A deterministic affine-quadratic optimal control problem∗
School of Mathematics, Yunnan Normal University,
Kunming, 650500, P.R.
2 Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA
Received: 22 June 2013
Revised: 11 October 2013
A deterministic affine-quadratic optimal control problem is considered. Due to the nature of the problem, optimal controls exist under some very mild conditions. Further, it is shown that under some assumptions, the optimal control is unique which leads to the differentiability of the value function. Therefore, the value function satisfies the corresponding Hamilton–Jacobi–Bellman equation in the classical sense, and the optimal control admits a state feedback representation. Under some additional conditions, it is shown that the value function is actually twice differentiable and the so-called quasi-Riccati equation is derived, whose solution can be used to construct the state feedback representation for the optimal control.
Mathematics Subject Classification: 49J15 / 49K15 / 49L20 / 49N10
Key words: Affine quadratic optimal control / dynamic programming / Hamilton–Jacobi–Bellman equation / quasi-Riccati equation / state feedback representation
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