Families of Control-Cost-Parametrized Inverse-Optimal Universal Stabilizers
2026-06-08 • Machine Learning
Machine Learning
AI summaryⓘ
The authors present a new way to create stabilizing control systems that lets users flexibly choose how costly control actions are, unlike traditional methods that have no user options. They develop a mathematical formula that adjusts an existing controller based on this chosen cost, involving complex function operations. Their approach allows for efficient approximations using neural networks and guarantees stable control with predictable performance. This method is called 'half-direct-optimal' because it balances between fully optimal control design and fully inverse optimal control. The authors also show their method working through computer simulations.
stabilizing feedback lawinverse optimal controlnonlinear operatorLipschitz continuityinfinite-horizon optimal controlneural operator approximationsemiglobal practical asymptotic stabilitysuboptimality boundscontrol cost functional
Authors
Miroslav Krstic, Luke Bhan
Abstract
A classical universal stabilization formula offers the practitioner no design freedom: it is a single, parameter-free object. We introduce a cost-parametrized family of stabilizing feedback laws, where (1) the user chooses a function that serves as the running cost on control in an inverse-optimal cost functional, and (2) obtains, through a formula, a nonlinear "expander" of a pre-existing universal controller, which solves an infinite-horizon optimal control problem with a meaningful cost on the state. The cost-to-expander formula is a three-step construction, involving, inter alia, cost differentiation and function inversion-overall, a nonlinear infinite-dimensional operator. The cost-to-expander operator is proven Lipschitz, which enables uniform neural operator approximation of the entire family and supports both offline performance exploration and online adaptation. Semiglobal practical asymptotic stability and second-order suboptimality bounds are established under the approximation. The operator learning and its use in semiglobal stabilization are illustrated numerically. We call the result 'half-direct-optimal' because the paper's design is less than a general 'direct optimal' (HJB-inducing) control, but more than the fully inverse optimal, since the user performs minimization for an arbitrary given cost on control. The dual to the half-direct problem we solve is the problem in which the cost on the state is arbitrary and given. This dual problem is easier and outside of the scope of the paper.