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, a method for reducing controllers for systems described by partial differential equations (PDEs) is applied to Burgers' equation with periodic boundary conditions, which differs from the typical approach of reducing the model and then designing the controller.
Abstract: A method for reducing controllers for systems described by partial differential equations (PDEs) is applied to Burgers’ equation with periodic boundary conditions. This approach differs from the typical approach of reducing the model and then designing the controller, and has developed over the past several years into its current form. In earlier work it was shown that functional gains for the feedback control law served well as a dataset for reduced order basis generation via the proper orthogonal decomposition (POD). However, the test problem was the two-dimensional heat equation, a problem in which the physics dominates the system in such a way that controller efficacy is difficult to generalize. Here, we additionally incorporate a nonlinear observer by including the nonlinear terms of the state equation in the differential equation for the compensator.
104 citations
TL;DR: A grouping algorithm is proposed which reduces the area decomposition problem to obtaining a basis for the slow subsystem and performing a Gaussian elimination.
104 citations
TL;DR: In this article, the authors considered the discrete time matrix Riccati equation and proved the convergence of the policy space approximation technique, which is analogous to those known for the continuous-time Riccaci equation, but the techniques used are simpler.
Abstract: This paper is concerned with the discrete time matrix Riccati equation. The properties established are those of minimality, convergence, uniqueness and stability. Further the convergence of the policy space approximation technique is proved. These results are analogous to those known for the continuous-time Riccati equation, but the techniques used are simpler.
103 citations
103 citations
TL;DR: In this paper, the relations of a number of bounds for the solutions of the algebraic Riccati and Lyapunov equations that have been reported during the last two decades are investigated.
Abstract: This paper summarizes and investigates the relations of a number of bounds for the solutions of the algebraic Riccati and Lyapunov equations that have been reported during the last two decades. Also presented are bounds for the unified Riccati equation using the delta operator and it is shown that some bounds for the continuous and discrete Riccati equations can be unified by them.
103 citations