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arXiv · 2607.03952

L1 Optimal Control of Continuous-Time Stochastic Positive Systems

Alba Gurpegui·Takashi Tanaka·Anders Rantzer
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Abstract

We present an L1-optimal control problem class with linear nonnegative costs subject to multiplicative It\^o diffusion processes with elementwise linear input constraints. Forward invariance of the positive orthant is established for the considered stochastic dynamics, and a simulation method consistent with this invariance property is proposed. Both finite-horizon and discounted infinite-horizon stochastic L1-optimal control problems are considered. These problems admit explicit solutions characterized by a vector-valued ordinary differential equation in the finite-horizon case and by an algebraic equation in the infinite-horizon case. Notably, the optimal value function and feedback policy coincide with those of the corresponding deterministic problem, demonstrating robustness to multiplicative stochastic uncertainty. A portfolio example illustrates our results.

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Alba Gurpegui, Takashi Tanaka, Anders Rantzer. 2026-07-04. L1 Optimal Control of Continuous-Time Stochastic Positive Systems. https://arxiv.org/abs/2607.03952

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