arXiv subjects
Publications and source records attributed to Vittorio De Iuliis.
We present a candidate counterexample to a conjecture stating that the existence of a Lyapunov-Krasovskii functional with a pointwise dissipation rate is sufficient for the input-to-state stability of time-delay systems. The counterexample has been derived through interactions with large language models.
This paper proposes modifications to the data-enabled policy optimization (DeePO) algorithm to mitigate state perturbations. DeePO is an adaptive, data-driven approach designed to iteratively compute a feedback gain equivalent to the certainty-equivalence LQR gain. Like other data-driven approaches based on Willems' fundamental lemma, DeePO requires persistently exciting input signals. However, linear state-feedback gains from LQR designs cannot inherently produce such inputs. To address this, probing noise is conventionally added to the control signal to ensure persistent excitation. However, the added noise may induce undesirable state perturbations. We first identify two key issues that jeopardize the desired performance of DeePO when probing noise is not added: the convergence of states to the equilibrium point, and the convergence of the controller to its optimal value. To address these challenges without relying on probing noise, we propose Perturbation-Free DeePO (PFDeePO) built on two fundamental principles. First, the algorithm pauses the control gain updating in DeePO process when system states are near the equilibrium point. Second, it applies a multiplicative noise, scaled by a mean value of $1$ as a gain for the control signal, when the controller converges. This approach minimizes the impact of noise as the system approaches equilibrium while preserving stability. We demonstrate the effectiveness of PFDeePO through simulations, showcasing its ability to eliminate state perturbations while maintaining system performance and stability.