Topic
Riccati equation
About: Riccati equation is a research topic. Over the lifetime, 10428 publications have been published within this topic receiving 210015 citations. The topic is also known as: Riccati's differential equation.
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TL;DR: In this paper, a new integrable equation derived recently by Degasperis and Procesi is investigated, and sufficient conditions on the initial data are established to guarantee the formulation of a singularity in the sense that the derivative of the solution blows up in finite time.
65 citations
TL;DR: In this article, a systematic method is given to derive Lie point symmetries of nonlinear fractional ordinary differential equations and illustrate its applicability through the fractional Riccati equation and nonlinear FDE of Lienard type with Riemann-Liouville fractional derivative.
Abstract: A systematic method is given to derive Lie point symmetries of nonlinear fractional ordinary differential equations and illustrate its applicability through the fractional Riccati equation and nonlinear fractional ordinary differential equation of Lienard type with Riemann–Liouville fractional derivative. Using the obtained Lie point symmetries, we construct their exact solutions wherever possible.
65 citations
TL;DR: A novel non-probabilistic time-variant reliability-based optimization (NTRBO) strategy is presented for closed-loop controller design of vibration reduction issues and reveals that uncertainty factors in optimal active control can be addressed from a new time-Variant reliability perspective.
64 citations
TL;DR: A finite-time H∞ controller for uncertain robotic manipulators that achieves high-precision tracking performance without requiring the solution of a Hamilton-Jacobi equation or a Riccati equation is derived using the backstepping method.
Abstract: In this study, a finite-time ${H_\infty }$ controller for uncertain robotic manipulators that achieves high-precision tracking performance without requiring the solution of a Hamilton–Jacobi equation or a Riccati equation is derived using the backstepping method. First, a theory of robust finite-time stability for a class of uncertain nonlinear systems is studied. This theory is then used to develop a simple robust tracking controller for robotic manipulators that provides high precision, strong robustness, and fast response. Not only is the closed-loop system globally finite-time stable, but the L 2 gain is also less than or equal to γ. Simulations and experiments indicate that the proposed control approach is highly effective.
64 citations
01 Jan 1978
TL;DR: In this article, the spatially homogeneous model of a high activation energy thermal explosion is studied when the heat loss parameter a is close to the classically defined critical value a = e. The solution properties of this nonlinear equation permit one to define a value of A = a which separates subsequent subcritical and supercritical behaviour.
Abstract: The spatially homogeneous model of a high activation energy thermal explosion is studied when the heat loss parameter a is close to the classically-defined critical value a = e. Asymptotic solutions are developed which describe the time- history of the temperature and reactant depletion. It is shown that there is a critical time period, large with respect to the characteristic conduction time, in which the temperature variation is described by a Riccati equation. The solution properties of this nonlinear equation permit one to define a value of A = a — e which separates subsequent subcritical and supercritical behaviour.
64 citations