Constrained stabilization problems for linear plants

Linear systems with magnitude and rate constraints on both the state and control variables are considered. For such systems, semi-global and global constrained stabilization problems are formulated when state feedback controllers are used. Necessary and sufficient conditions for the solvability of the formulated problems are developed. Moreover, design methodologies for such constrained stabilization problems are presented. An important aspect of our development here is a taxonomy of constraints to show clearly for what type of constraints what can or cannot be achieved.     

Constrained stabilization problems for discrete‐time linear plants

In this paper we study discrete‐time linear systems with full or partial constraints on both input and state. It is shown that the solvability conditions of stabilization problems are closely related to important concepts, such as the right‐invertibility of the constraints, the location of constraint invariant zeros and the order of constraint infinite zeros. The main results show that for right‐invertible constraints the order of constrained infinite zeros cannot be greater than one in order to achieve global or semi‐global stabilization. This is in contrast to the continuous‐time case. Controllers for both state feedback and measurement feedback are constructed in detail. Issues regarding non‐right invertible constraints are discussed as well. Copyright © 2004 John Wiley & Sons, Ltd.     

应用Delaunay图的拓扑控制

无线传感器网络拓扑控制的主要任务是减少节点的能量消耗,从而延长整个网络的生存时间。而无线传感器网络的能量消耗主要集中在无线通信模块上,因此,通过降低无线通信模块的能量消耗和控制邻居节点集,减少通信链路,把通信限制在重要链路中,可以减少节点的能量消耗。基于以上因素,将MG模型与Delaunay图结合,在Delaunay图中限制通信链路并保留最优能耗路,得到MEDel算法。该算法具有强连通性、对称性和平均度有界的优点。     

Simultaneous stabilization of linear single-input/single-output plants

The problem of designing a single compensator that simultaneously stabilizes several distinct plants is considered here using the fractional representation approach owing to Saeks and Murray (1982, 1983). Necessary and sufficient conditions for the existence of such a compensator are given and a design algorithm is proposed.     

New graph decompositions with applications to emulations

In this paper we present a new type of graph decomposition calleda cut-cover that combines the notions of graph separators andt-neighborhood covers. We show that graphs with good cut-covers can be emulated in hypercubes and we show that planar and certain minor-excluded graphs have good cut-covers. In particular, we show how to emulate anyN-node bounded degree planar graph or anyN-node bounded degree graph that excludes $K_{log^{0(1)} N} $ as a minor with constant slowdown on hypercube networks.     

New graph decompositions with applications to emulations

In this paper we present a new type of graph decomposition calleda cut-cover that combines the notions of graph separators andt-neighborhood covers. We show that graphs with good cut-covers can be emulated in hypercubes and we show that planar and certain minor-excluded graphs have good cut-covers. In particular, we show how to emulate anyN-node bounded degree planar graph or anyN-node bounded degree graph that excludes as a minor with constant slowdown on hypercube networks. The research of C. Kaklamanis and D. Krizanc was supported in part by the NEC Research Institute.     

Reliable stabilization of linear plants using a two-controller configuration

A reliable controller design method is developed for linear, time-invariant, multi-input multi-output control systems; two controllers are designed to stabilize the closed-loop system when acting together and acting independently if one fails. All reliable controllers which achieve closed-loop stability are characterized for strongly stabilizable plants using a factorization approach.     

Exponential stabilization for nonlinear systems with applications to nonholonomic systems

The paper proposes a general framework to study the exponential stabilization problem for a wide class of nonlinear systems. By combining the concept of dilation with the method of σ-processing, a simple stability criterion is given in terms of the stability property of an augmented system. Moreover, the global ρ-exponential stability of the closed-loop system can be achieved by employing continuous controllers. A well-known nonholonomic system is given to illustrate the effectiveness of the proposed results.     

