Optimal control of a stochastic hybrid system with discounted cost

We address the optimal control problem of a very general stochastic hybrid system with both autonomous and impulsive jumps. The planning horizon is infinite and we use the discounted-cost criterion for performance evaluation. Under certain assumptions, we show the existence of an optimal control. We then derive the quasivariational inequalities satisfied by the value function and establish well-posedness. Finally, we prove the usual verification theorem of dynamic programming.

Shape optimization of RC flexural members

A natural velocity field method for shape optimization of reinforced concrete (RC) flexural members has been demonstrated. The possibility of shape optimization by modifying the shape of an initially rectangular section, in addition to variation of breadth and depth along the length, has been explored. Necessary shape changes have been computed using the sequential quadratic programming (SQP) technique. Genetic algorithm (Goldberg and Samtani 1986) has been used to optimize the diameter and number of main reinforcement bars. A limit-state design approach has been adopted for the nonprismatic RC sections. Such relevant issues as formulation of optimization problem, finite-element modeling, and solution procedure have been described. Three design examples-a simply supported beam, a cantilever beam, and a two-span continuous beam, all under uniformly distributed loads-have been optimized. The results show a significant savings (40-56%) in material and cost and also result in aesthetically pleasing structures. This procedure will lead to considerable cost saving, particularly in cases of mass-produced precast members and a heavy cast-in-place member such as a bridge girder.

A fixed-grid finite element based enthalpy formulation for generalized phase change problems: role of superficial mushy region

The enthalpy method is primarily developed for studying phase change in a multicomponent material, characterized by a continuous liquid volume fraction (phi(1)) vs temperature (T) relationship. Using the Galerkin finite element method we obtain solutions to the enthalpy formulation for phase change in 1D slabs of pure material, by assuming a superficial phase change region (linear (phi(1) vs T) around the discontinuity at the melting point. Errors between the computed and analytical solutions are evaluated for the fluxes at, and positions of, the freezing front, for different widths of the superficial phase change region and spatial discretizations with linear and quadratic basis functions. For Stefan number (St) varying between 0.1 and 10 the method is relatively insensitive to spatial discretization and widths of the superficial phase change region. Greater sensitivity is observed at St = 0.01, where the variation in the enthalpy is large. In general the width of the superficial phase change region should span at least 2-3 Gauss quadrature points for the enthalpy to be computed accurately. The method is applied to study conventional melting of slabs of frozen brine and ice. Regardless of the forms for the phi(1) vs T relationships, the thawing times were found to scale as the square of the slab thickness. The ability of the method to efficiently capture multiple thawing fronts which may originate at any spatial location within the sample, is illustrated with the microwave thawing of slabs and 2D cylinders. (C) 2002 Elsevier Science Ltd. All rights reserved.

Band Structures of Bilayer Graphene Superlattices

We formulate a low energy effective Hamiltonian to study superlattices in bilayer graphene (BLG) using a minimal model which supports quadratic band touching points. We show that a one dimensional (1D) periodic modulation of the chemical potential or the electric field perpendicular to the layers leads to the generation of zero-energy anisotropic massless Dirac fermions and finite energy Dirac points with tunable velocities. The electric field superlattice maps onto a coupled chain model comprised of ``topological'' edge modes. 2D superlattice modulations are shown to lead to gaps on the mini-Brillouin zone boundary but do not, for certain symmetries, gap out the quadratic band touching point. Such potential variations, induced by impurities and rippling in biased BLG, could lead to subgap modes which are argued to be relevant to understanding transport measurements.

Viscoelastic phenomenology based structure assignment for closed-loop vibration control of a beam with sensors and actuators

In this paper we incorporate a novel approach to synthesize a class of closed-loop feedback control, based on the variational structure assignment. Properties of a viscoelastic system are used to design an active feedback controller for an undamped structural system with distributed sensor, actuator and controller. Wave dispersion properties of onedimensional beam system have been studied. Efficiency of the chosen viscoelastic model in enhancing damping and stability properties of one-dimensional viscoelastic bar have been analyzed. The variational structure is projected on a solution space of a closed-loop system involving a weakly damped structure with distributed sensor and actuator with controller. These assign the phenomenology based internal strain rate damping parameter of a viscoelastic system to the usual elastic structure but with active control. In the formulation a model of cantilever beam with non-collocated actuator and sensor has been considered. The formulation leads to the matrix identification problem of two dynamic stiffness matrices. The method has been simplified to obtain control system gains for the free vibration control of a cantilever beam system with collocated actuator-sensor, using quadratic optimal control and pole-placement methods.

