New Framework for Parametrized Optimal Control Stabilizers Using Neural Operators
A new preprint presents a cost-parametrized family of stabilizing feedback control laws that gives practitioners design freedom absent from classical universal stabilizers. The construction links a user-chosen control-cost function to a nonlinear 'expander' of an existing controller via a three-step operator, proven to be Lipschitz-continuous. This enables neural operator approximation of the entire controller family, supporting both offline tuning and online adaptation with formal stability and near-optimality guarantees.
Researchers at arXiv (cs.LG / eess.SY) have submitted a preprint introducing what they term 'half-direct-optimal' control: a framework that parametrizes a family of stabilizing feedback laws by the user's choice of running cost on control inputs. Classical universal stabilizers offer no such design freedom, producing a single fixed controller. The proposed cost-to-expander operator takes a user-specified cost function and outputs a nonlinear expansion of a pre-existing universal controller that solves an infinite-horizon optimal control problem with a meaningful state cost. The operator is proven Lipschitz-continuous, a property that guarantees uniform approximation by neural operators across the entire family of controllers. Under this approximation, the authors establish semiglobal practical asymptotic stability and second-order suboptimality bounds. Numerical experiments illustrate both the operator learning procedure and its application to semiglobal stabilization. The authors note a dual problem—where the state cost is arbitrary and given rather than the control cost—is theoretically easier but is left outside the scope of this work.
What's missing
As a preprint, this work has not yet undergone peer review. The paper does not benchmark the computational cost of the three-step operator against existing optimal control solvers. The scalability of the neural operator approximation to high-dimensional state spaces is not empirically demonstrated. The authors acknowledge the dual problem (arbitrary state cost) remains unsolved.
What different sources said
- arXiv cs.LGCenter
Families of Control-Cost-Parametrized Inverse-Optimal Universal Stabilizers
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