Topic
Piecewise
About: Piecewise is a research topic. Over the lifetime, 21064 publications have been published within this topic receiving 432096 citations. The topic is also known as: piecewise-defined function & hybrid function.
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TL;DR: A control strategy proposed by the authors in previous works to reduce the effect of chattering led to the solution of a differential inequality involving the first and second derivatives of the control signal and a parameter for a first-order observer, which is now removed.
Abstract: A control strategy proposed by the authors in previous works to reduce the effect of chattering led to the solution of a differential inequality involving the first and second derivatives of the control signal and a parameter for a first-order observer. The analysis was carried out assuming this parameter to be constant. In the present paper, this assumption is removed, thus allowing the solution of the differential inequality to be a function of a piecewise continuous first derivative of the control signal, without need for assuming a priori knowledge of bounds to the plant trajectories.
125 citations
TL;DR: In this article, the problem of optimization of the structure of a power system where redundant elements are included in order to provide a desired level of reliability is considered, and a procedure which determines the minimal cost series-parallel system configuration is proposed which allows elements with different parameters to be allocated in parallel.
125 citations
TL;DR: In this article, a piecewise continuous adaptive law is introduced, along with the low pass-filtered control signal that allows for achieving arbitrarily close tracking of the input and the output signals of the reference system, the transfer function of which is not required to be strictly positive real.
Abstract: This paper presents an extension of the L 1 adaptive output-feedback controller to systems of unknown relative degree in the presence of time-varying uncertainties without restricting the rate of their variation. As compared with earlier results in this direction, a new piecewise continuous adaptive law is introduced, along with the low-pass-filtered control signal that allows for achieving arbitrarily close tracking of the input and the output signals of the reference system, the transfer function of which is not required to be strictly positive real. Stability of this reference system is proved using a small-gain-type argument. The performance bounds between the closed-loop reference system and the closed-loop L 1 adaptive system can be rendered arbitrarily small by reducing the step size of integration. Missile longitudinal autopilot design is used as an example to illustrate the theoretical results.
124 citations
TL;DR: In this paper, it was shown that the Green's function can be approximated in two dimensions by piecewise linear functions with an error O(h) = O (h)
Abstract: Convergence of the finite element solutionu h of the Dirichlet problem Δu=? is proved, where ? is the Dirac ?-function (unit impulse). In two dimensions, the Green's function (fundamental solution)u lies outsideH 1, but we are able to prove that $$\parallel u - u^h \parallel _{L^2 } = O (h)$$ . Since the singularity ofu is logarithmic, we conclude that in two dimensions the function log ? can be approximated inL 2 near the origin by piecewise linear functions with an errorO (h). We also consider the Dirichlet problem Δu=f, wheref is piecewise smooth but discontinuous along some curve. In this case,u just fails to be inH 5/2, but as with the approximation to the Green's function, we prove the full rate of convergence:?u?u h ?1=O (h 8/2) with, say, piecewise quadratics.
124 citations
TL;DR: In this article, the authors relax the monotonicity constraint in a geometric framework in which the median function plays a crucial role, and present algorithms for piecewise cubic interpolants, which preserve monoticity as well as uniform third and fourth-order accuracy.
Abstract: Monotone piecewise cubic interpolants are simple and effective. They are generally third-order accurate, except near strict local extrema where accuracy degenerates to second-order due to the monotonicity constraint. Algorithms for piecewise cubic interpolants, which preserve monotonicity as well as uniform third and fourth-order accuracy are presented. The gain of accuracy is obtained by relaxing the monotonicity constraint in a geometric framework in which the median function plays a crucial role.
124 citations