A probabilistic algorithm for global optimization

In this paper the authors validate the Wiener process as a suitable stochastic model of the global behaviour of a functionf (x), x∈XCR ¹. An algorithm is given, which exploits the properties of the model, for an effective approximation of the global minimum off (x).     

Wiener system modelling by exponentially weighted aggregation

In the paper the aggregation algorithm for Wiener system modelling is proposed. The method uses exponential weights to combine (aggregate) models from a given collection of D _λ linear dynamic and D _m nonlinear static models of the genuine system blocks (that can be a priori hypotheses, other system identification outcomes, etc.). The resulting model has a noteworthy property: it is almost as accurate as the best hypothetical Wiener model built from a given collection. This is caused by the fact that the error introduced by the aggregation routine decreases (in the mean squared sense) with growing number of measurements N as fast as CqN ^?1ln?(D _m D _λ ), where C and q are known constants. Simulations confirm theoretical findings and demonstrate applicability of the algorithm in engineering problems for small and moderate measurement data-sets.     

Controller reduction via stable factorization and balancing

A controller reduction procedure based on a representation of a controller as a matrix function defined using stable proper transfer functions and employing a balancing technique is studied in this paper. For a certain right coprime factorization of an LQG designed controller K(s) = N(s)D^-1(s), we approximate using a balancing technique the pair [D(s), N(s)]^T by a low-order pair [D₁(s), N₁(s)]^T defining a factorization of the reduced-order controller K ₁(s) = N₁(s)D₁ ^-1(s). We show that reducing the controller order in this way is motivated in a natural way, which leads to the expectation of both good stability properties and good accuracy of approximation of closed-loop behaviour. This is also demonstrated in some examples.     

A robust model for finding optimal evolutionary trees

Constructing evolutionary trees for species sets is a fundamental problem in computational biology. One of the standard models assumes the ability to compute distances between every pair of species, and seeks to find an edge-weighted treeT in which the distanced _ij ^T in the tree between the leaves ofT corresponding to the speciesi andj exactly equals the observed distance,d _ij . When such a tree exists, this is expressed in the biological literature by saying that the distance function or matrix isadditive, and trees can be constructed from additive distance matrices in0(n ²) time. Real distance data is hardly ever additive, and we therefore need ways of modeling the problem of finding the best-fit tree as an optimization problem.In this paper we present several natural and realistic ways of modeling the inaccuracies in the distance data. In one model we assume that we have upper and lower bounds for the distances between pairs of species and try to find an additive distance matrix between these bounds. In a second model we are given a partial matrix and asked to find if we can fill in the unspecified entries in order to make the entire matrix additive. For both of these models we also consider a more restrictive problem of finding a matrix that fits a tree which is not only additive but alsoultrametric. Ultrametric matrices correspond to trees which can be rooted so that the distance from the root to any leaf is the same. Ultrametric matrices are desirable in biology since the edge weights then indicate evolutionary time. We give polynomial-time algorithms for some of the problems while showing others to be NP-complete. We also consider various ways of fitting a given distance matrix (or a pair of upper- and lower-bound matrices) to a tree in order to minimize various criteria of error in the fit. For most criteria this optimization problem turns out to be NP-hard, while we do get polynomial-time algorithms for some.Supported by DIMACS under NSF Contract STC-88-09648.Supported by NSF Grant CCR-9108969.This work was begun while this author was visiting DIMACS in July and August 1992, and was supported in part by the U.S. Department of Energy under Contract DE-AC04-76DP00789.     

Reachability Analysis of Synchronized PA Systems

We present a generic approach for the analysis of concurrent programs with (unbounded) dynamic creation of threads and recursive procedure calls. We define a model for such programs based on a set of term rewrite rules where terms represent control configurations. The reachability problem for this model is undecidable. Therefore, we propose a method for analyzing such models based on computing abstractions of their sets of computation paths. Our approach allows to compute such abstractions as least solutions of a system of (path language) constraints. More precisely, given a program and two regular sets of configurations (process terms) T and T^′, we provide (1) a construction of a system of constraints which characterizes the set of computation paths leading from T to T^′, and (2) a generic framework, based on abstract interpretation, allowing to solve this system in various abstract domains leading to abstract analysis with different precision and cost.     

On a simplified untiming procedure for supervisory control of timed automata when the time increases strictly monotonically

Given a timed automaton G accepting the timed language L ^T a finite state machine G′ can be constructed, known as the region automaton, which accepts the untimed language Untime (L ^T). In this paper we construct an alternative finite state machine which also accepts the language Untime (L ^T), but has fewer states than G′. This is shown for languages of both finite and infinite traces given that the time values in the time sequence increase strictly monotonically. The supervisory control design for timed automata, when the simplified untiming procedure is used and the time is strictly positive, is studied.     

