Exact and Approximate Convex Reformulation of Linear Stochastic Optimal Control with Chance Constraints
This work addresses control under uncertainty for applications like robotics, offering less conservative solutions, though it is incremental in refining existing convex optimization approaches.
The paper tackled the problem of stochastic optimal control with chance constraints by presenting an exact convex reformulation for linear constraints and a tight convex relaxation for quadratic constraints, achieving strict improvements in feasibility and optimality, with validation showing feasibility at noise levels an order of magnitude beyond prior methods.
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.