Decomposition Of State Space Research Articles

NAVIGATION AMONG MOVABLE OBSTACLES: REAL-TIME REASONING IN COMPLEX ENVIRONMENTS

In this paper, we address the problem of Navigation Among Movable Obstacles (NAMO): a practical extension to navigation for humanoids and other dexterous mobile robots. The robot is permitted to reconfigure the environment by moving obstacles and clearing free space for a path. This paper presents a resolution complete planner for a subclass of NAMO problems. Our planner takes advantage of the navigational structure through state-space decomposition and heuristic search. The planning complexity is reduced to the difficulty of the specific navigation task, rather than the dimensionality of the multi-object domain. We demonstrate real-time results for spaces that contain large numbers of movable obstacles. We also present a practical framework for single-agent search that can be used in algorithmic reasoning about this domain.

Foldamer dynamics expressed via Markov state models. II. State space decomposition

The structural landscape of poly-phenylacetylene (pPA), otherwise known as m-phenylene ethynylene oligomers, has been shown to consist of a very diverse set of conformations, including helices, turns, and knots. Defining a state space decomposition to classify these conformations into easily identifiable states is an important step in understanding the dynamics in relation to Markov state models. We define the state decomposition of pPA oligomers in terms of the sequence of discretized dihedral angles between adjacent phenyl rings along the oligomer backbone. Furthermore, we derive in mathematical detail an approach to further reduce the number of states by grouping symmetrically equivalent states into a single parent state. A more challenging problem requires a formal definition for knotted states in the structural landscape. Assuming that the oligomer chain can only cross the ideal helix path once, we propose a technique to define a knotted state derived from a helical state determined by the position along the helical nucleus where the chain crosses the ideal helix path. Several examples of helical states and knotted states from the pPA 12-mer illustrate the principles outlined in this article.

THE DECOMPOSITION OF STATE SPACE FOR MARKOV CHAIN IN RANDOM ENVIRONMENT

This paper is a continuation of [8] and [9]. The author obtains the decomposition of state space X of an Markov chain in random environment by making use of the results in [8] and [9], gives three examples, random walk in random environment, renewal process in random environment and queue process in random environment, and obtains the decompositions of the state spaces of these three special examples.

Clustering Based Approximation Procedure for Semi-Markov Decision Processes with Incomplete State Information

It is well-known that in practice it is rather difficult to calculate the minimal value function and optimal policies for decision processes with countable state space. Thus in general, approximation procedures are investigated. In this paper we show how the concepts and use of clustering techniques for large data sets, by adequate grouping of objects, can be useful in decision making processes. Using a linear-time clustering algorithm for the state space decomposition, we introduce an approximation procedure for a numerical solution of a finite horizon incomplete state-information semi-Markov decision processes with countable state space, finite action and signal spaces. We introduce the concept of admissibility for the decomposition of the state space, and for the new semi-Markov decision processes obtained, we calculate the minimal value functions and the optimal policies by dynamic programming. Finally, the convergence theorems are also proved.

Hydrological response to earthquakes in the Haibara well, central Japan - I. Groundwater level changes revealed using state space decomposition of atmospheric pressure, rainfall and tidal responses

SUMMARY For the groundwater level observed at the Haibara well, Shizuoka Prefecture, central Japan, time series analysis using state-space modelling is applied to extract hydrological anomalies related to earthquakes. This method can decompose observed groundwater level time series into five components: atmospheric pressure, tidal, and precipitation responses, observation noise, and residual water level. The decomposed responses to atmospheric pressure and precipitation are independently determined and are consistent with the expected response to surface loading. In the groundwater level at the Haibara well, 28 coseismic changes can be discerned during the period from 1981 April to 1997 December. There is a threshold in the relationship between earthquake magnitude and the well–hypocentre distance, above which earthquakes cause coseismic changes in the residual water level. All of the coseismic water level changes at the Haibara well are decreases, although 33 per cent of the estimated coseismic volumetric strain steps are contraction, which would be expected to cause water level increases. The coseismic changes in groundwater level are more closely proportional to the estimated ground motion than to coseismic volumetric strain steps, suggesting that ground motion due to earthquakes is the major cause of the coseismic water level drops and that the contribution from static strain is rather small. Possible pre- or inter–earthquake water level changes have occurred at the Haibara well and may have been caused by local aseismic crustal deformation.

