This is the fifth paper in a series in which we construct and study the so-called Runge-Kutta Discontinuous Galerkin method for numerically solving hyperbolic conservation laws. In this paper, we extend the method to multidimensional nonlinear systems of conservation laws. The algorithms

Done well, separation of concerns can provide many software engineering benefits, including reduced complexity, improved reusability, and simpler evolution. The choice of boundaries for separate concerns depends on both requirements on the system and on the kind(s) of decompositionand composition a

The extended Kalman filter (EKF) is probably the most widely used estimation algorithm for nonlinear systems. However, more than 35 years of experience in the estimation community has shown that is difficult to implement, difficult to tune, and only reliable for systems that are almost linear

The Kalman filter(KF) is one of the most widely used methods for tracking and estimation due to its simplicity, optimality, tractability and robustness. However, the application of the KF to nonlinear systems can be difficult. The most common approach is to use the Extended Kalman Filter (EKF

in discrete time (the algebraic view), then progresses to the view of it in continuous time (the analytical view). A 5-dimensional depiction is developed, which completely describes the system. These analyses lead to a generalized model of the algorithm, containing a set of coefficients to control the system

Increasingly, for many application areas, it is becoming important to include elements of nonlinearity and non-Gaussianity in order to model accurately the underlying dynamics of a physical system. Moreover, it is typically crucial to process data on-line as it arrives, both from the point of view

to linear hybrid systems. In particular, we consider symbolic model-checking and minimization procedures that are based on the reachability analysis of an infinite state space. The procedures iteratively compute state sets that are definable as unions of convex polyhedra in multidimensional real space. We

In order to handle spatial data efficiently, as required in computer aided design and geo-data applications, a database system needs an index mechanism that will help it retrieve data items quickly according to their spatial locations However, traditional indexing methods are not well suited

feature representation and extraction, multidimensional indexing, and system design, three of the fundamental bases of content-based image retrieval. Furthermore, based on the state-of-the-art technology available now and the demand from real-world applications, open research issues are identified

, planning under uncertainty, sensor-based planning, visibility, decision-theoretic planning, game theory, information spaces, reinforcement learning, nonlinear systems, trajectory planning, nonholonomic planning, and kinodynamic planning.