Fast edge splitting and Edmonds' arborescence construction for unweighted graphs

Given an unweighted undirected or directed graph with n vertices, m edges and edge connectivity c, we present a new deterministic algorithm for edge splitting. Our algorithm splits-off any specified subset S of vertices satisfying standard conditions (even degree for the undirected case and in-degree ≥ out-degree for the directed case) while maintaining connectivity c for vertices outside S in Õ(m+nc2) time for an undirected graph and Õ(mc) time for a directed graph. This improves the current best deterministic time bounds due to Gabow [8], who splits-off a single vertex in Õ(nc2+m) time for an undirected graph and Õ(mc) time for a directed graph. Further, for appropriate ranges of n, c, |S| it improves the current best randomized bounds due to Benczúr and Karger [2], who split-off a single vertex in an undirected graph in Õ(n2) Monte Carlo time. We give two applications of our edge splitting algorithms. Our first application is a sub-quadratic (in n) algorithm to construct Edmonds' arborescences. A classical result of Edmonds [5] shows that an unweighted directed graph with c edge-disjoint paths from any particular vertex r to every other vertex has exactly c edge-disjoint arborescences rooted at r. For a c edge connected unweighted undirected graph, the same theorem holds on the digraph obtained by replacing each undirected edge by two directed edges, one in each direction. The current fastest construction of these arborescences by Gabow [7] takes Õ(n2c2) time. Our algorithm takes Õ(nc3+m) time for the undirected case and Õ(nc4+mc) time for the directed case. The second application of our splitting algorithm is a new Steiner edge connectivity algorithm for undirected graphs which matches the best known bound of Õ(nc2 + m) time due to Bhalgat et al [3]. Finally, our algorithm can also be viewed as an alternative proof for existential edge splitting theorems due to Lovász [9] and Mader [11].

Volume Change behaviour in Calcitic Soil influenced with Sulphuric Acid using Artificial Neural Networks

This paper elucidates the methodology of applying artificial neural network model (ANNM) to predict the percent swell of calcitic soil in sulphuric acid solutions, a complex phenomenon involving many parameters. Swell data required for modelling is experimentally obtained using conventional oedometer tests under nominal surcharge. The phases in ANN include optimal design of architecture, operation and training of architecture. The designed optimal neural model (3-5-1) is a fully connected three layer feed forward network with symmetric sigmoid activation function and trained by the back propagation algorithm to minimize a quadratic error criterion.The used model requires parameters such as duration of interaction, calcite mineral content and acid concentration for prediction of swell. The observed strong correlation coefficient (R2 = 0.9979) between the values determined by the experiment and predicted using the developed model demonstrates that the network can provide answers to complex problems in geotechnical engineering.

Linear stability, transient growth and the role of viscosity stratification in compressible Couette flow

Linear stability and the nonmodal transient energy growth in compressible plane Couette flow are investigated for two prototype mean flows: (a) the uniform shear flow with constant viscosity, and (b) the nonuniform shear flow with stratified viscosity. Both mean flows are linearly unstable for a range of supersonic Mach numbers (M). For a given M, the critical Reynolds number (Re) is significantly smaller for the uniform shear flow than its nonuniform shear counterpart; for a given Re, the dominant instability (over all streamwise wave numbers, α) of each mean flow belongs to different modes for a range of supersonic M. An analysis of perturbation energy reveals that the instability is primarily caused by an excess transfer of energy from mean flow to perturbations. It is shown that the energy transfer from mean flow occurs close to the moving top wall for “mode I” instability, whereas it occurs in the bulk of the flow domain for “mode II.” For the nonmodal transient growth analysis, it is shown that the maximum temporal amplification of perturbation energy, Gmax, and the corresponding time scale are significantly larger for the uniform shear case compared to those for its nonuniform counterpart. For α=0, the linear stability operator can be partitioned into L∼L̅ +Re2 Lp, and the Re-dependent operator Lp is shown to have a negligibly small contribution to perturbation energy which is responsible for the validity of the well-known quadratic-scaling law in uniform shear flow: G(t∕Re)∼Re2. In contrast, the dominance of Lp is responsible for the invalidity of this scaling law in nonuniform shear flow. An inviscid reduced model, based on Ellingsen-Palm-type solution, has been shown to capture all salient features of transient energy growth of full viscous problem. For both modal and nonmodal instability, it is shown that the viscosity stratification of the underlying mean flow would lead to a delayed transition in compressible Couette flow.

Maximum Margin Classifiers with Specified False Positive and False Negative Error Rates

This paper addresses the problem of maximum margin classification given the moments of class conditional densities and the false positive and false negative error rates. Using Chebyshev inequalities, the problem can be posed as a second order cone programming problem. The dual of the formulation leads to a geometric optimization problem, that of computing the distance between two ellipsoids, which is solved by an iterative algorithm. The formulation is extended to non-linear classifiers using kernel methods. The resultant classifiers are applied to the case of classification of unbalanced datasets with asymmetric costs for misclassification. Experimental results on benchmark datasets show the efficacy of the proposed method.

