Uncertain optimal control of linear quadratic models with jump. (English) Zbl 1286.93202

Summary: Based on the uncertain optimal control with jump, in this paper, we study a kind of special uncertain optimal control problem: linear-quadratic \((LQ)\) uncertain optimal control problem with jump which has a quadratic objective function for a linear uncertain control system with jump. We obtain a necessary and sufficient condition for the existence of optimal control. As an application, we discuss an uncertain \(LQ\) optimal control problem for the enterprize’s investment decisions.


93E20 Optimal stochastic control
49N10 Linear-quadratic optimal control problems
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