Stable linear fractional transformations with applications to stabilization and multistage H∞ control design

Stable linear fractional transformations (SLFTs) resulting from a 2 × 2-block unit Z in the ring of stable real rational proper matrices are considered in this paper. Several general properties are obtained, including properties with respect to possible pole-zero cancellations and a generic McMillan degree relationship between a transfer matrix and its image under an SLFT. The problem of representing a plant as an SLFT of another plant such that the order of the original plant is exactly equal to the sums of the orders of the SLFT and of the new plant is solved. All such representations can be found by searching for all matching pairs of stable invariant subspaces associated with the plant. In relation to applications of SLFTs, it is shown that if two plants are related by an SLFT, then a one-to-one correspondence between their two respective sets of all stabilizing controllers can be established via a different SLFT. Also, it is shown how to decompose a standard H^∞ control problem by means of SLFT into two individual H^∞ subproblems, the first involving a nominal plant model and the second involving a certain frequency-shaped approximation error. An example is presented to illustrate the idea of decomposing the complexity of an H^∞ control problem.     

Simultaneous stabilization of linear dynamic plants by the variable-structure controller

Consideration was given to the design of a unique controller with state feedback stabilizing the finite family of linear dynamic plants of identical orders. It was proposed to use for that the variable-structure controllers giving rise to sliding modes in the closed-loop systems. Constructive existence conditions for a universal variable-structure stabilizer of the given finite family of dynamic plants were formulated.     

不完备数据的鲁棒多视角图学习及其聚类应用

现有多视角图学习方法主要建立在数据具有较好完备性的前提假设下,没有充分地考虑由于特征缺失引起的不完备数据的学习问题.针对此问题,提出一种不完备数据的多视角图学习方法.一方面,从局部视角内将数据重建和图学习放入同一框架,通过不完备数据补偿,实现从重建数据中学习视角专属的近邻关系,弥补特征缺失对数据分布的影响.另一方面,为了保持近邻图的二维结构,引入张量分析,从全局角度构造基于多视角的融合图学习约束,捕获缺失数据下视角间图结构的高阶潜在关联性.框架交替的优化数据重建、视角专属图学习和融合张量图结构学习,使其在迭代中相互促进,有效提高模型对不完备多视角数据的学习能力.将所提出的方法应用于两类不完备数据的多视角聚类实验,其结果表明所提出方法在多项性能指标和鲁棒性方面均优于当前主流的多视角聚类方法.     

Dynamic topology learning with the probabilistic self-organizing graph

Self-organizing neural networks are usually focused on prototype learning, while the topology is held fixed during the learning process. Here a method to adapt the topology of the network so that it reflects the internal structure of the input distribution is proposed. This leads to a self-organizing graph, where each unit is a mixture component of a mixture of Gaussians (MoG). The corresponding update equations are derived from the stochastic approximation framework. This approach combines the advantages of probabilistic mixtures with those of self-organization. Experimental results are presented to show the self-organization ability of our proposal and its performance when used with multivariate datasets in classification and image segmentation tasks.     

Fuzzy control stabilization with applications to motorcycle control

This study develops fuzzy control that is designed with sliding modes to achieve stability of the fuzzy controller. Fuzzy control is formulated in the form of variable structure system (VSS) control. In contrast to previous works in which Lyapunov functions are used to examine the stability, the current study investigates the stability of fuzzy control from the viewpoints of differential geometric methods and the sliding mode theory. Best values for parameters in fuzzy control rules are determined with the aid of sliding modes. In order to improve control performance, a tuning algorithm is executed to adjust parameters for dealing with uncertainties and disturbances. Both computer simulations and experiments with regard to an inverted pendulum hinged to a rotating disk are carried out to validate the proposed method. This apparatus can to some extent represent cornering motion of a motorcycle on which a rider leans to maintain stability. Effects of rider's leaning angle on both stability and handling control are examined according to Bode plots.     

