For earth observation from a three-axis stabilized geostationary (GEO) remote-sensing satellite, a highly accurate onboard thermal motion compensation (TMC) method for real-time correction of the satellite sensor’s line-of-sight (LOS) pointing error due to thermally induced structural distortion internal to the sensor during the diurnal cycle remains a global concern to date. In this letter, we propose a novel TMC method for GEO sensors. Compared with the traditional TMC methods, this method has the following two advantages. First, we define the LOS misalignment angle to model the comprehensive impact of the sensor’s internal thermal misalignment angles on the sensor’s LOS pointing behavior, which makes the optical path modeling simpler and more generic. Second, we fit the repeatable diurnal variations of the LOS misalignment angle based on long time-series star observations; therefore, the calculation and the use of the TMC amount are no longer limited to the assumption that the sensor’s internal thermal misalignment angles remain constant within a certain period of time, as in the traditional method. The proposed TMC method is theoretically applicable to all types of GEO sensors, including optical and microwave sensors, and is verified by Fengyun-4A advanced geosynchronous radiation imager (FY-4A/AGRI) TMC experiments.

This paper is concerned with the connection between the local maximum principle and the dynamic programming principle for controlled fully coupled forward-backward stochastic differential equations (FBSDEs) when the control domain is convex and the diffusion term does not contain the variable z. The relation among the adjoint variables and the value function is obtained within the viscosity solution framework. The first-order adjoint equation of [M. S. Hu, S. L. Ji and X. L. Xue, A global stochastic maximum principle for fully coupled forward-backward stochastic systems, arXiv: 1803.02109] can be derived from the adjoint FBSDE of [Z. Wu, Maximum principle for optimal control problem of fully coupled forward-backward stochastic systems, Systems Science and Mathematical Sciences, vol. 11, 1998, pp. 249-259], by our main theorem. Additionally, we give an example to show the applications of the theoretical result.

This paper studies the optimal control problem for stochastic differential equations (SDEs) of mean-field type, in which the coefficients depend on the state of the solution process as well as its expected value. Moreover, the cost functional is also of mean-field type. This makes the control problem time inconsistent in the sense that the Bellman optimality principle does not hold. It is shown that the necessary conditions of optimality (Buckdahn et al., Appl. Math. Optim., vol. 64, pp. 197-216, 2011), along with some convexity/concavity conditions, constitute sufficient conditions of optimality for such problems. As an illustrating example, we apply the result to the linear quadratic stochastic optimal control problem of mean-field type.