we consider the Linear Dynamic Complementarity Problem (LDCP), the Generalized Linear Complementarity Problem (GLCP) and the Extended Linear Complementarity Problem (ELCP). In this note we show that the LDCP is a special case of the ELCP and the GLCP. 相似文献
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In this paper, a method for modelling electromechanical systems (EMS) with variable structure in the electrical subsystem is proposed. This structural variability may result from real switches (e.g. relay) or from components with switching characteristics (e.g. diode in first approximation). The aim of the work is to provide a method to model EMS with variable structure in both domains using a unified mathematical theory. For this purpose, the usage of the linear complementarity problem (LCP) for modelling electrical systems containing components with switching characteristics is shown. Starting point of the complete approach is a method for modelling EMS based on the Lagrange formalism. A unified mathematical theory is used to represent such systems taking into account all interactions between the physically heterogeneous substructures. Applying the LCP, it is possible to include switching components into this theory and, this way, to extend the class of EMS which can be captured. 相似文献
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Nowadays the theory of multi-body systems including unilateral constraints is quite well established. However, the tendency
towards more and more detailed and complex models may not be compensated with increasing computer power. In fact the growing
computational effort demands for improved numerical methods in order to solve large systems. In this paper a time-stepping
method is proposed for the computation of multi-body systems with many unilateral constraints. Stability and accuracy are
discussed with respect to the given discretisation. In order to handle many contacts an iterative algorithm is applied based
on a Gauss-Seidel relaxation scheme. A numerical example shows the efficiency of the relaxation scheme in comparison with
Lemke's method and an Augmented Lagrangian approach. 相似文献
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We consider discrete mechanical systems subject to perfect unilateral constraints. Moreau's impact law uses the decomposition of the velocity on the normaland tangent cones to the set of admissible positions at the impact point, and it iswell-known that this gives the only possible rule in the case of a singleperfect unilateral constraint. In the multi-constraint case, there areother possible energetically and geometrically consistant impact laws. Weshow here that in a number of cases, the limiting behavior of impact asits rigidity tends to infinity is given by Moreau's rule, i.e., in a more mathematical language, we justify this impact law by a penalty approach.First we describe the penalty method, then we apply it to amulti-constraint model problem. We choose an overdamped approximationand we obtain Moreau's rule for inelastic shocks in the limit. Finally,we present the computational drawbacks of the penalty method. 相似文献
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讨论周期时变线性系统的一般线性二次型最优控制问题, 即状态方程为非齐次方程且二次型性能指标包含线性项的一般情况. 给出了该问题可解的一系列充分必要条件, 同时给出了最优控制的解析构造以及最优性能指标值. 相似文献
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S. L. Kryvyi 《Cybernetics and Systems Analysis》2002,38(1):17-29
Criteria of compatibility of a system of linear Diophantine equations, strict inequations, and nonstrict inequations are considered. Upper bounds for components of a minimal set of solutions and algorithms of construction of minimal generating sets of solutions for all types of systems are given. These criteria and the corresponding algorithms for constructing a minimal supporting set of solutions can be used in solving all the considered types of systems and systems of mixed types. 相似文献
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对参数摄动系统的互联结构阵及其线性分式变换给出了可在统一框架下进行处理的 结构可用于控制系统的鲁棒性能分析。 相似文献
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In this paper, adaptive linear quadratic regulator (LQR) is proposed for continuous-time systems with uncertain dynamics. The dynamic state-feedback controller uses input-output data along the system trajectory to continuously adapt and converge to the optimal controller. The result differs from previous results in that the adaptive optimal controller is designed without the knowledge of the system dynamics and an initial stabilizing policy. Further, the controller is updated continuously using input-output data, as opposed to the commonly used switched/intermittent updates which can potentially lead to stability issues. An online state derivative estimator facilitates the design of a model-free controller. Gradient-based update laws are developed for online estimation of the optimal gain. Uniform exponential stability of the closed-loop system is established using the Lyapunov-based analysis, and a simulation example is provided to validate the theoretical contribution. 相似文献
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The problem of inconsistency between constraints often arises in practice as the result, among others, of the complexity of real models or due to unrealistic requirements and preferences. To overcome such inconsistency two major actions may be taken: removal of constraints or changes in the coefficients of the model. This last approach, that can be generically described as model correction is the problem we address in this paper in the context of linear constraints over the reals. The correction of the right hand side alone, which is very close to a fuzzy constraints approach, was one of the first proposals to deal with inconsistency, as it may be mapped into a linear problem. The correction of both the matrix of coefficients and the right hand side introduces non linearity in the constraints. The degree of difficulty in solving the problem of the optimal correction depends on the objective function, whose purpose is to measure the closeness between the original and corrected model. Contrary to other norms, that provide corrections with quite rigid patterns, the optimization of the important Frobenius norm was still an open problem. We have analyzed the problem using the KKT conditions and derived necessary and sufficient conditions which enabled us to unequivocally characterize local optima, in terms of the solution of the Total Least Squares and the set of active constraints. These conditions justify a set of pruning rules, which proved, in preliminary experimental results, quite successful in a tree search procedure for determining the global minimizer. 相似文献
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Tong Zhang 《Machine Learning》2002,46(1-3):91-129
In this paper, we study a general formulation of linear prediction algorithms including a number of known methods as special cases. We describe a convex duality for this class of methods and propose numerical algorithms to solve the derived dual learning problem. We show that the dual formulation is closely related to online learning algorithms. Furthermore, by using this duality, we show that new learning methods can be obtained. Numerical examples will be given to illustrate various aspects of the newly proposed algorithms. 相似文献
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本文把分段线性函数引入到求解延时系统的最优控制中,推得延时线性系统二次型最优控制问题的分段控制解答及其状态轨线估计,算例结果表明,该算法比方块脉冲函数算法具有更高的计算精度。 相似文献
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本文研究线性时变离散系统的稳定性,采用一种解的估计技巧,简化了[1]用Gauss-Seidel迭代法建立的稳定性判据的证明,并获得一些新的代数判据。 相似文献
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In this paper, a new iterative learning control based on the double differential of the error is proposed for the linear time varying system having relative degree greater than one. The convergence criterion of the proposed method is proved. Furthermore, it is shown by simulations that convergence of error can be increased considerably by using our proposed controller as compared to the iterative learning controller using error or single differential of the error for the modification of the control input without increasing the learning gain. 相似文献