Abstract
This paper addresses a version of the stochastic linear quadratic control problem on time scales S Δ LQ , which includes the discrete time and continuous time as special cases. Riccati equations on time scales are given, and the optimal control can be expressed as a linear state feedback. Furthermore, we present the uniqueness and existence of the solution to the Riccati equation on time scales. Furthermore, we give an example to illustrate the theoretical results.
Highlights
Time scales were first introduced by Hilger [4] in 1988 in order to unite and extend the continuous and discrete analysis into a general framework
The stochastic linear quadratic control problem is studied in the version of time scales
It is well known that the optimal control problem on time scales is an important field for both theory and applications
Summary
Time scales were first introduced by Hilger [4] in 1988 in order to unite and extend the continuous and discrete analysis into a general framework. The stochastic linear quadratic control problem is studied in the version of time scales. E existence of optimal control for the dynamic systems on time scales was considered in [14, 15]. In [18, 19], some results were obtained for the deterministic linear quadratic control problems on time scales.
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