• 대한수학회지
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• 제38권1호
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• pp.177-191
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• 2001

We consider a linear differential game described by the delay-differential equation in a Hilbert space H; (※Equations, See Full-text) U and V are Hilbert spaces, and B(t) and C(t) are families of bounded operators on U and V to H, respectively. A(sub)0 generates an analytic semigroup T(t) = e(sup)tA(sub)0 in H. The control variables g, and u and v are supposed to be restricted in the norm bounded sets (※Equations, See Full-text). For given x(sup)0 ∈ H and a given time t > 0, we study $\xi$-approximate controllability to determine x($.$) for a given g and v($.$) such that the corresponding solution x(t) satisfies ∥x(t) - x(sup)0∥ $\leq$ $\xi$($\xi$ > 0 : a given error).

• 한국군사과학기술학회지
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• 제23권4호
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• pp.399-406
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• 2020

In this paper, we propose a time-varying proportional navigation guidance law that determines the proportional navigation gain in real-time according to the operating situation. When intercepting a target, an unidentified evasion strategy causes a loss of optimality. To compensate for this problem, proper proportional navigation gain is derived at every time step by solving an optimal control problem with the inferred evader's strategy. Recently, deep reinforcement learning algorithms are introduced to deal with complex optimal control problem efficiently. We adapt the actor-critic method to build a proportional navigation gain network and the network is trained by the Proximal Policy Optimization(PPO) algorithm to learn an evasion strategy of the target. Numerical experiments show the effectiveness and optimality of the proposed method.