Identification of complex nonlinear processes based on fuzzy decomposition of the steady state space

Abstract A methodology for identification and control of complex nonlinear plants using multi-model approach is presented in this paper. The proposed methodology is based on fuzzy decomposition of the steady state map. It is shown that such a decomposition strategy facilitates the design of input perturbation signals and helps in identifying linear or simple nonlinear models for each local region. A composition strategy to aggregate the local model predictions is proposed and shown to give excellent cross validation as well as to facilitate smooth switching between the local models. A novel control scheme that is based on the multi model strategy is proposed. The practicality of the identification and control scheme presented here is demonstrated by application to the continuous fermenter of Henson and Seborg (M.A. Henson, D.E. Seborg, Nonlinear control strategies for continuous fermenter, in: Proceedings of 1990 American Control Conference, San Diego, 1990), which exhibits severe nonlinearities and gain directionality changes.

Sliding mode control for two-time scale systems: stability issues

The paper presents some results on global exponential stability of linear time invariant systems with different time scales. The full system is decomposed in two reduced ones by means of singular perturbations and a smooth approximation of a Variable Structure Control is synthesized for each of them using Reaching Law approach. The global closed loop stability is then proved for the whole system using Lyapunov methods and a particular state space decomposition. Moreover a literal form for ε ∗ (a parameter which measures the minimum separation between time scales) is derived.

Low-Frequency Movements in Stock Prices: A State-Space Decomposition

Previous analyses have concluded that expectations of future excess stock returns rather than future real dividend growth or real interest rates are responsible for most of the volatility in stock prices. In this paper, we employ a state-space model to model the dynamics of the log price-dividend ratio along with long-term and short-term interest rates, real dividend growth, and inflation. The advantage of the state-space approach is that we can parsimoniously model the low-frequency movements present in the data. We find that, if one allows permanent changes, even though very small, in real dividend growth, real interest rates, and inflation-but not excess stock returns-then expectations of real dividend growth and real interest rates become significant contributors to fluctuations in stock prices. However, we also show that stock price decompositions are very sensitive to assumptions about which unobserved market fundamentals have a permanent component. When we allow excess stock returns to have a perma...

Distributed predicate detection in series-parallel systems

This paper addresses the problems of state space decomposition and predicate detection in a distributed computation involving asynchronous messages. We introduce a natural communication dependency which leads to the definition of the communication graph. This abstraction proves to be a useful tool to decompose the state lattice of a distributed computation into simpler structures, known as concurrent intervals. Efficient algorithms have been proposed in the literature to detect special classes of predicates, such as conjunctive predicates and bounded sum predicates. We show that more general classes of predicates can be detected when proper constraints are imposed on the underlying computations. In particular, we introduce a class of predicates, defined as separable predicates, that properly includes the above-mentioned classes. We show that separable predicates can be efficiently detected on distributed computations whose communication graphs satisfy the series-parallel constraint.

A new importance sampling Monte Carlo method for a flow network reliability problem

AbstractThe exact evaluation of the probability that the maximum st‐flow is greater than or equal to a fixed demand in a stochastic flow network is an NP‐hard problem. This limitation leads one to consider Monte Carlo alternatives. In this paper, we propose a new importance sampling Monte Carlo method. It is based on a recursive use of the state space decomposition methodology of Doulliez and Jamoulle during the simulation process. We show theoretically that the resulting estimator belongs to the variance‐reduction family and we give an upper bound on its variance. As shown by experimental tests, the new sampling principle offers, in many cases, substantial speedups with respect to a previous importance sampling based on the same decomposition procedure and its best performances are obtained when highly reliable networks are analyzed. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 204–228, 2002; DOI 10.1002/nav.10004

