Strong Duality and Dual Ascent Approach to Continuous-Time Chance-Constrained Stochastic Optimal Control
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909922282700800 |
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| author | Patil, Apurva Duarte, Alfredo Bisetti, Fabrizio Tanaka, Takashi |
| author_facet | Patil, Apurva Duarte, Alfredo Bisetti, Fabrizio Tanaka, Takashi |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_19451 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strong Duality and Dual Ascent Approach to Continuous-Time Chance-Constrained Stochastic Optimal Control Patil, Apurva Duarte, Alfredo Bisetti, Fabrizio Tanaka, Takashi Systems and Control Robotics 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. |
| title | Strong Duality and Dual Ascent Approach to Continuous-Time Chance-Constrained Stochastic Optimal Control |
| topic | Systems and Control Robotics |
| url | https://arxiv.org/abs/2511.19451 |