Stability analysis of optimal control problems with time-dependent costs
Sifeddine Benahmed, Romain Postoyan, Mathieu Granzotto, Lucian, Bu\c{s}oniu, Jamal Daafouz, Dragan Ne\v{s}i\'c
TL;DR
This paper establishes stability conditions for nonlinear discrete-time systems with time-dependent costs, extending existing results on discounted control to more general systems and cost functions, ensuring global asymptotic and exponential stability.
Contribution
It generalizes stability analysis of optimal control problems to broader classes of systems and time-dependent costs, beyond discounted problems.
Findings
Established global asymptotic stability conditions.
Proved exponential stability for general attractors.
Extended stability results to non-discounted, time-varying costs.
Abstract
We present stability conditions for deterministic time-varying nonlinear discrete-time systems whose inputs aim to minimize an infinite-horizon time-dependent cost. Global asymptotic and exponential stability properties for general attractors are established. This work covers and generalizes the related results on discounted optimal control problems to more general systems and cost functions.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Adaptive Control of Nonlinear Systems · Advanced Control Systems Optimization