Isotropic color gradient for simulating very high-density ratios with a two-phase flow lattice Boltzmann model

This study presents the integration of isotropic color gradient discretization into a lattice Boltzmann Rothman–Keller (RK) model designed for two-phase flow simulation. The proposed model removes one limitation of the RK model, which concerns the handling of O(1000) large density ratios between the fluids for a wide range of parameters. Taylor’s series expansions are used to characterize the difference between an isotropic gradient discretization and the commonly used anisotropic gradient. The proposed color gradient discretization can reduce, by one order of magnitude, the spurious current problem that affects the interface between the phases. A set of numerical tests is conducted to show that a rotationally invariant discretization enables widening of the parameter range for the surface tension. Surface tensions from O(10⁻²) to O(10⁻⁸), depending on the density ratio, are accurately simulated. An extreme density ratio of O(10,000) is successfully tested for a steady bubble with an error of 0.5% for Laplace’s law across a sharp interface, with a thickness of about 5–6 lattice units.     

The hierarchical control of ST-finite-state machines

This paper follows (Caines and Wei, 1995) where a new notion of state aggregation for finite machines was introduced via the concept of the dynamical consistency (DC) relation between the blocks of states in any given state-space partition Π. This formulation results in a definition of high-level dynamics on the finite (partition) machine whose states correspond to the given partition elements. This paper treats the more general case of ST-systems where there is a preferred sense of flow from a set of source states (S) to a set of target states (T) which is to be achieved by hierarchical control. A generalisation of the theory of Caines and Wei to ST-systems is given which includes the generalisation of the notions of dynamical consistency in block controllability and hierarchical feedback control on the associated hierarchical lattices.     

High‐order internal model‐based iterative learning control design for nonlinear distributed parameter systems

This article deals with the problem of iterative learning control algorithm for a class of nonlinear parabolic distributed parameter systems (DPSs) with iteration‐varying desired trajectories. Here, the variation of the desired trajectories in the iteration domain is described by a high‐order internal model. According to the characteristics of the systems, the high‐order internal model‐based P‐type learning algorithm is constructed for such nonlinear DPSs, and furthermore, the corresponding convergence theorem of the presented algorithm is established. It is shown that the output trajectory can converge to the desired trajectory in the sense of (L²,λ) ‐norm along the iteration axis within arbitrarily small error. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.     

Dynamical Properties of Timed Automata

Timed automata are an important model for specifying and analyzing real-time systems. The main analysis performed on timed automata is the reachability analysis. In this paper we show that the standard approach for performing reachability analysis is not correct when the clocks drift even by a very small amount. Our formulation of the reachability problem for timed automata is as follows: we define the set R ^*(T,Z ₀)=_>0 Reach(T, Z ₀ where T is obtained from timed automaton T by allowing an drift in the clocks. R ^*(T,Z ₀) is the set of states which can be reached in the timed automatonT from the initial states in Z₀ when the clocks drift by an infinitesimally small amount. We present an algorithm for computing R ^*(T,Z ₀)and provide a proof of its correctness. We show that R ^*(T,Z ₀)is robust with respect to various types of modeling errors. To prove the correctness of our algorithm, we need to understand the dynamics of timed automata—in particular, the structure of the limit cycles of timed automata.     

QFT template generation for time-delay plants based on zero-inclusion test

Plant template generation is the key step in applying quantitative feedback theory (QFT) to design robust control for uncertain systems. In this paper we propose a technique for generating plant templates for a class of linear systems with an uncertain time delay and affine parameter perturbations in coefficients. The main contribution lies in presenting a necessary and sufficient condition for the zero inclusion of the value set f(T,Q)={f(τ,q): τT[τ⁻,τ⁺], qQ∏_k=0^m−1[q_k⁻,q_k⁺]}, where f(τ,q)=g(q)+h(q)e^−jτω*, g(q) and h(q) are both complex-valued affine functions of the m-dimensional real vector q, and ω^* is a fixed frequency. Based on this condition, an efficient algorithm which involves, in the worst case, evaluation of m algebraic inequalities and solution of m2^m−1 one-variable quadratic equations, is developed for testing the zero inclusion of the value set f(T,Q). This zero-inclusion test algorithm allows one to utilize a pivoting procedure to generate the outer boundary of a plant template with a prescribed accuracy or resolution. The proposed template generation technique has a linear computational complexity in resolution and is, therefore, more efficient than the parameter gridding and interval methods. A numerical example illustrating the proposed technique and its computational superiority over the interval method is included.     

