We consider the problem of adaptively monitoring a wildfire front using a mobile agent (e.g., a drone), whose trajectory determines where sensor data is collected and thus influences the accuracy of fire propagation estimation. This is a challenging problem, as the stochastic nature of wildfire evolution requires the seamless integration of sensing, estimation, and control, often treated separately in existing methods. State-of-the-art methods either impose linear-Gaussian assumptions to establish optimality or rely on approximations and heuristics, often without providing explicit performance guarantees. To address these limitations, we formulate the fire front monitoring task as a stochastic optimal control problem that integrates sensing, estimation, and control. We derive an optimal recursive Bayesian estimator for a class of stochastic nonlinear elliptical-growth fire front models. Subsequently, we transform the resulting nonlinear stochastic control problem into a finite-horizon Markov decision process and design an information-seeking predictive control law obtained via a lower confidence bound-based adaptive search algorithm with asymptotic convergence to the optimal policy.

翻译：本文研究利用移动智能体（如无人机）自适应监测野火火锋的问题，其飞行轨迹决定了传感器数据的采集位置，从而影响火势传播估计的精度。该问题具有挑战性，因为野火演化的随机性要求实现感知、估计与控制的无缝集成，而现有方法往往将三者割裂处理。当前最先进的方法要么强加线性高斯假设以建立最优性，要么依赖近似与启发式策略，通常无法提供明确的性能保证。为克服这些局限，我们将火锋监测任务形式化为一个集成感知、估计与控制的随机最优控制问题。针对一类随机非线性椭圆增长火锋模型，我们推导出最优递归贝叶斯估计器。随后，将所得非线性随机控制问题转化为有限时域马尔可夫决策过程，并通过基于置信下界的自适应搜索算法设计信息寻求预测控制律，该算法能以渐近收敛方式逼近最优策略。