Our papers on safety-critical control via recurrent tracking functions [1] and on data-driven practical stabilization via chain policies [2] have been accepted to the American Control Conference. Congrats Jixian and Roy!
[Bibtex] [Abstract] [Download PDF]
This paper addresses the challenge of synthesizing safety-critical controllers for high-order nonlinear systems, where constructing valid Control Barrier Functions (CBFs) remains computationally intractable. Leveraging layered control, we design CBFs in reduced-order models (RoMs) while regulating full-order models’ (FoMs) dynamics at the same time. Traditional Lyapunov tracking functions are required to decrease monotonically, but systematic synthesis methods for such functions exist only for fully-actuated systems. To overcome this limitation, we introduce Recurrent Tracking Functions (RTFs), which replace the monotonic decay requirement with a weaker finite-time recurrence condition. This relaxation permits transient deviations of tracking errors while ensuring safety. By augmenting CBFs for RoMs with RTFs, we construct recurrent CBFs (RCBFs) whose zero-superlevel set is control $τ$-recurrent, and guarantee safety for all initial states in such a set when RTFs are satisfied. We establish theoretical safety guarantees and validate the approach through numerical experiments, demonstrating RTFs’ effectiveness and the safety of FoMs.
@inproceedings{lm2026acc,
abstract = {This paper addresses the challenge of synthesizing safety-critical controllers for high-order nonlinear systems, where constructing valid Control Barrier Functions (CBFs) remains computationally intractable. Leveraging layered control, we design CBFs in reduced-order models (RoMs) while regulating full-order models' (FoMs) dynamics at the same time. Traditional Lyapunov tracking functions are required to decrease monotonically, but systematic synthesis methods for such functions exist only for fully-actuated systems. To overcome this limitation, we introduce Recurrent Tracking Functions (RTFs), which replace the monotonic decay requirement with a weaker finite-time recurrence condition. This relaxation permits transient deviations of tracking errors while ensuring safety. By augmenting CBFs for RoMs with RTFs, we construct recurrent CBFs (RCBFs) whose zero-superlevel set is control $τ$-recurrent, and guarantee safety for all initial states in such a set when RTFs are satisfied. We establish theoretical safety guarantees and validate the approach through numerical experiments, demonstrating RTFs' effectiveness and the safety of FoMs.},
author = {Liu, Jixian and Mallada, Enrique},
bdsk-url-3 = {https://doi.org/10.23919/ACC55779.2023.10156212},
booktitle = {American Control Conference (ACC)},
grants = {Global-Centers-2330450; DOE-ASCR-826565},
month = {5},
pages = {1-7},
pubstate = {accepted},
record = {accepted Feb. 2026, submitted Sep. 2025},
title = {Safety-Critical Control via Recurrent Tracking Functions},
url = {https://mallada.ece.jhu.edu/pubs/2026-ACC-LM.pdf},
year = {2026}
}[Bibtex] [Abstract] [Download PDF]
We propose a method for data-driven practical stabilization of nonlinear systems with provable guarantees, based on the concept of \emphNonparametric Chain Policies (NCPs). The approach employs a normalized nearest-neighbor rule to assign, at each state, a finite-duration control signal derived from stored data, after which the process repeats. Unlike recent works that model the system as linear, polynomial, or polynomial fraction, we only assume the system to be locally Lipschitz. Our analysis build son the framework of Recurrent Lyapunov Functions (RLFs), which enable data-driven certification of (practical) stability using standard norm functions instead of requiring the explicit construction of a classical Lyapunov function. To extend this framework, we introduce the concept of Recurrent Control Lyapunov Functions (R-CLFs), which can certify the existence of an NCP that practically stabilizes an arbitrarily small $c$-neighborhood of an equilibrium point. We also provide an explicit sample complexity guarantee of $\mathcalO\!łeft((3/h̊o)^d łog(R/c)\g̊ht)$ number of trajectories—where $R$ is the domain radius, $d$ the state dimension, and $\r$̊ a system-dependent constant. The proposed Chain Policies are nonparametric, thus allowing new verified data to be readily incorporated into the policy to either improve convergence rate or enlarge the certified region. Numerical experiments illustrate and validate these properties.
@inproceedings{sm2026acc,
abstract = {We propose a method for data-driven practical stabilization of nonlinear systems with provable guarantees, based on the concept of \emphNonparametric Chain Policies (NCPs). The approach employs a normalized nearest-neighbor rule to assign, at each state, a finite-duration control signal derived from stored data, after which the process repeats.
Unlike recent works that model the system as linear, polynomial, or polynomial fraction, we only assume the system to be locally Lipschitz.
Our analysis build son the framework of Recurrent Lyapunov Functions (RLFs), which enable data-driven certification of (practical) stability using standard norm functions instead of requiring the explicit construction of a classical Lyapunov function. To extend this framework, we introduce the concept of Recurrent Control Lyapunov Functions (R-CLFs), which can certify the existence of an NCP that practically stabilizes an arbitrarily small $c$-neighborhood of an equilibrium point.
We also provide an explicit sample complexity guarantee of $\mathcalO\!łeft((3/h̊o)^d łog(R/c)\g̊ht)$ number of trajectories---where $R$ is the domain radius, $d$ the state dimension, and $\r$̊ a system-dependent constant. The proposed Chain Policies are nonparametric, thus allowing new verified data to be readily incorporated into the policy to either improve convergence rate or enlarge the certified region. Numerical experiments illustrate and validate these properties.},
author = {Siegelmann, Roy and Mallada, Enrique},
bdsk-url-3 = {https://doi.org/10.23919/ACC55779.2023.10156212},
booktitle = {American Control Conference (ACC)},
grants = {Global-Centers-2330450; DOE-ASCR-826565},
month = {5},
pages = {1-8},
pubstate = {accepted},
record = {accepted Feb. 2026, submitted Sep. 2025},
title = {Data-driven Practical Stabilization of Nonlinear Systems via Chain Policies: Sample Complexity and Incremental Learning},
url = {https://mallada.ece.jhu.edu/pubs/2026-ACC-SgM.pdf},
year = {2026}
}