Multidimensional visualisation for process historical data analysis: a comparative study with multivariate statistical process control

This paper describes a comparative study of a multidimensional visualisation technique and multivariate statistical process control (MSPC) for process historical data analysis. The visualisation technique uses parallel coordinates which visualise multidimensional data using two dimensional presentations and allow identification of clusters and outliers, therefore, can be used to detect abnormal events. The study is based on a database covering 527 days of operation of an industrial wastewater treatment plant. It was found that both the visualisation technique and MSPC based on T² chart captured the same 17 days as “clearly abnormal” and another eight days as “likely abnormal”. Pattern recognition using K-means clustering was also applied to the same data in literature and was found to have identified 14 out of the 17 “clearly abnormal” days.     

An empirical approach to retrieving monthly evapotranspiration over Amazonia

The extent of evapotranspiration (E _T) over the Brazilian Amazon rainforest remains uncertain because in situ measurement sites do not cover the entire domain, and the fetch of these sites is only of the order of 10³ m. In this investigation we developed an empirical method to estimate E _T over the Brazilian Legal Amazon (BLA). The work was based on an improved physical understanding of what controls E _T over the Amazonia rainforest resulting from analyses of recent in situ observations. Satellite data used in this study include the Enhanced Vegetation Index (EVI) from the Moderate Resolution Imaging Spectroradiometer (MODIS) and the surface radiation budget from the International Satellite Cloud Climatology Project (ISCCP). The empirical model was validated by measurements performed at four upland forest sites. The observed values and the calculated modelled values at these sites had the same mean and variance. On a seasonal scale, regional modelled E _T peaks during the austral spring (September to November), as reported in the literature. In addition, the empirical model allows us to estimate the regional seasonal and interannual distributions of E _T/precipitation rates.     

Correction to ‘A note on the discrete Lyapunov and Riccati matrix equations’

In Tran and Sawan (1984), we derived a lower bound for the determinant of the discrete algebraic Riccati equation where A, B, P, Q are n x n matrices, Q = Q ^T > 0 and Rank (B) = n. We assumed that BB ^T>Q and the matrix A is stable. The purpose of this note is to include an additional assumption about the above equation in order for the result of Theorem 1 given in Tran and Sawan (1984) to be valid. Without the additional assumption, this theorem would be invalid as has been pointed out by Kwon and Youn (1985). The additional assumption is given below with the same notation as in Tran and Sawan (1984).     

Index of critical points in rational l-approximation

This article is concerned with the l²-approximation of a given transfer function f by a rational one whose order is prescribed. We show that the sum of the indices of the critical points of the criterion is generically equal to 1, and in particular does not depend on f.     

Time-Limited Time-Invariant Wiener Filtering

For the estimation of a signal observed with additive white noise, it is shown that the optimum linear least-squares filter constrained to have its impulse response time-limited to the interval [0,T] satisfies a truncated version of the Wiener-Hopf equation. To solve this equation the covariance for the observed process need only be known for time lags less than T. There is a unique extension of the covariance for lags greater than T, for which the time-limited filter is the optimum Wiener filter; furthermore this same extension is that extension of the covariance for which the optimum Wiener filter gives maximum mean square error, i.e., given limited covariance information we have found the “worst possible” extension of the known information. Parallels are drawn with discrete-time maximum-entropy spectral analysis.     

Robust camera pose and scene structure analysis for service robotics

Successful path planning and object manipulation in service robotics applications rely both on a good estimation of the robot’s position and orientation (pose) in the environment, as well as on a reliable understanding of the visualized scene. In this paper a robust real-time camera pose and a scene structure estimation system is proposed. First, the pose of the camera is estimated through the analysis of the so-called tracks. The tracks include key features from the imaged scene and geometric constraints which are used to solve the pose estimation problem. Second, based on the calculated pose of the camera, i.e. robot, the scene is analyzed via a robust depth segmentation and object classification approach. In order to reliably segment the object’s depth, a feedback control technique at an image processing level has been used with the purpose of improving the robustness of the robotic vision system with respect to external influences, such as cluttered scenes and variable illumination conditions. The control strategy detailed in this paper is based on the traditional open-loop mathematical model of the depth estimation process. In order to control a robotic system, the obtained visual information is classified into objects of interest and obstacles. The proposed scene analysis architecture is evaluated through experimental results within a robotic collision avoidance system.