2022/05/02 by Apurva Patil, Patil, Apurva, Alfredo Duarte +7 · 1 citation
Economics, Econometrics and Finance · Energy · Engineering · #Climate Change Policy and Economics #Energy, Environment, and Transportation Policies #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Robotics (cs.RO) #Systems and Control (eess.SY) #Water resources management and optimization #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2205.00628
openalex publication_date 2022/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper addresses a continuous-time continuous-space chance-constrained stochastic optimal control (SOC) problem via a Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE). Through Lagrangian relaxation, we convert the chance-constrained (risk-constrained) SOC problem to a risk-minimizing SOC problem, the cost function of which possesses the time-additive Bellman structure. We show that the risk-minimizing control synthesis is equivalent to solving an HJB PDE whose boundary condition can be tuned appropriately to achieve a desired level of safety. Furthermore, it is shown that the proposed risk-minimizing control problem can be viewed as a generalization of the problem of estimating the risk associated with a given control policy. Two numerical techniques are explored, namely the path integral and the finite difference method (FDM), to solve a class of risk-minimizing SOC problems whose associated HJB equation is linearizable via the Cole-Hopf transformation. Using a 2D robot navigation example, we validate the proposed control synthesis framework and compare the solutions obtained using path integral and FDM.