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, Wu et al. make use of an extended tanh-function method and symbolic computation to obtain respectively four kinds of soliton solutions for a new generalized Hirota-Satsuma coupled KdV equation and a new coupled MKdV equations.
251 citations
TL;DR: In this paper, the quadratic Riccati differential equation is solved by He's variational iteration method with considering Adomian's polynomials, and the results reveal that the proposed method is very effective and simple.
251 citations
TL;DR: These are the first adaptive controllers for unstable PDEs without relative degree limitations, open-loop stability assumptions, or domain-wide actuation, and most of the designs presented are state feedback but two benchmark designs with output feedback which have infinite relative degree are presented.
Abstract: We develop adaptive controllers for parabolic partial differential equations (PDEs) controlled from a boundary and containing unknown destabilizing parameters affecting the interior of the domain. These are the first adaptive controllers for unstable PDEs without relative degree limitations, open-loop stability assumptions, or domain-wide actuation. It is the first necessary step towards developing adaptive controllers for physical systems such as fluid, thermal, and chemical dynamics, where actuation can be only applied non-intrusively, the dynamics are unstable, and the parameters, such as the Reynolds, Rayleigh, Prandtl, or Peclet numbers are unknown because they vary with operating conditions. Our method builds upon our explicitly parametrized control formulae to avoid solving Riccati or Bezout equations at each time step. Most of the designs we present are state feedback but we present two benchmark designs with output feedback which have infinite relative degree.
251 citations
TL;DR: A design method of the reduced-order observer that is dependent on the solution of the Riccati equation is presented and an example is given to illustrate effects of the design method.
Abstract: This note deals with the design of reduced-order observers for Lipschitz nonlinear systems. It shows that the conditions under which a full-order observer exists also guarantee the existence of a reduced-order observer. A design method of the reduced-order observer that is dependent on the solution of the Riccati equation is then presented and an example is given to illustrate effects of the design method.
250 citations
TL;DR: In this article, the authors considered linear systems of the form E\dot{x} = Ax + Bu with E singular and proved that the optimal control can be found by solving a reduced order Riccati equation.
Abstract: Linear systems of the form E\dot{x} = Ax + Bu with E singular are treated. It is desired to find a control which drives the system asymptotically to the origin, minimizing a quadratic cost functional. No restrictions are placed on initial conditions. The cost associated with the impulsive behavior of the system is examined as well as existence and uniqueness of the optimal control. Through a sequence of coordinate transformations it is proven that the optimal control can be found by solving a reduced order Riccati equation.
246 citations