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This paper presents an approach to derive the optimal feedback control laws by solving the finite time Hamilton Jacobi Ballman equation. Conventional methods to solve the HJB equation suffer from curse of dimensionality as the number of spatial variables is equal to the state dimension, which is twice the number of degrees of freedom of a mechanical system. The presented approach exploits the recently...
This paper presents a framework to manage sensor systems for the effective characterization and monitoring of uncertainty in distributed sensing problems. The problem of Space Situational Awareness, where a multitude of Resident space objects has to be tracked by a limited number of sensors is taken as the primary example. The central motive of the paper is to iteratively update sensor modalities...
This paper describes the problem of multiple target tracking and localization using dynamic sensors such as Unmanned Ariel Vehicles. Often the location or path of the target is uncertain and has to be accounted along with UAV fuel costs while optimally planning the dynamic sensor trajectory. The coupled problem of optimal target state estimation and sensor path planning is computationally expensive...
This paper presents a minimum entropy approach for the design of an optimal bang-bang control for linear dynamical systems with parametric uncertainty. The curse of dimensionality is of major concern when the dimension of the uncertain parameter space increases while designing robust controllers. In this paper an alternative probabilistic approach is developed to account for parameter uncertainty...
Active sensors need to be optimally deployed or configured so as to make the best measurements at any given time. Then of immediate concern is the problem of characterising or measuring sensor performance before the measurement has been taken. In this paper, the well known concept of Mutual Information is chosen as the utility function for optimizing the sensor parameters. The standard problem of...
This paper presents a few novel quadrature rules to evaluate expectation integrals with respect to a uniform probability density function. In 1-dimensional expectation integrals the most widely used numerical method is the Gauss-Legendre quadratures as they are exact for polynomials. As for a generic N-dimensional integral, the tensor product of 1-dimensional Gauss-Legendre quadratures results in...
This paper presents an extension to the unscented transformation to evaluate expectation integrals in general N-dimensional space by satisfying higher order moment equations. New sets of sigma points are defined to satisfy moment equations up to eighth order. The proposed methodology can be used as an efficient alternative to Gaussian quadrature rule with significantly reduced number of function evaluations...
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