In mathematics, a Riccati equation in the narrowest sense is any first-order ordinary differential equation that is quadratic in the unknown function...

An algebraic Riccati equation is a type of nonlinear equation that arises in the context of infinite-horizon optimal control problems in continuous time...

Francesco Riccati (28 May 1676 – 15 April 1754) was a Venetian mathematician and jurist from Venice. He is best known for having studied the equation which...

obtain the usual Riccati equation for the Hessian of the value function as is usual for Linear-quadratic-Gaussian control. Bellman equation, discrete-time...

_{0}\end{bmatrix}}} Matrix differential equation Difference equation Linear difference equation Dynamical system Algebraic Riccati equation Cull, Paul; Flahive, Mary;...

P {\displaystyle P} is found by solving the continuous time Riccati differential equation: A T P ( t ) + P ( t ) A − ( P ( t ) B + N ) R − 1 ( B T P (...

Fiziki. 77: 617–629. Bibcode:1979ZhETF..77..617R. ISSN 0044-4510. "Riccati equation - Encyclopedia of Mathematics". encyclopediaofmath.org. Retrieved 2024-06-03...

the underlying Riccati equation are not guaranteed to be positive definite. One way of improving performance is the faux algebraic Riccati technique which...

a tool for model reduction and for solving Lyapunov and Algebraic Riccati equation in a technical report of Cambridge University, which was later published...

continuous-time Lyapunov equation, as desired. Sylvester equation, which generalizes the Lyapunov equation Algebraic Riccati equation Kalman filter Parks,...

systems. Algebraic Riccati equation Ball and beam system Bellman equation for optimal policy Boltzmann equation Colebrook equation General relativity...

example Riccati equation). Some ODEs can be solved explicitly in terms of known functions and integrals. When that is not possible, the equation for computing...

Functional equation Functional equation (L-function) Constitutive equation Laws of science Defining equation (physical chemistry) List of equations in classical...

\mathbf {S} (t)} is the solution of the differential Riccati equation. The differential Riccati equation is given as S ˙ ( t ) = − S ( t ) A − A T S ( t )...

Bernoulli equation y ′ − 2 y x = − x 2 y 2 {\displaystyle y'-{\frac {2y}{x}}=-x^{2}y^{2}} (in this case, more specifically a Riccati equation). The constant...

differential equation Cauchy–Euler equation Riccati equation Hill differential equation Gauss–Codazzi equations Chandrasekhar's white dwarf equation Lane-Emden...

w_{0}} are real numbers, this difference equation is called a Riccati difference equation. Such an equation can be solved by writing w t {\displaystyle...

equation Singular solution Poincaré–Bendixson theorem Riccati equations Functional differential equation Exponential growth Malthusian catastrophe Exponential...

first matrix Riccati differential equation solves the linear–quadratic estimation problem (LQE). The second matrix Riccati differential equation solves the...

Aircraft Reactor Experiment, a US military program in the 1950s Algebraic Riccati equation, in control theory Asymptotic relative efficiency, in statistics AU-rich...

f_{0}(x)=0} , the equation reduces to a Bernoulli equation, while if f 3 ( x ) = 0 {\displaystyle f_{3}(x)=0} the equation reduces to a Riccati equation. The substitution...

positive definite solution of the conjugate discrete-time algebraic Riccati equation, Journal of Computational and Applied Mathematics, Volume 350, Pages...

hypothetical cylindrical infinite potential barrier. This differential equation, and the Riccati–Bessel solutions, also arises in the problem of scattering of...

Sylvester equation has a closed form solution. Lyapunov equation, a special case of the Sylvester equation Algebraic Riccati equation This equation is also...

response matrix of the state equation, but still with a linear state equation and quadratic objective function, a Riccati equation can still be obtained for...

v^{2}AC_{d}.} Although this is a Riccati equation that can be solved by reduction to a second-order linear differential equation, it is easier to separate variables...

continuous time. The second differential equation, for the covariance, is an example of a Riccati equation. Nonlinear generalizations to Kalman–Bucy...

stations and advertisement sales representatives Discrete Algebraic Riccati equation, a mathematical relationship Drug Abuse Resistance Education, an anti-drug...

Sciences. Riccati's main research continued the work of his father in mathematical analysis, especially in the fields of the differential equations and physics...

Optimal projection equations — method for reducing dimension of LQG control problem Algebraic Riccati equation — matrix equation occurring in many optimal...