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ricati
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There are 6 letters in RICATI ( A1C3I1R1T1 )
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In mathematics, a Riccati equation in the narrowest sense is any first-order ordinary differential equation that is quadratic in the unknown function. In other words, it is an equation of the form* * * * * y * ′ * * ( * x * ) * = * * q * * 0 * * * ( * x * ) * + * * q * * 1 * * * ( * x * ) * * y * ( * x * ) * + * * q * * 2 * * * ( * x * ) * * * y * * 2 * * * ( * x * ) * * * {\displaystyle y'(x)=q_{0}(x)+q_{1}(x)\,y(x)+q_{2}(x)\,y^{2}(x)} * where * * * * * q * * 0 * * * ( * x * ) * ≠ * 0 * * * {\displaystyle q_{0}(x)\neq 0} * and * * * * * q * * 2 * * * ( * x * ) * ≠ * 0 * * * {\displaystyle q_{2}(x)\neq 0} * . If * * * * * q * * 0 * * * ( * x * ) * = * 0 * * * {\displaystyle q_{0}(x)=0} * the equation reduces to a Bernoulli equation, while if * * * * * q * * 2 * * * ( * x * ) * = * 0 * * * {\displaystyle q_{2}(x)=0} * the equation becomes a first order linear ordinary differential equation. * The equation is named after Jacopo Riccati (1676–1754).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. |