Strong, simultaneous, and reliable stabilization offinite-dimensional linear time-varying plants

Some issues related to the stabilization of linear, time-varying (LTV) plants are studied. The authors consider the class of finite-dimensional LTV plants that are internally stabilizable by output feedback, and show that every plant in the class can be stabilized by a stable LTV controller; moreover, they give a parameterization of all nonlinear time-varying controllers that stabilize a given LTV plant. Using these results, they show that every finite collection of LTV plants can be simultaneously stabilized by a stable LTV. Finally, the authors prove that every LTV plant can always be stabilized by a pair of simultaneously acting LTV controllers, each reliable against a failure of the other     

A fast technique for comparing graph representations with applications to performance evaluation

Finding efficient, effective ways to compare graphs arising from recognition processes with their corresponding ground-truth graphs is an important step toward more rigorous performance evaluation.In this paper, we examine in detail the graph probing paradigm we first put forth in the context of our work on table understanding and later extended to HTML-coded Web pages. We present a formalism showing that graph probing provides a lower bound on the true edit distance between two graphs. From an empirical standpoint, the results of two simulation studies and an experiment using scanned pages show that graph probing correlates well with the latter measure. Moreover, our technique is very fast; graphs with tens or hundreds of thousands of vertices can be compared in mere seconds. Ease of implementation, scalability, and speed of execution make graph probing an attractive alternative for graph comparison.Received: 1 October 2002, Accepted: 15 January 2003, Published online: 6 February 2004Correspondence to: D. Lopresti     

Lexicographic perturbation for multiparametric linear programming with applications to control

Optimal control problems for constrained linear systems with a linear cost can be posed as multiparametric linear programs (mpLPs) with a parameter in the cost, or equivalently the right-hand side of the constraints, and solved explicitly offline. Degeneracy occurs when the control input, or optimiser, is non-unique, which can cause chattering of the control input and overlap of the polyhedral regions of the explicit solution. This paper introduces a new and efficient approach to the computation of the solution to a degenerate mpLP with the parameter in the cost. Rather than solve the degenerate problem directly, we solve a lexicographically (symbolically) perturbed version of it that is guaranteed to be non-degenerate. We show that every optimal solution of the perturbed problem is an optimal solution to the original and that the perturbed solution is continuous, unique and defined over a set of non-overlapping polyhedral regions. Furthermore, we introduce a new method for computing the optimal solution in an adjacent region, which is very efficient in all cases and reduces to a single simplex pivot for non-degenerate regions. The proposed algorithm is particularly suited for the calculation of the explicit solution to a class of constrained optimal control problems, since it ensures that the control input is everywhere continuous and unique, thereby removing the danger of chattering in problems with linear costs. The algorithm is compared through example to existing proposals and a significant complexity improvement is demonstrated.     

Semi-global stabilization and output regulation of constrained linear plants via measurement feedback

Semi-global stabilization and output regulation of linear systems subject to state and/or input constraints have been studied in our earlier work by using state feedback. For the same problems, observer based measurement feedback control designs are the topics of this paper. High-gain observers are used in the feedback design in order to obtain accurate estimates of the state so that the constraint violation can be avoided. Due to the peaking phenomenon associated with a high-gain observer, a special saturation protection is built in the control laws to avoid possible constraint violation. The results in this paper show that the semi-global stabilization and semi-global output regulation problems for constrained linear systems are solvable via measurement feedback under solvability conditions similar to those in the state feedback.     

Some applications of topology to program semantics

The relationship between programs and the set of partial correctness assertions that they satisfy, constitutes a Galois connection. The topology resulting from this Galois connection is closely related to the Lindenbaum baum topology for the language in which these partial correctness assertions are stated. This relationship provides us with a tool for understanding the incompleteness of Hoare Logics and for answering certain natural questions about the connection between the relational semantics and the partial correctness assertion semantics for programs, especially in connection with the question of modularity of programs. Two questions to which we shall find topological answers in this paper are “When is a language expressive for a program?”, and “When can we have rules of inference which are adequate to infer the properties of the complex program ±#β from those of its components ±,β?” We also obtain a natural answer to the question “What can the set{(A, B)|{A}±{B} is true) look like for arbitraryα?”.     

Dynamic average consensus with topology balancing under a directed graph

In this paper, the distributed average tracking problem is studied on the premise of a strongly connected directed graph. To this end, we propose a weight balance strategy that could potentially make the adjacency matrix doubly stochastic for any strongly connected directed graph. The proposed scheme is fully distributive with finite time convergence and we again prove that network connectivity (described by the first left eigenvector) is instrumental in networked control systems. Then, a discrete‐time average tracking observer is introduced to ensure that all networked systems can track the average of the reference signals with bounded error. Simulation results verify the effectiveness of the proposed methods.