Multiclass Core Vector Machine

Even though several techniques have been proposed in the literature for achieving multiclass classification using Support Vector Machine(SVM), the scalability aspect of these approaches to handle large data sets still needs much of exploration. Core Vector Machine(CVM) is a technique for scaling up a two class SVM to handle large data sets. In this paper we propose a Multiclass Core Vector Machine(MCVM). Here we formulate the multiclass SVM problem as a Quadratic Programming(QP) problem defining an SVM with vector valued output. This QP problem is then solved using the CVM technique to achieve scalability to handle large data sets. Experiments done with several large synthetic and real world data sets show that the proposed MCVM technique gives good generalization performance as that of SVM at a much lesser computational expense. Further, it is observed that MCVM scales well with the size of the data set.

A Combinatorial Family of Near Regular LDPC Codes

An elementary combinatorial Tanner graph construction for a family of near-regular low density parity check (LDPC) codes achieving high girth is presented. These codes are near regular in the sense that the degree of a left/right vertex is allowed to differ by at most one from the average. The construction yields in quadratic time complexity an asymptotic code family with provable lower bounds on the rate and the girth for a given choice of block length and average degree. The construction gives flexibility in the choice of design parameters of the code like rate, girth and average degree. Performance simulations of iterative decoding algorithm for the AWGN channel on codes designed using the method demonstrate that these codes perform better than regular PEG codes and MacKay codes of similar length for all values of Signal to noise ratio.

Executable Analysis using Abstract Interpretation with Circular Linear Progressions

We propose a new abstract domain for static analysis of executable code. Concrete states are abstracted using circular linear progressions (CLPs). CLPs model computations using a finite word length as is seen in any real life processor. The finite abstraction allows handling overflow scenarios in a natural and straight-forward manner. Abstract transfer functions have been defined for a wide range of operations which makes this domain easily applicable for analyzing code for a wide range of ISAs. CLPs combine the scalability of interval domains with the discreteness of linear congruence domains. We also present a novel, lightweight method to track linear equality relations between static objects that is used by the analysis to improve precision. The analysis is efficient, the total space and time overhead being quadratic in the number of static objects being tracked.

Rough Core Vector Clustering

Support Vector Clustering has gained reasonable attention from the researchers in exploratory data analysis due to firm theoretical foundation in statistical learning theory. Hard Partitioning of the data set achieved by support vector clustering may not be acceptable in real world scenarios. Rough Support Vector Clustering is an extension of Support Vector Clustering to attain a soft partitioning of the data set. But the Quadratic Programming Problem involved in Rough Support Vector Clustering makes it computationally expensive to handle large datasets. In this paper, we propose Rough Core Vector Clustering algorithm which is a computationally efficient realization of Rough Support Vector Clustering. Here Rough Support Vector Clustering problem is formulated using an approximate Minimum Enclosing Ball problem and is solved using an approximate Minimum Enclosing Ball finding algorithm. Experiments done with several Large Multi class datasets such as Forest cover type, and other Multi class datasets taken from LIBSVM page shows that the proposed strategy is efficient, finds meaningful soft cluster abstractions which provide a superior generalization performance than the SVM classifier.

Localization induced base isolation in fractionally damped non linear system

In the present article we take up the study of nonlinear localization induced base isolation of a 3 degree of freedom system having cubic nonlinearities under sinusoidal base excitation. The damping forces in the system are described by functions of fractional derivative of the instantaneous displacements, typically linear and quadratic damping are considered here separately. Under the assumption of smallness of certain system parameters and nonlinear terms an approximate estimate of the response at each degree of freedom of the system is obtained by the Method of Multiple Scales approach. We then consider a similar system where the nonlinear terms and certain other parameters are no longer small. Direct numerical simulation is made use of to obtain the amplitude plot in the frequency domain for this case, which helps us to establish the efficacy of this method of base isolation for a broad class of systems. Base isolation obtained this way has no counterpart in the linear theory.

An algebraic formulation of exact force-, moment-isotropy in spatial parallel manipulators

In this paper, we present an algebraic method to study and design spatial parallel manipulators that demonstrate isotropy in the force and moment distributions.We use the force and moment transformation matrices separately,and derive conditions for their isotropy individually as well as in combination. The isotropy conditions are derived in closed-form in terms of the invariants of the quadratic forms associated with these matrices. The formulation has been applied to a class of Stewart platform manipulators. We obtain multi-parameter families of isotropic manipulator analytically. In addition to computing the isotropic configurations of an existing manipulator,we demonstrate a procedure for designing the manipulator for isotropy at a given configuration.