Computation of the constrained infinite time linear quadratic regulator

This paper presents an efficient algorithm for computing the solution to the constrained infinite-time, linear quadratic regulator (CLQR) problem for discrete time systems. The algorithm combines multi-parametric quadratic programming with reachability analysis to obtain the optimal piecewise affine (PWA) feedback law. The algorithm reduces the time necessary to compute the PWA solution for the CLQR when compared to other approaches. It also determines the minimal finite horizon , such that the constrained finite horizon LQR problem equals the CLQR problem for a compact set of states . The on-line computational effort for the implementation of the CLQR can be significantly reduced as well, either by evaluating the PWA solution or by solving the finite dimensional quadratic program associated with the CLQR for a horizon of .     

Modeling of electromagnetic fields in rectangular waveguides by coupled finite–infinite elements

The paper describes the 3D infinite element for modeling of stationary harmonic electromagnetic fields in waveguides. The proposed approximation is a straightforward modification of the analogous approach developed for analysis of scattering problems in unbounded 2D and 3D domains [Comp. Meth. Appl. Mech. Engrg. 188 (2000) 625; Int. J. Num. Meth. Engrg. 57 (2003) 899]. Exponential shape functions in the longitudinal direction are used similarly as in [Comp. Meth. Appl. Mech. Engrg. 140 (1997) 221]. However, arbitrary order of approximation in the tangential direction may be selected due to compatibility with the hp-adaptive edge FE element discretization for Maxwell’s equations in bounded domains reported in [Comp. Meth. Appl. Mech. Engrg. 152 (1998) 103; Int. J. Num. Meth. Engrg. 53 (2002) 147; Comp. Meth. Appl. Mech. Engrg. 169 (1999) 331].     

Analysis of stub-girders using substructuring

This paper deals with the application of the method of substructures to calculate deflections in stub-girders. A stub-girder is a new type of composite beam recently introduced in the United States. It consists of a steel beam and a reinforced concrete slab separated by a series of short steel rolled sections called stubs. The openings between the adjacent stubs are used as service ducts.Since most of the panels of a stub-girder are identical in shape and size, the method of substructures, which requires the physical partitioning of the structure into smaller units, is particularly suitable for its analysis. For the analysis presented herein a substructure, i.e. a smaller unit of the stub-girder, was discretized into an assemblage of plane stress rectangular finite elements. The two dimensional analysis was chosen because a preliminary investigation indicated that the matrix storage requirements for a 3-D analysis were so large that the amount of storage and the cost of the analysis would be prohibitive for most practical cases.The method of analysis is illustrated by application to three stub-girders. The computed results were compared with those determined experimentally. Two different idealizations were used to replace the flanges. The computed deflection values for one of the idealizations showed acceptable agreement with the experimental results. The computer program developed for this investigation can also be used to calculate the deflection in a beam with a series of rectangular openings.     

An efficient method for optimal structural design by substructuring

An optimal structural design technique incorporating the concept of substructuring in its formulation is presented. The method is developed using functional analysis techniques and the state space formulation of the optimal design problem. Design sensitivity analysis for the problem is discussed and an integrated computational algorithm for optimal design is presented. As an application of the method, optimal design of general trusses is presented. Numerical results for two standard truss structures of 25 and 200 members are obtained, using substructuring, and are compared with results obtained without substructuring. It is shown that the algorithm with substructuring is up to 66% more efficient.     

Optimal design of frames with substructuring

This paper presents a formulation for optimal design of large scale, two and three dimensional framed structures. Von Mises equivalent stress constraints and displacement constraints are imposed at all points in the structure. Member size constraints and constraints based on Schilling's approach for member buckling are also imposed. Three example problems of varying degrees of difficulty are solved, using a gradient projection algorithm with state space design sensitivity analysis and substructuring. Results of these examples are analyzed and conclusions are presented.     

