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.
Papers published on a yearly basis
Papers
More filters
TL;DR: It is proved that any finite-horizon value function of the DSLQR problem is the pointwise minimum of a finite number of quadratic functions that can be obtained recursively using the so-called switched Riccati mapping.
Abstract: In this paper, we derive some important properties for the finite-horizon and the infinite-horizon value functions associated with the discrete-time switched LQR (DSLQR) problem. It is proved that any finite-horizon value function of the DSLQR problem is the pointwise minimum of a finite number of quadratic functions that can be obtained recursively using the so-called switched Riccati mapping. It is also shown that under some mild conditions, the family of the finite-horizon value functions is homogeneous (of degree 2), is uniformly bounded over the unit ball, and converges exponentially fast to the infinite-horizon value function. The exponential convergence rate of the value iterations is characterized analytically in terms of the subsystem matrices.
101 citations
TL;DR: In this article, a semigroup model with no explicit delays in control, but with an unbounded control operator is introduced, and it is shown that the optimal feedback control and the minimum cost are characterized by the solution of a Riccati equation.
Abstract: The quadratic cost problem of evolution equations with delays in control is considered. A semigroup model which involves no explicit delays in control, but contains an unbounded control operator is introduced. With the aid of a family of approximating systems, it is shown that the optimal feedback control and the minimum cost are characterized by the solution of a Riccati equation. Three examples are given to illustrate the theory. The filtering problem of evolution equations with observation delays is also solved through the duality relation.
101 citations
TL;DR: Compared to the classical single-rate sampled-data feedback in which the state is always sampled at the same rate, the multirate system can provide a better response with a considerable reduction in the optimal cost.
Abstract: The optimal multirate design of linear, continuous-time, periodic and time-invariant systems is considered. It is based on solving the continuous linear quadratic regulation (LQR) problem with the control being constrained to a certain piecewise constant feedback. Necessary and sufficient conditions for the asymptotic stability of the resulting closed-loop system are given. An explicit multirate feedback law that requires the solution of an algebraic discrete Riccati equation is presented. Such control is simple and can be easily implemented by digital computers. When applied to linear time-invariant systems, multirate optimal feedback optimal control provides a satisfactory response even if the state is sampled relatively slowly. Compared to the classical single-rate sampled-data feedback in which the state is always sampled at the same rate, the multirate system can provide a better response with a considerable reduction in the optimal cost. In general, the multirate scheme offers more flexibility in choosing the sampling rates. >
100 citations
TL;DR: Barbu et al. as discussed by the authors study the local stabilization of the three-dimensional Navier-Stokes equations around an unstable stationary solution w, by means of a feedback boundary control.
100 citations