Piecewise linear function

About: Piecewise linear function is a research topic. Over the lifetime, 8133 publications have been published within this topic receiving 161444 citations.

Testing hypotheses in an I(2) model with piecewise linear trends. An analysis of the persistent long

Abstract: This paper discusses the I(2) model with breaks in the deterministic component and illustrates with an analysis of German and US prices, exchange rates, and interest rates in 1975-1999. It provides new results on the likelihood ratio test of overidentifying restrictions on the cointegrating relations when they contain piecewise linear trends. One important aim of the paper is to demonstrate that a structured I(2) analysis is useful for a better understanding of the empirical regularities underlying the persistent swings in nominal exchange rates, typical in periods of ‡oating exchange rates.

An analytical shock-fitting algorithm for LWR kinematic wave model embedded with linear speed–density relationship

Abstract: In this paper, we propose a simple and efficient shock-fitting solution algorithm for the LWR model assuming a linear speed–density relationship or parabolic fundamental diagram. The solution is exact if the boundary conditions for density variable on the spatial axis are piecewise linear and those on the time axis are piecewise constant. Discontinuities are explicitly handled. The method utilizes the concept that for a linear speed–density relationship, a linear density variation along the spatial axis remains linear if not interrupted by shocks. Explicit expressions for the nonlinear shock path trajectory between two linear density functions are also derived. Two numerical examples are used to illustrate the effectiveness of the proposed method.

Fault Detection and Optimal Sensor Location in Vehicle Suspensions

Abstract: A statistical system identification methodology is applied for performing parametric identification and fault detection studies in nonlinear vehicle systems. The vehicle nonlinearities arise due to the function of the suspension dampers, which assume a different damping coefficient in tension than in compression. The suspension springs may also possess piecewise linear characteristics. These lead to models with parameter discontinuities. Emphasis is put on investigating issues of unidentifiability arising in the system identification of nonlinear systems and the importance of sensor configuration and excitation characteristics in the reliable estimation of the model parameters. A methodology is proposed for designing the optimal sensor configuration (number and location of sensors) so that the corresponding measured data are most informative about the condition of the vehicle. The effects of excitation characteristics on the quality of the measured data are systematically explored. The effectiveness of th...

Real-time continuous curvature path planning of UAVS in cluttered environments

Abstract: This paper presents a method for curvature continuous (G2 continuous) path generation for a UAV flying in a cluttered environment in real-time. First we generate a collision free path using a rapidly-exploring random tree (RRT). However a UAV cannot fly this path since it consists of piecewise linear segments. G2 continuous path algorithm using cubic Bezier spiral curves is presented in this paper. Simulation results show the superiority of cubic Bezier spiral curves to Dubins path and C1 continuous cubic Bezier curves.

Discretized Lyapunov functional for uncertain systems with multiple time-delay

Abstract: The stability of uncertain systems with multiple time-delay is studied using a quadratic Lyapunov functional. By choosing piecewise linear parameters for the kernel of a quadratic expression, the guaranteed stability condition is formulated in the form of linear matrix inequality. The extent of conservatism depends on the grid size. However, numerical results show that even a very coarse discretization can produce quite satisfactory results. The possibility of non-uniform grid size and more general Lyapunov functional is of interest even for a single delay system. Numerical examples are presented.