Some Properties for the Euclidean Distance Matrix and Positive Semidefinite Matrix Completion Problems

The Euclidean distance matrix (EDM) completion problem and the positive semidefinite (PSD) matrix completion problem are considered in this paper. Approaches to determine the location of a point in a linear manifold are studied, which are based on a referential coordinate set and a distance vector whose components indicate the distances from the point to other points in the set. For a given referential coordinate set and a corresponding distance vector, sufficient and necessary conditions are presented for the existence of such a point that the distance vector can be realized. The location of the point (if it exists) given by the approaches in a linear manifold is independent of the coordinate system, and is only related to the referential coordinate set and the corresponding distance vector. An interesting phenomenon about the complexity of the EDM completion problem is described. Some properties about the uniqueness and the rigidity of the conformation for solutions to the EDM and PSD completion problems are presented.     

Application of a Near-Optimal Reinforcement Learning Controller to a Robotics Problem in Manufacturing: A Hybrid Approach

Optimization theory provides a framework for determining the best decisions or actions with respect to some mathematical model of a process. This paper focuses on learning to act in a near-optimal manner through reinforcement learning for problems that either have no model or the model is too complex. One approach to solving this class of problems is via approximate dynamic programming. The application of these methods are established primarily for the case of discrete state and action spaces. In this paper we develop efficient methods of learning which act in complex systems with continuous state and action spaces. Monte-Carlo approaches are employed to estimate function values in an iterative, incremental procedure. Derivative-free line search methods are used to obtain a near-optimal action in the continuous action space for a discrete subset of the state space. This near-optimal control policy is then extended to the entire continuous state space via a fuzzy additive model. To compensate for approximation errors, a modified procedure for perturbing the generated control policy is developed. Convergence results under moderate assumptions and stopping criteria are established.     

Robust Output Tracking Control of an Uncertain Linear System via a Modified Optimal Linear-Quadratic Method

This study investigates the robust output tracking problem for a class of uncertain linear systems. The uncertainties are assumed to be time invariant and to satisfy the matching conditions. According to the selected nominal parameters, an optimal solution with a prescribed degree of stability is determined. Then, an auxiliary input via the use of an adapting factor, connected to the nominal optimal control, is introduced to guarantee the robustness and prescribed degree of stability for the output tracking control of the uncertain linear systems. This method is very simple and effective and can reject bounded uncertainties imposed on the states. A maglev vehicle model example is given to show its effectiveness.     

The Topology of Algebra: Combinatorics of Squaring

We study the graph each of whose edges connects an element of a given ring with the square of itself. For a finite commutative group (e.g., for the multiplicative group of coprime residue classes modulo a positive integer), we describe this graph explicitly: each of its connected components is an oriented attracting cycle equipped with identical -vertex rooted trees of special form whose roots reside on the cycle. We also compute the graphs of permutation groups on not too many elements and of the subgroups of even permutations; the connected components of these graphs are also uniformly equipped cycles.     

Constrained Minimum-Time-Oriented Feedback Control for the Stabilization of Nonholonomic Systems in Chained Form

In this paper, a discontinuous state-feedback law is proposed for the stabilization of nonholonomic systems in power form. The feedback law is based on a receding-horizon strategy in which the open-loop optimization problem is a minimum-time steering process. Suboptimal formulations are used explicitly to meet the real-time implementability requirements. Stability is established in a sampled-data context and illustrative simulations are given to show the effectiveness and the real-time implementability of the proposed scheme.     

The additive multiboxes

We introduce the new notion of additive “multibox” for linear logic proof-nets. Thanks to this notion, we define a cut-elimination procedure which associates with every proof-net of multiplicative and additive linear logic a unique cut-free one.     

Stability analysis of impulsive control systems

This paper studies impulsive control systems. Several stability criteria are established by employing the method of Lyapunov functions. These criteria may be used for impulsive feedback control design. As an application, impulsive control of the Lorenz chaotic system is discussed. Numerical experiments are carried out for the control of the Lorenz system. It is shown that small and frequent impulses need to be used in order to stabilize the Lorenz system.     

Existence of Optimal Controls for Semilinear Parabolic Equations without Cesari-Type Conditions

   Abstract. Optimal control problems governed by semilinear parabolic partial differential equations are considered. No Cesari-type conditions are assumed. By proving the existence theorem and the Pontryagin maximum principle of optimal ``state-control" pairs for the corresponding relaxed problems, an existence theorem of optimal pairs for the original problem is established.     

矩阵方程AXB=D的最小二乘Hermite解及其加权最佳逼近

本中,我们讨论了矩阵方程AXB=D的最小二乘Hermite解,通过运用广义奇异值分解(GSVD)，获得了解的通式。此外,对于给定矩阵F，也得到了它的加权最佳逼近表达式。     

AT&T准则下完全检验的最优设计(英文)

本文研究了完全检验的质量控制问题,将广泛用于X-控制图的AT＆amp;T准则应用于完全检验,并根据完全检验的特点,提出一种新的最优模型,数值实验结果表明AT＆amp;T准则下的完全检验优于传统的完全检验。