arXiv subjects

Alfredo Duarte

Publications and source records attributed to Alfredo Duarte.

2 recordsLinked to original sources

arXiv2025

Strong Duality and Dual Ascent Approach to Continuous-Time Chance-Constrained Stochastic Optimal Control

The paper addresses a continuous-time continuous-space chance-constrained stochastic optimal control (SOC) problem where the probability of failure to satisfy given state constraints is explicitly bounded. We leverage the notion of exit time from continuous-time stochastic calculus to formulate a chance-constrained SOC problem. Without any conservative approximation, the chance constraint is transformed into an expectation of an indicator function which can be incorporated into the cost function by considering a dual formulation. We then express the dual function in terms of the solution to a Hamilton-Jacobi-Bellman partial differential equation parameterized by the dual variable. Under a certain assumption on the system dynamics and cost function, it is shown that a strong duality holds between the primal chance-constrained problem and its dual. The Path integral approach is utilized to numerically solve the dual problem via gradient ascent using open-loop samples of system trajectories. We present simulation studies on chance-constrained motion planning for spatial navigation of mobile robots and the solution of the path integral approach is compared with that of the finite difference method.

eess.SY↗

arXiv2022

Chance-Constrained Stochastic Optimal Control via Path Integral and Finite Difference Methods

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.

math.OC↗