Exact and Approximate Convex Reformulation of Linear Stochastic Optimal Control with Chance Constraints

Tanmay Dokania; Yashwanth Kumar Nakka

eess.SYMar 19, 2026

Exact and Approximate Convex Reformulation of Linear Stochastic Optimal Control with Chance Constraints

Authors: Tanmay Dokania, Yashwanth Kumar Nakka

Organizations: Authors are with the Daniel Guggenheim School of Aerospace Engineering at the Georgia Institute of Technology, Atlanta, GA, 30332 USA.

Abstract

In this paper, we present an equivalent convex optimization formulation for discrete-time stochastic linear systems subject to linear chance constraints, alongside a tight convex relaxation for quadratic chance constraints. By lifting the state vector to encode moment information explicitly, the formulation captures linear chance constraints on states and controls across multiple time steps exactly, without conservatism, yielding strict improvements in both feasibility and optimality. For quadratic chance constraints, we derive convex approximations that are provably less conservative than existing methods. We validate the framework on minimum-snap trajectory generation for a quadrotor, demonstrating that the proposed approach remains feasible at noise levels an order of magnitude beyond the operating range of prior formulations.

Figures & tables

Panel of Figure 1 — Fig. 1 : Minimum Snap Path Planning for the linearized lateral dynamics of a quadrotor under the two different setups under stochastic perturbation forces ( $\sigma_{1}=\sigma_{2}=0.05$ ). The proposed approach leads to a cost reduction as compared to [ 7 ] , as it can shape the covariance.

TABLE II : Performance comparison across varying noise levels (

\sigma

) and environment parameters for the Circle Arena and Funnel Corridor scenarios.

\checkmark

and

\times

indicate successful completion and infeasibility, respectively.

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Jan 26, 2026J/K move · Enter open · S save

Convex Chance-Constrained Stochastic Control under Uncertain Specifications with Application to Learning-Based Hybrid Powertrain Control

Teruki Kato, Ryotaro Shima, Kenji Kashima

Toyota Central R&D Labs., Inc., Nagakute, Aichi, Japan · Graduate School of Informatics, Kyoto University, Kyoto, Japan

Chance-Constrained Optimization Stochastic Optimal Control

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This paper proposes a strictly convex chance-constrained stochastic control framework that accounts for uncertainty in control specifications such as reference trajectories and operational constraints. Control inputs and risk allocation are jointly optimized under general, possibly non-Gaussian, uncertainties through sufficient deterministic conditions for probabilistic constraint satisfaction. A decreasing risk regularizer ensures existence and full use of the allowable risk. Under the stated regularity assumptions, the joint solution is unique and locally Lipschitz-continuous, supporting stable numerical optimization. The formulation is extended to learning-based exactly linearizable (EL) models through monotone state and input transformations. A hybrid powertrain example compares deterministic control, equal risk allocation, and optimized risk allocation with and without regularization in terms of charge sustaining, constraint violations, closed-loop cost, and solver time.

Abstract

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