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This paper aims to deal with the indefinite linear quadratic regulator(ILQR) for stochastic systems. It provides both the analytic solution to the ILQR and the sufficient and necessary condition under which the ILQR is solvable. Different from the existed literature, we obtain the results in a novel way. In order to obtain a tighter necessary condition, we investigate the solution structure of a two-point...
In this paper, we established a rating charge model of transfer tax (RCTT) to solve transboundary air pollution control problem of China. Firstly, by using the bi-level nonlinear programming model. In this model, the leader is China's central government and the followers consist of China's 31 provinces. The leader aims to decrease the nation's total pollutant control costs, whereas each province attempts...
The main purpose of the paper is to provide the adapted and casual solution to the stochastic linear quadratic control problem for systems with multiple input-delays (SLQD). We introduce a special stochastic discrete-time maximum principle (SDMP) where instead of the admissible set consisting of the Fk−1-measurable control variable uk for any k, the admissible set is restricted to compose of the F...
The main purpose of the paper is to settle the stochastic linear quadratic control problem for systems with multiple input-delays (SDLQ) which is very intractable and remains to be solved. We introduce a different version of stochastic discrete-time maximum principle (SDMP) where it is shown that the auxiliary variable depends on the optimal system state through a stochastic matrix and the expectation...
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