Loss behavior in space priority queue with batch Markovian arrival process — discrete-time case

This paper applies matrix-analytic approach to the examination of the loss behavior of a space priority queue. In addition to the evaluation of the long-term high-priority and low-priority packet loss probabilities, we examine the bursty nature of packet losses by means of conditional statistics with respect to critical and non-critical periods that occur in an alternating manner. The critical period corresponds to having more than a certain number of packets in the buffer; non-critical corresponds to the opposite. Hence there is a threshold buffer level that splits the state space into two. By such a state-space decomposition, two hypothesized Markov chains are devised to describe the alternating renewal process. The distributions of various absorbing times in the two hypothesized Markov chains are derived to compute the average durations of the two periods and the conditional high-priority packet loss probability encountered during a critical period. These performance measures greatly assist the space priority mechanism for determining a proper threshold. The overall complexity of computing these performance measures is of the order O( K 2 m 1 3 m 2 3), where K is the buffer capacity, and m 1 and m 2 are the numbers of phases of the underlying Markovian structures for the high-priority and low-priority packet arrival processes, respectively. Thus the results obtained are computationally tractable and numerical results show that, by choosing a proper threshold, a space priority queue not only can maintain the quality of service for the high-priority traffic but also can provide the near-optimum utilization of the capacity for the low-priority traffic.

Nonlinear system decomposition in differential vector space 1

Abstract This paper studies controllability and observability of nonlinear systems in differential vector space. It generalizes the coordinate invariant state space decomposition of linear systems to nonlinear systems. As a result, the dual-state space of nonlinear systems can be decomposed into controllable-observable, controllable-unobservable, uncontrollable-observable and uncontrollable-unobservable subspaces in the differential vector space.

A Monte Carlo simulation of the flow network reliability using importance and stratified sampling

We consider the evaluation of the flow network reliability parameter. Because its exact computation has exponential time complexity, simulation methods are alternatives used to evaluate large networks. In this paper, we use the state space decomposition methodology of Doulliez and Jamoulle in order to construct a new simulation method which combines the importance and the stratified Monte Carlo principles. We show that the related estimator belongs to the variance reduction family and it offers more accurate estimates than those obtained by a previous stratified sampling technique based on the same decomposition, By experimental results, we show the interest of the proposed method when compared to previous methods.

Composite system reliability evaluation using state space pruning

This paper presents a method of computing the reliability indices of a composite generation-transmission system by performing Monte Carlo simulation selectively on those regions of the state space where loss of load states are more likely to occur. These regions are isolated by performing state space decomposition to remove coherent acceptable subspaces. It is shown that this method results in a significant reduction in the number of sampled states, thereby reducing the computational effort required to compute the system and bus indices. The method assumes a DC flow model, and is tested using the IEEE Reliability Test System. The proposed method is not intended to replace existing variance reduction techniques; in fact, such techniques may be used in conjunction with the proposed method to further improve its efficiency.

Automatic state space decomposition for approximate FSM traversal based on circuit analysis

Exploiting circuit structure is a key issue in the implementation of algorithms for state space decomposition when the target is approximate FSM traversal. Given the gate-level description of a sequential circuit, the information about its structure can be captured by evaluating the affinity between pairs or groups of latches. Two main factors have to be considered in carrying out the structural analysis of a sequential circuit: latch connectivity and latch correlation. The first one takes into account the mutual dependency of each memory element on the others; the second one tells us how related are the functions realized by the logic feeding each latch. In this paper we estimate the affinity of two latches by combining these two factors, and we use this measure to formulate the state space decomposition problem as a graph partitioning problem. We propose an algorithm to automatically determine good partitions of the latch set which induce state space decomposition, and we present approximate FSM traversal and logic optimization results for the largest ISCAS'89 sequential benchmarks.

