A compositional approach to stochastic optimal control with co-safe temporal logic specifications
A compositional approach to stochastic optimal control with co-safe temporal logic specifications
复制标题
具有共同安全时序逻辑规范的随机最优控制组合方法
DOI：
10.1109/iros.2014.6942750
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
R. Murray
中科院分区：
文献类型：
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作者：
Matanya B. Horowitz;Eric M. Wolff;R. Murray
我们介绍了一种算法的最优控制随机非线性系统的时间逻辑约束的行为。我们直接在系统的状态空间上计算，避免了离散抽象的昂贵的预计算。对应于时序逻辑规范的自动机指导控制策略的计算，该控制策略最大化系统满足规范的概率。这减少了控制器的合成解决一系列的随机约束的可达性问题。每个个体的可达性问题通过随机最优控制理论中的Hamilton-Jacobi-Bellman（HJB）偏微分方程求解。为了提高我们的方法的效率，我们利用一类系统的HJB方程是线性的，由于噪声的结构假设。偏微分方程的线性允许我们预先计算控制策略原语，然后以基本上为零的成本将它们组合起来，以保守地满足复杂的时序逻辑规范。
We introduce an algorithm for the optimal control of stochastic nonlinear systems subject to temporal logic constraints on their behavior. We compute directly on the state space of the system, avoiding the expensive pre-computation of a discrete abstraction. An automaton that corresponds to the temporal logic specification guides the computation of a control policy that maximizes the probability that the system satisfies the specification. This reduces controller synthesis to solving a sequence of stochastic constrained reachability problems. Each individual reachability problem is solved via the Hamilton-Jacobi-Bellman (HJB) partial differential equation of stochastic optimal control theory. To increase the efficiency of our approach, we exploit a class of systems where the HJB equation is linear due to structural assumptions on the noise. The linearity of the partial differential equation allows us to pre-compute control policy primitives and then compose them, at essentially zero cost, to conservatively satisfy a complex temporal logic specification.