Computation of finite and infinite zeros of linear multivariable systems: a state space approach

An iterative algorithm, developed by the authors to compute the finite zeros of a linear multivariable system (Sebakhy et al. 1983), is extended to compute the infinite zeros of the system as well. The method is simple, efficient and suitable for programming on a digital computer     

Generation of quadratic potential force fields from flow fields for distributed manipulation

Distributed manipulation systems induce motions on objects through the application of many external forces. Many of these systems are abstracted as planar programmable force fields. Quadratic potential fields form a class of such fields that lend themselves to analytical study and exhibit useful stability properties. This paper introduces a new methodology to build quadratic potential fields with simple devices using the naturally existing phenomena of airflow, which is an improvement to the traditional use of the complicated programmable actuator arrays. It also provides a basis for the exploitation, in distributed manipulation, of natural phenomena like airflow, which require rigorous analysis and display stability difficulties. A demonstration and verification of the theoretical results for the special case of the elliptic field with airflows is also presented.     

Optimal design of wing structures with substructuring

An iterative method for optimal design of large scale structures that incorporates the concept of substructuring is extensively applied to wing-type structures to demonstrate its generality, effectiveness and efficiency. Optimum designs for several wing-type structures are obtained and compared with results available in the literature. It is shown that considerable efficiencies can be achieved by integration of the substructuring concept into a structural optimization algorithm.     

Computation by Time

Over the last years, the amount of research performed in the field of spiking neural networks has been growing steadily. Spiking neurons are modeled to approximate the complex dynamic behavior of biological neurons. They communicate via discrete impulses called spikes with the actual information being encoded in the timing of these spikes. As already pointed out by Maass in his paper on the third generation of neural network models, this renders time a central factor for neural computation. In this paper, we investigate at different levels of granularity how absolute time and relative timing enable new ways of biologically inspired neural information processing. At the lowest level of single spiking neurons, we give an overview of coding schemes and learning techniques which rely on precisely timed neural spikes. A high-level perspective is provided in the second part of the paper which focuses on the role of time at the network level. The third aspect of time considered in this work is related to the interfacing of neural networks with real-time systems. In this context, we discuss how the concepts of computation by time can be implemented in computer simulations and on specialized neuromorphic hardware. The contributions of this paper are twofold: first, we show how the exact modeling of time in spiking neural networks serves as an important basis for powerful computation based on neurobiological principles. Second, by presenting a range of diverse learning techniques, we prove the biologically plausible applicability of spiking neural networks to real world problems like pattern recognition and path planning.     

Iterative solvers by substructuring for the p-version finite element method

We study a class of substructuring methods well-suited for iterative solution of large systems of linear equations arising from the p-version finite element method. The p-version offers a natural decomposition with every element treated as a substructure. We use the preconditioned conjugate gradient method with preconditioning constructed by a decomposition of the local function space on each element. We develop an elementary theory giving bounds on the condition numbers which do not depend on the number of elements if a sparse system with only few variables per element is solved in each iteration. This bound can be evaluated considering one element at a time and we compute such condition numbers numerically for various elements.     

Constrained motion control using vector potential fields

Discusses the generation of a control signal that would instruct the actuators of a robotics manipulator to drive motion along a safe and well-behaved path to a desired target. The proposed concept of navigation control along with the tools necessary for its construction achieve this goal. The most significant tool is the artificial vector potential field which shows a better ability to steer motion than does a scalar potential field. The synthesis procedure emphasizes flexibility so that the effort needed to modify the control is commensurate with the change in the geometry of the workspace. Theoretical development along with simulation results are provided     

Computation of localized flow for steady and unsteady vector fields and its applications

We present, extend, and apply a method to extract the contribution of a sub-region of a data set to the global flow. To isolate this contribution, we decompose the flow in the subregion into a potential flow that is induced by the original flow on the boundary and a localized flow. The localized flow is obtained by subtracting the potential flow from the original flow. Since the potential flow is free of both divergence and rotation, the localized flow retains the original features and captures the region-specific flow that contains the local contribution of the considered subdomain to the global flow. In the remainder of the paper, we describe an implementation on unstructured grids in both two and three dimensions for steady and unsteady flow fields. We discuss the application of some widely used feature extraction methods on the localized flow and describe applications like reverse-flow detection using the potential flow. Finally, we show that our algorithm is robust and scalable by applying it to various flow data sets and giving performance figures.     

