Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: stability and moving-horizon approximations

Stability results are given for a class of feedback systems arising from the regulation of time-varying discrete-time systems using optimal infinite-horizon and moving-horizon feedback laws. The class is characterized by joint constraints on the state and the control, a general nonlinear cost function and nonlinear equations of motion possessing two special properties. It is shown that weak conditions on the cost function and the constraints are sufficient to guarantee uniform asymptotic stability of both the optimal infinite-horizon and movinghorizon feedback systems. The infinite-horizon cost associated with the moving-horizon feedback law approaches the optimal infinite-horizon cost as the moving horizon is extended.

Minimizing total completion time on a batch processing machine with job families

We consider the problem of minimizing the total completion time on a single batch processing machine. The set of jobs to be scheduled can be partitioned into a number of families, where all jobs in the same family have the same processing time. The machine can process at most B jobs simultaneously as a batch, and the processing time of a batch is equal to the processing time of the longest job in the batch. We analyze that properties of an optimal schedule and develop a dynamic programming algorithm of polynomial time complexity when the number of job families is fixed. The research is motivated by the problem of scheduling burn-in ovens in the semiconductor industry

Minimizing total completion time on batch processing machines

We study the problem of minimizing total completion time on single and parallel batch processing machines. A batch processing machine is one which can process up to B jobs simultaneously. The processing time of a batch is equal to the largest processing time among all jobs in the batch. This problem is motivated by burn-in operations in the final testing stage of semiconductor manufacturing and is expected to occur in other production environments. We provide an exact solution procedure for the single-machine problem and heuristic algorithms for both single and parallel machine problems. While the exact algorithms have limited applicability due to high computational requirements, extensive experiments show that the heuristics are capable of consistently obtaining near-optimal solutions in very reasonable CPU times.

Specification of Real-Time Systems

Inspite of numerous research advancements made in recent years in the area of formal techniques, specification of real-time systems is still proving to be a very challenging and difficult problem. In this context, this paper critically examines state-of-the-art specification techniques for real-time systems and analyzes the emerging trends.

Monte-Carlo estimation of time-dependent statistical characteristics of random dynamical systems

The problem of estimating the time-dependent statistical characteristics of a random dynamical system is studied under two different settings. In the first, the system dynamics is governed by a differential equation parameterized by a random parameter, while in the second, this is governed by a differential equation with an underlying parameter sequence characterized by a continuous time Markov chain. We propose, for the first time in the literature, stochastic approximation algorithms for estimating various time-dependent process characteristics of the system. In particular, we provide efficient estimators for quantities such as the mean, variance and distribution of the process at any given time as well as the joint distribution and the autocorrelation coefficient at different times. A novel aspect of our approach is that we assume that information on the parameter model (i.e., its distribution in the first case and transition probabilities of the Markov chain in the second) is not available in either case. This is unlike most other work in the literature that assumes availability of such information. Also, most of the prior work in the literature is geared towards analyzing the steady-state system behavior of the random dynamical system while our focus is on analyzing the time-dependent statistical characteristics which are in general difficult to obtain. We prove the almost sure convergence of our stochastic approximation scheme in each case to the true value of the quantity being estimated. We provide a general class of strongly consistent estimators for the aforementioned statistical quantities with regular sample average estimators being a specific instance of these. We also present an application of the proposed scheme on a widely used model in population biology. Numerical experiments in this framework show that the time-dependent process characteristics as obtained using our algorithm in each case exhibit excellent agreement with exact results. (C) 2010 Elsevier Inc. All rights reserved.

Maintaining dynamic sequences under equality tests in polylogarithmic time

We present a randomized and a deterministic data structure for maintaining a dynamic family of sequences under equality tests of pairs of sequences and creations of new sequences by joining or splitting existing sequences. Both data structures support equality tests in O(1) time. The randomized version supports new sequence creations in O(log(2) n) expected time where n is the length of the sequence created. The deterministic solution supports sequence creations in O(log n (log m log* m + log n)) time for the mth operation.

The actor-critic algorithm as multi-time-scale stochastic approximation

The actor-critic algorithm of Barto and others for simulation-based optimization of Markov decision processes is cast as a two time Scale stochastic approximation. Convergence analysis, approximation issues and an example are studied.

Conflict-Tolerant Real-Time Specifications in Metric Temporal Logic

A framework based on the notion of "conflict-tolerance" was proposed in as a compositional methodology for developing and reasoning about systems that comprise multiple independent controllers. A central notion in this framework is that of a "conflict-tolerant" specification for a controller. In this work we propose a way of defining conflict-tolerant real-time specifications in Metric Interval Temporal Logic (MITL). We call our logic CT-MITL for Conflict-Tolerant MITL. We then give a clock optimal "delay-then-extend" construction for building a timed transition system for monitoring past-MITL formulas. We show how this monitoring transition system can be used to solve the associated verification and synthesis problems for CT-MITL.

