Stochastic Optimal Avoidance of Multiple Engagement Zones

This work formulates the feedback control strategies for vehicles to reach a goal point amongst a field of dynamic risk regions. Whereas previous work has considered deterministic versions of this problem, we consider the scenario in the context of uncertainty. This uncertainty could be due to unknown wind or other external disturbances. The risk regions’ dynamics are tightly coupled to the state of the vehicle and as a result the task of navigating through a field dynamically changes as the vehicle traverses through it. Rather than using a nonlinear program solver, the approach taken here is one of formulating the problem as a stochastic optimal control problem wherein a feedback control law is derived. This feedback control law allows a single or multiple vehicles to reach the desired goal location efficiently and with minimal risk incursion. When inside a risk region, there is a probability rate of the vehicle being neutralized. The stochastic dynamical system is modeled as a hybrid system, i.e., regime switching diffusion. The hybrid system is comprised of continuous spatial dynamics and discrete operational states corresponding to “normal” and “neutralized”. The optimal control problem is discretized into a field of vehicle states and control. Using Value Iteration, the control signal at each discrete location is optimized, providing a feedback control strategy over the field. Following a discussion of the methods and approaches, this problem is formulated, simulations are performed, and conclusions and remarks are made.