Face-based selection of corners in 3D substructuring

In most recent substructuring methods, a fundamental role is played by the coarse space. For some of these methods (e.g. BDDC and FETI-DP), its definition relies on a ‘minimal’ set of coarse nodes (sometimes called corners) which assures invertibility of local subdomain problems and also of the global coarse problem. This basic set is typically enhanced by enforcing continuity of functions at some generalized degrees of freedom, such as average values on edges or faces of subdomains. We revisit existing algorithms for selection of corners. The main contribution of this paper consists of proposing a new heuristic algorithm for this purpose. Considering faces as the basic building blocks of the interface, inherent parallelism, and better robustness with respect to disconnected subdomains are among features of the new technique. The advantages of the presented algorithm in comparison to some earlier approaches are demonstrated on three engineering problems of structural analysis solved by the BDDC method.     

Recursive identification of modal participation in substructuring applications

The utility of modal models in substructuring applications is well known. A recursive scheme for identifying the contributions of subsystem modes to the coupled system is presented. The modal contributions are characterised by evaluating an index based on the difference in the frequency response functions (FRFs), at arbitrarily selected frequencies of interest, between the coupled system containing all available modes and a series of coupled systems with reduced modes. It is shown that the contribution of the subsystem modes can be quantified by eliminating one mode at a time, performing coupling, and evaluating the FRFs at the frequencies of interest.     

Computation of molecular electrostatic potential: An efficient algorithm and parallelization

An efficient algorithm fortified by the use of rigorous inequalities has been developed for the computation of molecular electrostatic potential maps. The algorithm has further been parallelized to obtain high computation speeds. This algorithm was tested on some hydrocarbons, azide and nitrate ions, using STO-3G and 4-31G basis-sets. The parallel version of the algorithm implemented on a 32-node machine (Parsytec) is found to give a considerable CPU time factor ranging from 60 to 200 over the HP 9050 AM series machine. The results are found to be accurate up to 6 decimal digits.     

Drawing graphs with nonuniform nodes using potential fields

Graphs with nonuniform nodes arise naturally in many real-world applications. Although graph drawing has been a very active research in the computer science community during the past decade, most of the graph drawing algorithms developed thus far have been designed for graphs whose nodes are represented as single points. As a result, it is of importance to develop drawing methods for graphs whose nodes are of different sizes and shapes, in order to meet the need of real-world applications. To this end, a potential field approach, coupled with an idea commonly found in force-directed methods, is proposed in this paper for drawing graphs with nonuniform nodes in 2-D and 3-D. In our framework, nonuniform nodes are uniformly charged, while edges are modelled by springs. Using certain techniques developed in the field of potential-based path planning, we are able to find analytically tractable procedures for computing the repulsive force and torque of a node in the potential field induced by the remaining nodes. The crucial feature of our approach is that the rotation of every nonuniform node and the multiple edges between two nonuniform nodes are taken into account. In comparison with the existing algorithms found in the literature, our experimental results suggest this new approach to be promising, as drawings of good quality for a variety of moderate-sized graphs in 2-D and 3-D can be produced reasonably efficiently. That is, our approach is suitable for moderate-sized interactive graphs or larger-sized static graphs. Furthermore, to illustrate the usefulness of our new drawing method for graphs with zero-sized nodes, we give an application to the visualization of hierarchical clustered graphs, for which our method offers a very efficient solution.     

基于二重势函数法的集群航路规划

人工势场法由于其在构型组织能力上的不足,影响了该方法在集群航路规划上的应用,为此提出基于二重势函数法的集群航路规划法,通过第一重势能场形成集群到目标的可行路径,通过第二重势能场形成构型,从而实现集群航路规划.此外,针对人工势场法存在无谓避碰、陷阱问题等不足,通过引入碰撞危险度来确定障碍物影响距离以及虚拟障碍物,提出改进...     

Distributed control of multi-robot systems using bifurcating potential fields

The distributed control of multi-robot systems has been shown to have advantages over that of conventional single-robot systems. These include scalability, flexibility and robustness to failures. This paper considers pattern formation and reconfigurability in a multi-robot system using a new control algorithm developed through bifurcating potential fields. It is shown how various patterns can be achieved autonomously through a simple free parameter change, with the stability of the system proven to ensure that desired behaviours always occur.