Algorithms for approximate FSM traversal based on state space decomposition

This paper presents algorithms for approximate finite state machine traversal based on state space decomposition. The original finite state machine is partitioned in component submachines, and each of them is traversed separately; the result of the computation is an over-estimation of the set of reachable states of the original machine. Different traversal strategies, which reduce the effects of the degrees of freedom introduced by the decomposition, are discussed. Efficient partitioning is a key point for the performance of the traversal techniques; a method to heuristically find a good decomposition of the overall finite state machine, based on the exploration of its state variable dependency graph, is proposed. Applications of the approximate traversal methods to logic optimization of sequential circuits and behavioral verification of finite state machines are described; experimental results for such applications, together with data concerning pure traversal, are reported.

Decentralized control of interconnected electric power systems in competitive markets

This paper investigates the prospects of decentralized control in the emerging competitive electricity markets. The weaknesses of current control performance criteria for dealing with such markets are discussed and it is hypothesized that decentralized control, providing full control over economically independent electrically interconnected areas, is necessary in such markets. To study the feasibility of such a decentralization rigorously, a state space decomposition method is introduced and applied to the model of an interconnected system. As a result it is shown that, in electric power systems, regardless of the number and location of the tie lines and implemented control schemes, the frequency and phase of each area are in the controllable subspaces of all areas in the interconnection. This shows that, if decentralization is to be achieved, flexible links which decouple the phases of areas must be utilized. The side effects of such implementations are also discussed.

A note on state-space decomposition methods for analyzing stochastic flow networks

Consider a flow network with single source s and single sink t with demand d>0. Assume that the nodes do not restrict flow transmission and the arcs have finite random discrete capacities. This paper has two objectives: (1) it corrects errors in well-known algorithms by Doulliez and Jamoulle (1972) for (a) computing the probability that the demand is satisfied (or network reliability), (b) the probability that an arc belongs to a minimum cut which limits the flow below d, and (c) the probability that a cut limits the flow below d; and (2) it discusses the applicability of these procedures. The Doulliez and Jamoulle algorithms are frequently referenced or used by researchers in the areas of power and communication systems and appear to be very effective for the computation of the network reliability when the demand is close to the largest possible maximum flow value. Extensive testing is required before the Doulliez and Jamoulle algorithms are disposed in favor of alternative approaches. Such testing should compare the performance of existing methods in a variety of networks including grid networks and dense networks of various sizes.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Output deadbeat control using state feedback of discrete-time multivariable systems

In this note the problem of output deadbeat regulation with internal stability using state feedback is solved in its full generality. That is, the only assumption made is that the system is described by a linear time-invariant recurrence equation. By making an appropriate state-space decomposition it is shown that the results obtained by Kimura et al. (1981) can be generalized in a straightforward way. An advantage of this approach is that it facilitates an easy proof of the basic solvability condition, gives a good insight into the basics of the problem, and provides a synthesis procedure to construct a minimal-time deadbeat controller. The approach is used to parametrize a set of weight matrices which turn the corresponding minimum variance controller into a minimal-time deadbeat one

FSM Decomposition and Functional Verification ofFSM Networks

Here we present a new method for the decomposition of a Finite State Machine (FSM) into a network of interacting FSMs and a framework for the functional verification of the FSM network at different levels of abstraction. The problem of decomposition is solved by output partitioning and state space decomposition using a multiway graph partitioning technique. The number of submachines is determined dynamically during the partitioning process. The verification algorithm can be used to verify (a) the result of FSM decomposition on a behavioral level, (b) the encoded FSM network, and (c) the FSM network after logic optimization. Our verification technique is based on an efficient enumeration‐simulation method which involves traversal of the state transition graph of the prototype machine and simulation of the decomposed machine network. Both the decomposition and verification/simulation algorithms have been implemented as part of an interactive FSM synthesis system and tested on a set of benchmark examples.