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 Riccati equations are scaled so that the solution has unit norm to eliminate instabilities associated with the inversion step of invariant-subspace-based (Schur) methods without changing the relative condition number of the underlying problem.
51 citations
TL;DR: In this article, the duality between the filtering and optimal control equations is not straightforward and a generalization of the concepts of detectability and stabilizability, as well as a discussion of how the dualness between these concepts should be understood, is presented Conditions for existence and uniqueness of a positive semi-definite solution to a set of coupled Riccati equations in a generic form are provided in terms of these concepts.
51 citations
TL;DR: This paper constructs an optimal feedback control-strategy pair for the game in a closed-loop form based on the solution of a Riccati equation and demonstrates an indefinite phenomenon arising from the linear-quadratic game.
Abstract: In this paper, we study a two-person zero-sum linear-quadratic stochastic differential game problem. From a new viewpoint, we construct an optimal feedback control-strategy pair for the game in a closed-loop form based on the solution of a Riccati equation. A key part of our analysis involves proving the global solvability of this Riccati equation, which is interesting in its own right. Moreover, we demonstrate an indefinite phenomenon arising from the linear-quadratic game.
51 citations
TL;DR: In this article, a model is developed to predict the dynamic response of a mechanical stack called a ''piezoceramic element'' which is composed of a piezoelectric sensor, a viscoelastic damper and an actuator of which the applied voltage is fed back by the sensor voltage.
Abstract: A model is developed to predict the dynamic response of a mechanical stack called a `piezoceramic element' which is composed of a piezoelectric sensor, a viscoelastic damper and a piezoelectric actuator of which the applied voltage is fed back by the sensor voltage. This stack works by stretching: a model based on Euler-Bernoulli beam equations is chosen. This model is then used to investigate the effect of the `piezoceramic element' on the active vibration control of a cantilevered beam. An optimal control law is determined by using a state observer and the Riccati equation. Finally, the theoretical results are simulated and compared with the results obtained in the open-loop condition.
50 citations
TL;DR: Variable separation exponential-form solution of (1+1)-dimensional coupled integrable dispersionless equations in physics and mathematics is obtained via the projective Riccati equation method and the singularity structure without the physical meaning is found for the original components of the system.
50 citations