A linear-quadratic optimal-control problem has linear state dynamics and running and terminal costs defined by quadratic forms. Its value function is quadratic in the state, the optimal feedback is linear, and its coefficient obeys a Riccati equation.
A backward scalar or matrix recurrence for the quadratic coefficients in a value function for a linear-quadratic optimal control problem. It results from completing the control square in the Bellman equation. Multiplicative noise modifies the quadratic coefficients through its second moments.

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  1. Hamilton-Jacobi-Bellman equation
  2. Bellman equation
  3. Dynamic programming
  4. Mathematical optimization
  5. Area of mathematics
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