In mathematics, a Riccati equation is any first-order ordinary differential equation that is quadratic in the unknown function. In other words, it is an equation of the form
where 
and 
. If 
the equation reduces to a Bernoulli equation, while if 
the equation becomes a first order linear ordinary differential equation.
and . If the equation reduces to a Bernoulli equation, while if the equation becomes a first order linear ordinary differential equation.
The equation is named after Count Jacopo Francesco Riccati (1676–1754).[1]
More generally, the term "Riccati equation" is used to refer to matrix equations with an analogous quadratic term, which occur in both continuous-time and discrete-time linear-quadratic-Gaussian control. The steady-state (non-dynamic) version of these is referred to as the algebraic Riccati equation.
Sem comentários:
Enviar um comentário