Stochastic Game Theoretic trajectory optimization in continuous time
Stochastic Game Theoretic trajectory optimization in continuous time
复制标题
连续时间内的随机博弈论轨迹优化
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
P. Tsiotras
中科院分区：
文献类型：
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作者：
Wei Sun;Evangelos A. Theodorou;P. Tsiotras
提出了一种求解随机动态微分对策问题的随机博弈论微分动态规划(SGT-DDP)算法。我们给出了两个局中人的最小化和最大化控制的更新律，并给出了一组二阶值函数逼近的向后微分方程组。与原GTDDP相比，我们计算了由随机假设产生的后向传播方程中的附加项。给出了SGT-DDP算法，并在博弈论模型下分析了代价函数的设计对控制策略的前馈和反馈部分的影响。然后通过对一阶非线性系统、倒立摆和小车极点冲突控制问题的仿真研究了SGT-DDP的性能。我们以一些未来可能的扩展来结束。
A Stochastic Game Theoretic Differential Dynamic Programming (SGT-DDP) algorithm is derived to solve a differential game under stochastic dynamics. We present the update law for the minimizing and maximizing controls for both players and provide a set of backward differential equations for the second order value function approximation. We compute the extra terms in the backward propagation equations that arise from the stochastic assumption compared with the original GTDDP. We present the SGT-DDP algorithm and analyze how the design of the cost function affects the feed-forward and feedback parts of the control policies under the game theoretic formulation. The performance of SGT-DDP is then investigated through simulations on two examples, namely, a first order nonlinear system, the inverted pendulum and the cart pole problems with conflicting controls. We conclude with some possible future extensions.