Dynamic path profile aided recompilation in a JAVA just-in-time compiler

Just-in-Time (JIT) compilers for Java can be augmented by making use of runtime profile information to produce better quality code and hence achieve higher performance. In a JIT compilation environment, the profile information obtained can be readily exploited in the same run to aid recompilation and optimization of frequently executed (hot) methods. This paper discusses a low overhead path profiling scheme for dynamically profiling AT produced native code. The profile information is used in recompilation during a subsequent invocation of the hot method. During recompilation tree regions along the hot paths are enlarged and instruction scheduling at the superblock level is performed. We have used the open source LaTTe AT compiler framework for our implementation. Our results on a SPARC platform for SPEC JVM98 benchmarks indicate that (i) there is a significant reduction in the number of tree regions along the hot paths, and (ii) profile aided recompilation in LaTTe achieves performance comparable to that of adaptive LaTTe in spite of retranslation and profiling overheads.

Finding a Box Representation for a Graph in $O(n^2\Delta^2\ln n)$ time

An axis-parallel box in $b$-dimensional space is a Cartesian product $R_1 \times R_2 \times \cdots \times R_b$ where $R_i$ (for $1 \leq i \leq b$) is a closed interval of the form $[a_i, b_i]$ on the real line. For a graph $G$, its boxicity is the minimum dimension $b$, such that $G$ is representable as the intersection graph of (axis-parallel) boxes in $b$-dimensional space. The concept of boxicity finds application in various areas of research like ecology, operation research etc. Chandran, Francis and Sivadasan gave an $O(\Delta n^2 \ln^2 n)$ randomized algorithm to construct a box representation for any graph $G$ on $n$ vertices in $\lceil (\Delta + 2)\ln n \rceil$ dimensions, where $\Delta$ is the maximum degree of the graph. They also came up with a deterministic algorithm that runs in $O(n^4 \Delta )$ time. Here, we present an $O(n^2 \Delta^2 \ln n)$ deterministic algorithm that constructs the box representation for any graph in $\lceil (\Delta + 2)\ln n \rceil$ dimensions.

Time Series Classification for Online Tamil Handwritten Character Recognition – A Kernel Based Approach

In this paper, we consider the problem of time series classification. Using piecewise linear interpolation various novel kernels are obtained which can be used with Support vector machines for designing classifiers capable of deciding the class of a given time series. The approach is general and is applicable in many scenarios. We apply the method to the task of Online Tamil handwritten character recognition with promising results.

Space-Time Scales of Northward Propagation of Convection during Boreal Summer

This study uses precipitation estimates from the Tropical Rainfall Measuring Mission to quantify the spatial and temporal scales of northward propagation of convection over the Indian monsoon region during boreal summer. Propagating modes of convective systems in the intraseasonal time scales such as the Madden-Julian oscillation can interact with the intertropical convergence zone and bring active and break spells of the Indian summer monsoon. Wavelet analysis was used to quantify the spatial extent (scale) and center of these propagating convective bands, as well as the time period associated with different spatial scales. Results presented here suggest that during a good monsoon year the spatial scale of this oscillation is about 30 degrees centered around 10 degrees N. During weak monsoon years, the scale of propagation decreases and the center shifts farther south closer to the equator. A strong linear relationship is obtained between the center/scale of convective wave bands and intensity of monsoon precipitation over Indian land on the interannual time scale. Moreover, the spatial scale and its center during the break monsoon were found to be similar to an overall weak monsoon year. Based on this analysis, a new index is proposed to quantify the spatial scales associated with propagating convective bands. This automated wavelet-based technique developed here can be used to study meridional propagation of convection in a large volume of datasets from observations and model simulations. The information so obtained can be related to the interannual and intraseasonal variation of Indian monsoon precipitation.

Combination of similarity measures for time series classification using genetic algorithms

Time series classification deals with the problem of classification of data that is multivariate in nature. This means that one or more of the attributes is in the form of a sequence. The notion of similarity or distance, used in time series data, is significant and affects the accuracy, time, and space complexity of the classification algorithm. There exist numerous similarity measures for time series data, but each of them has its own disadvantages. Instead of relying upon a single similarity measure, our aim is to find the near optimal solution to the classification problem by combining different similarity measures. In this work, we use genetic algorithms to combine the similarity measures so as to get the best performance. The weightage given to different similarity measures evolves over a number of generations so as to get the best combination. We test our approach on a number of benchmark time series datasets and present promising results.