arXiv subjects

Han-Lim Choi

Publications and source records attributed to Han-Lim Choi.

47 records · Page 3Linked to original sources

arXiv2016

A Topology-Guided Path Integral Approach for Stochastic Optimal Control

This work presents an efficient method to solve a class of continuous-time, continuous-space stochastic optimal control problems of robot motion in a cluttered environment. The method builds upon a path integral representation of the stochastic optimal control problem that allows computation of the optimal solution through sampling and estimation process. As this sampling process often leads to a local minimum especially when the state space is highly non-convex due to the obstacle field, we present an efficient method to alleviate this issue by devising a proposed topological motion planning algorithm. Combined with a receding-horizon scheme in execution of the optimal control solution, the proposed method can generate a dynamically feasible and collision-free trajectory while reducing concern about local optima. Illustrative numerical examples are presented to demonstrate the applicability and validity of the proposed approach.

eess.SY↗

arXiv2014

Complexity Analysis of Heuristic Pulse Interleaving Algorithms for Multi-Target Tracking with Multiple Simultaneous Receive Beams

This paper presents heuristic algorithms for interleaved pulse scheduling problems on multi-target tracking in pulse Doppler phased array radars that can process multiple simultaneous received beams. The interleaved pulse scheduling problems for element and subarray level digital beamforming architectures are formulated as the same integer program and the asymptotic time complexities of the algorithms are analyzed.

eess.SY↗

arXiv2014

Discretization of Planar Geometric Cover Problems

We consider discretization of the 'geometric cover problem' in the plane: Given a set $P$ of $n$ points in the plane and a compact planar object $T_0$, find a minimum cardinality collection of planar translates of $T_0$ such that the union of the translates in the collection contains all the points in $P$. We show that the geometric cover problem can be converted to a form of the geometric set cover, which has a given finite-size collection of translates rather than the infinite continuous solution space of the former. We propose a reduced finite solution space that consists of distinct canonical translates and present polynomial algorithms to find the reduce solution space for disks, convex/non-convex polygons (including holes), and planar objects consisting of finite Jordan curves.

cs.CG↗

arXiv2014

A Potential Game Approach for Information-Maximizing Cooperative Planning of Sensor Networks

This paper presents a potential game approach for distributed cooperative selection of informative sensors, when the goal is to maximize the mutual information between the measurement variables and the quantities of interest. It is proved that a local utility function defined by the conditional mutual information of an agent conditioned on the other agents' sensing decisions leads to a potential game with the global potential being the original mutual information of the cooperative planning problem. The joint strategy fictitious play method is then applied to obtain a distributed solution that provably converges to a pure strategy Nash equilibrium. Two numerical examples on simplified weather forecasting and range-only target tracking verify convergence and performance characteristics of the proposed game-theoretic approach.

eess.SY↗

arXiv2013

Search Optimization for Minimum Load under Detection Performance Constraints in Multifunction Radars

This paper presents a solution procedure of search parameter optimization for minimum load ensuring desired one-off and cumulative probabilities of detection in a multifunction phased array radar. The key approach is to convert this nonlinear optimization on four search parameters into a scalar optimization on signal-to-noise ratio by a semi-analytic process based on subproblem decomposition. The efficacy of the proposed solution approach is verified with theoretical analysis and numerical case studies.

eess.SY↗

arXiv2013

Mutual Information-Based Planning for Informative Windowed Forecasting of Continuous-Time Linear Systems

This paper presents expression of mutual information that defines the information gain in planning of sensing resources, when the goal is to reduce the forecast uncertainty of some quantities of interest and the system dynamics is described as a continuous-time linear system. The method extends the smoother approach in [5] to handle more general notion of verification entity - continuous sequence of variables over some finite time window in the future. The expression of mutual information for this windowed forecasting case is derived and quantified, taking advantage of underlying conditional independence structure and utilizing the fixed-interval smoothing formula with correlated noises. Two numerical examples on (a) simplified weather forecasting with moving verification paths, and (b) sensor network scheduling for tracking of multiple moving targets are considered for validation of the proposed approach.

eess.SY↗

arXiv2013

Pruning-Based Pareto Front Generation for Mixed-Discrete Bi-Objective Optimization

This note proposes an effective pruning-based Pareto front generation method in mixed-discrete bi-objective optimization. The mixed-discrete problem is decomposed into multiple continuous subproblems; two-phase pruning steps identify and prune out non-contributory subproblems to the Pareto front construction. The efficacy of the proposed method is demonstrated on two benchmark examples.

math.OC↗

arXiv2013

A Gaussian Process Emulator Approach for Rapid Contaminant Characterization with an Integrated Multizone-CFD Model

