... comprises terrain heights at locations oriented perpendicular to the direction of travel. A vector space is formed by the span of these vectors and a corresponding set of empirical basis vectors is developed. A set of analytic basis vectors is formed from Gegenbauer polynomials, parameterized to approximate...

...Umamaheswara Konda; Puneet Singla; Tarunraj Singh; Peter D. Scott The focus of this work is on the development of a framework permitting the unification of generalized polynomial chaos (gPC) with the linear moment propagation equations, to accurately characterize the state distribution for linear...

... 2009 15 01 2011 05 08 2011 05 08 2011 delays polynomials stability Delay often occurs in many dynamic systems such as communication systems, chemical systems, biological systems, and electrical networks. Meanwhile, delay is frequently a source of instability...

...James Fisher; Raktim Bhattacharya In this paper, we develop a framework for solving optimal trajectory generation problems with probabilistic uncertainty in system parameters. The framework is based on the generalized polynomial chaos theory. We consider both linear and nonlinear dynamics...

...Emmanuel D. Blanchard; Adrian Sandu; Corina Sandu Mechanical systems operate under parametric and external excitation uncertainties. The polynomial chaos approach has been shown to be more efficient than Monte Carlo for quantifying the effects of such uncertainties on the system response. Many...

...Brian A. Templeton; David E. Cox; Sean P. Kenny; Mehdi Ahmadian; Steve C. Southward This paper applies the H 2 norm along time and parameter domains. The norm is related to the probabilistic H 2 problem. It is calculated using polynomial chaos to handle uncertainty in the plant model. The structure...

...Chang-Chun Hua; Qing-Guo Wang; Peng Shi; Xin-Ping Guan The stabilization problem is investigated for a class of uncertain systems with multiple time-varying delays. The considered system includes the uncertain nonlinear time delay functions, whose bounds are in the form of polynomial-type functions...

... of several curves passing through every two consequent turning points. These curves adopt their shapes via a linear mapping strategy from the reference hysteresis curves with polynomial configurations. Experimental implementation of the proposed method demonstrates slight improvement over the widely used...

... and following a straight line in the Euclidean space. A path-planning technique based on a parametrization of the camera path through polynomials is proposed, which overcomes existing methods dealing with this problem. The generated image trajectory can be tracked by using an image-based visual servoing...

...Nataraj S. V. Paluri; Jayesh J. Barve We propose an algorithm to compute the spectral set of a polytope of polynomials. The proposed algorithm offers several key guarantees that are not available with existing techniques. It guarantees that the generated spectral set: (i) contains all the actual...

... that may contain a high-order polynomial with a time delay. Without the knowledge of these bounds, we present adaptive state feedback controllers that are continuous and independent of time delays. Based on the Lyapunov stability theorem, we prove that the controllers can render the closed loop systems...

... scheme using a quadratic polynomial pressure-torque relationship of the PMNN model is developed for transmission shift controller design. The results illustrate that the proposed pressure profiling technique can be applied to a wide range of operating conditions. This study demonstrates the potential...

...Yeong-Jeu Sun In this paper, we provide the annular bound, i.e., lower and upper circular bound, for the roots of characteristic equations of uncertain discrete systems. Such an annular bound can be easily obtained by estimating the largest nonnegative zero of the specific polynomial. Two examples...

...Michael V. Basin The paper presents the optimal nonlinear filter for quadratic state and linear observation equations confused with white Gaussian disturbances. The general scheme for obtaining the optimal filter in case of polynomial state and linear observation equations is announced...