Linear quadratic Pareto optimal control problem of stochastic singular systems

This paper is concerned with the finite horizon linear quadratic (LQ) Pareto optimal control problem of stochastic singular systems. By means of the square completion technique, for the finite horizon LQ optimal control of stochastic singular systems, we establish a new kind of generalized differential Riccati equations (GDREs) and present the existence condition of the solution of the GDREs. Then, for the finite horizon LQ Pareto optimal control, it is shown that under the solvability of the corresponding GDREs, all Pareto candidates can be obtained by solving a weighting sum optimal control. Finally, an example is provided to show the effectiveness of our main results.