This paper explores a Gaussian process emulator based approach for rapid Bayesian inference of contaminant source location and characteristics in an indoor environment. In the pre-event detection stage, the proposed approach represents transient contaminant fate and transport as a random function with multivariate Gaussian process prior. Hyper-parameters of the Gaussian process prior are inferred using a set of contaminant fate and transport simulation runs obtained at predefined source locations and characteristics. This paper uses an integrated multizone-CFD model to simulate contaminant fate and transport. Mean of the Gaussian process, conditional on the inferred hyper-parameters, is used as an computationally efficient statistical emulator of the multizone-CFD simulator. In the post event-detection stage, the Bayesian framework is used to infer the source location and characteristics using the contaminant concentration data obtained through a sensor network. The Gaussian process emulator of the contaminant fate and transport is used for Markov Chain Monte Carlo sampling to efficiently explore the posterior distribution of source location and characteristics. Efficacy of the proposed method is demonstrated for a hypothetical contaminant release through multiple sources in a single storey seven room building. The method is found to infer location and characteristics of the multiple sources accurately. The posterior distribution obtained using the proposed method is found to agree closely with the posterior distribution obtained by directly coupling the multizone-CFD simulator with the Markov Chain Monte Carlo sampling.

stat.AP↗

arXiv2012

A Dynamic Bi-orthogonal Field Equation Approach for Efficient Bayesian Calibration of Large-Scale Systems

This paper proposes a novel computationally efficient dynamic bi-orthogonality based approach for calibration of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on a decomposition of the solution into mean and a random field using a generic Karhunnen-Loeve expansion. The random field is represented as a convolution of separable Hilbert spaces in stochastic and spacial dimensions that are spectrally represented using respective orthogonal bases. In particular, the present paper investigates generalized polynomial chaos bases for stochastic dimension and eigenfunction bases for spacial dimension. Dynamic orthogonality is used to derive closed form equations for the time evolution of mean, spacial and the stochastic fields. The resultant system of equations consists of a partial differential equation (PDE) that define dynamic evolution of the mean, a set of PDEs to define the time evolution of eigenfunction bases, while a set of ordinary differential equations (ODEs) define dynamics of the stochastic field. This system of dynamic evolution equations efficiently propagates the prior parametric uncertainty to the system response. The resulting bi-orthogonal expansion of the system response is used to reformulate the Bayesian inference for efficient exploration of the posterior distribution. Efficacy of the proposed method is investigated for calibration of a 2D transient diffusion simulator with uncertain source location and diffusivity. Computational efficiency of the method is demonstrated against a Monte Carlo method and a generalized polynomial chaos approach.

stat.CO↗

arXiv2012

A Generalized Polynomial Chaos-Based Method for Efficient Bayesian Calibration of Uncertain Computational Models

This paper addresses the Bayesian calibration of dynamic models with parametric and structural uncertainties, in particular where the uncertain parameters are unknown/poorly known spatio-temporally varying subsystem models. Independent stationary Gaussian processes with uncertain hyper-parameters describe uncertainties of the model structure and parameters while Karhunnen-Loeve expansion is adopted to spectrally represent these Gaussian processes. The Karhunnen-Loeve expansion of a prior Gaussian process is projected on a generalized Polynomial Chaos basis, whereas intrusive Galerkin projection is utilized to calculate the associated coefficients of the simulator output. Bayesian inference is used to update the prior probability distribution of the generalized Polynomial Chaos basis, which along with the chaos expansion coefficients represent the posterior probability distribution. Parameters of the posterior distribution are identified that quantify credibility of the simulator model. The proposed method is demonstrated for calibration of a simulator of quasi-one-dimensional flow through a divergent nozzle.

stat.CO↗

arXiv2012

A Dynamic Bi-orthogonality based Approach for Uncertainty Quantification of Stochastic Systems with Discontinuities

The use of spectral projection based methods for simulation of a stochastic system with discontinuous solution exhibits the Gibbs phenomenon, which is characterized by oscillations near discontinuities. This paper investigates a dynamic bi-orthogonality based approach with appropriate post-processing for mitigating the effects of the Gibbs phenomenon. The proposed approach uses spectral decomposition of the spatial and stochastic fields in appropriate orthogonal bases, while the dynamic orthogonality condition is used to derive the resultant closed form evolution equations. The orthogonal decomposition of the spatial field is exploited to propose a Gegenbauer reprojection based post-processing approach, where the orthogonal bases in spatial dimension are reprojected on the Gegenbauer polynomials in the domain of analyticity. The resultant spectral expansion in Gegenbauer series is shown to mitigate the Gibbs phenomenon. Efficacy of the proposed method is demonstrated for simulation of a one-dimensional stochastic Burgers equation with uncertain initial condition.

stat.ME↗