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 article, the (2+1)-dimensional breaking soliton equation, the coupled KP equation with three potentials and a new (3+ 1)-dimensional nonlinear evolution equation are decomposed into systems of solvable ordinary differential equations with the help of the (1+1)dimensional AKNS equations.
Abstract: The known (2+1)-dimensional breaking soliton equation, the coupled KP equation with three potentials and a new (3+1)-dimensional nonlinear evolution equation are decomposed into systems of solvable ordinary differential equations with the help of the (1+1)-dimensional AKNS equations. The Abel–Jacobi coordinates are introduced to straighten out the associated flows, from which algebraic-geometrical solutions of the (2+1)-dimensional breaking soliton equation, the coupled KP equation and the (3+1)-dimensional evolution equation are explicitly given in terms of the Riemann theta functions.
117 citations
TL;DR: In this paper, the authors present an algorithm for the stabilization of a class of discrete-time uncertain systems suffering from uncertainty of the norm bounded time varying type by solving a certain discrete Riccati equation.
117 citations
TL;DR: In this paper, the authors demonstrate the simplicity and the beauty of a subject that is, in fact, the theory of the (explicit) integration of nonlinear differential equations.
Abstract: The “Painleve analysis” is quite often perceived as a collection of tricks reserved to experts. The aim of this chapter is to demonstrate the contrary and to unveil the simplicity and the beauty of a subject that is, in fact, the theory of the (explicit) integration of nonlinear differential equations.
116 citations
TL;DR: This paper collects the bounds that have been presented up to now and summarizes them in an unified form to prove particularly convenient for those wishing to get a ready estimate of the solution while solving the equations numerically or to develop theoretical results that rely on these bounds.
Abstract: In recent years, several bounds have been reported for different measures of the ‘ extent’ or ‘ size ’ of the solution of the algebraic matrix equations arising in control theory, such as the Riccati equation and the Lyapunov equation. This paper collects the bounds that have been presented up to now and summarizes them in an unified form. This will prove particularly convenient for those wishing to get a ready estimate of the solution while solving the equations numerically or to develop theoretical results that rely on these bounds.
116 citations
TL;DR: In this article, a feedback controller for bilinear control systems with quadratic cost is designed, and an iteration procedure in close proximity to the Riccati approach is presented, and the proof of convergence is outlined.
Abstract: For bilinear control systems with quadratic cost, the so-called bilinear-quadratic problems, a feedback controller for the finite-time case is designed. An iteration procedure in close proximity to the Riccati approach is presented, and the proof of convergence is outlined. The potential of the new method is discussed, and the design procedure is illustrated for two examples.
116 citations