[ { "id": "authors:j6jkn-nj815", "collection": "authors", "collection_id": "j6jkn-nj815", "cite_using_url": "https://authors.library.caltech.edu/records/j6jkn-nj815", "type": "article", "title": "Combinatorial Control Barrier Functions: Nested Boolean and p-choose-r Compositions of Safety Constraints", "author": [ { "family_name": "Ong", "given_name": "Pio", "orcid": "0000-0002-9665-1320", "clpid": "Ong-Pio" }, { "family_name": "Lee", "given_name": "Haejoon", "orcid": "0009-0001-1330-5087" }, { "family_name": "Molnar", "given_name": "Tamas G.", "orcid": "0000-0002-9379-7121" }, { "family_name": "Panagou", "given_name": "Dimitra", "orcid": "0000-0002-4547-167X" }, { "family_name": "Ames", "given_name": "Aaron D.", "orcid": "0000-0003-0848-3177", "clpid": "Ames-A-D" } ], "abstract": "

This letter investigates the problem of composing multiple control barrier functions (CBFs)—and matrix control barrier functions (MCBFs)—through logical and combinatorial operations. Standard CBF formulations naturally enable conjunctive (AND) combinations, but disjunctive (OR) and more general logical structures introduce nonsmoothness and possibly a combinatorial blow-up in the number of logical combinations. We introduce the framework of combinatorial CBFs that addresses p-choose-r safety specifications and their nested composition. The proposed framework ensures safety for the exact safe set in a scalable way, using the original number of primitive constraints. We establish theoretical guarantees on safety under these compositions, and we demonstrate their use on a patrolling problem in a multi-agent system.

", "doi": "10.1109/lcsys.2025.3640191", "issn": "2705 - 2710", "publisher": "IEEE", "publication": "IEEE Control Systems Letters", "publication_date": "2025-12-03", "volume": "9", "pages": "1-1" }, { "id": "authors:63dth-90524", "collection": "authors", "collection_id": "63dth-90524", "cite_using_url": "https://authors.library.caltech.edu/records/63dth-90524", "type": "article", "title": "Characterizing Smooth Safety Filters via the Implicit Function Theorem", "author": [ { "family_name": "Cohen", "given_name": "Max H.", "orcid": "0000-0001-6957-9645", "clpid": "Cohen-Max-H" }, { "family_name": "Ong", "given_name": "Pio", "orcid": "0000-0002-9665-1320", "clpid": "Ong-Pio" }, { "family_name": "Bahati", "given_name": "Gilbert", "clpid": "Bahati-Gilbert" }, { "family_name": "Ames", "given_name": "Aaron D.", "orcid": "0000-0003-0848-3177", "clpid": "Ames-A-D" } ], "abstract": "
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Optimization-based safety filters, such as control barrier function (CBF) based quadratic programs (QPs), have demonstrated success in controlling autonomous systems to achieve complex goals. These CBF-QPs can be shown to be continuous, but are generally not smooth, let alone continuously differentiable. In this letter, we present a general characterization of smooth safety filters – smooth controllers that guarantee safety in a minimally invasive fashion – based on the Implicit Function Theorem. This characterization leads to families of smooth universal formulas for safety-critical controllers that quantify the conservatism of the resulting safety filter, the utility of which is demonstrated through illustrative examples.
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", "doi": "10.1109/lcsys.2023.3341345", "issn": "2475-1456", "publisher": "IEEE", "publication": "IEEE Control Systems Letters", "publication_date": "2023-12-11", "volume": "7", "pages": "3890-3895" }, { "id": "authors:18nmc-z8947", "collection": "authors", "collection_id": "18nmc-z8947", "cite_using_url": "https://authors.library.caltech.edu/records/18nmc-z8947", "type": "conference_item", "title": "Intermittent Safety Filters for Event-Triggered Safety Maneuvers with Application to Satellite Orbit Transfers", "book_title": "2023 62nd IEEE Conference on Decision and Control (CDC)", "author": [ { "family_name": "Ong", "given_name": "Pio", "orcid": "0000-0002-9665-1320", "clpid": "Ong-Pio" }, { "family_name": "Ames", "given_name": "Aaron D.", "orcid": "0000-0003-0848-3177", "clpid": "Ames-A-D" } ], "abstract": "
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In balancing safety with the nominal control objectives, e.g., stabilization, it is desirable to reduce the time period when safety filters are in effect. Inspired by traditional spacecraft maneuvers, and with the ultimate goal of reducing the duration when safety is of concern, this paper proposes an event-triggered control framework with switching state-based triggers. Our first trigger in the scheme monitors safety constraints encoded by barrier functions, and thereby ensures safety without the need to alter the nominal controller—and when the boundary of the safety constraint is approached, the controller drives the system to the region where control actions are not needed. The second trigger condition determines if the safety constraint has improved enough for the success of the first trigger. We begin by motivating this framework for impulsive control systems, e.g., a satellite orbiting an asteroid. We then expand the approach to a more general nonlinear system through the use of safety-filtered controllers. Simulation results demonstrating satellite orbital maneuvers illustrate the utility of the proposed event-triggered framework.
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", "doi": "10.1109/cdc49753.2023.10383437", "isbn": "979-8-3503-0124-3", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2023-12", "pages": "870-877" }, { "id": "authors:3b3tb-r2g71", "collection": "authors", "collection_id": "3b3tb-r2g71", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220714-194256328", "type": "monograph", "title": "Stability and Safety through Event-Triggered Intermittent Control with Application to Spacecraft Orbit Stabilization", "author": [ { "family_name": "Ong", "given_name": "Pio", "orcid": "0000-0002-9665-1320", "clpid": "Ong-Pio" }, { "family_name": "Bahati", "given_name": "Gilbert", "clpid": "Bahati-Gilbert" }, { "family_name": "Ames", "given_name": "Aaron D.", "orcid": "0000-0003-0848-3177", "clpid": "Ames-A-D" } ], "abstract": "In systems where the ability to actuate is a scarce resource, e.g., spacecrafts, it is desirable to only apply a given controller in an intermittent manner--with periods where the controller is on and periods where it is off. Motivated by the event-triggered control paradigm, where state-dependent triggers are utilized in a sample-and-hold context, we generalize this concept to include state triggers where the controller is off thereby creating a framework for intermittent control. Our approach utilizes certificates--either Lyapunov or barrier functions--to design intermittent trigger laws that guarantee stability or safety; the controller is turned on for the period for which is beneficial with regard to the certificate, and turned off until a performance threshold is reached. The main result of this paper is that the intermittent controller scheme guarantees (set) stability when Lyapunov functions are utilized, and safety (forward set invariance) in the setting of barrier functions. As a result, our trigger designs can leverage the intermittent nature of the actuator, and at the same time, achieve the task of stabilization or safety. We further demonstrate the application and benefits of intermittent control in the context of the spacecraft orbit stabilization problem.", "doi": "10.48550/arXiv.arXiv.2204.03110", "publisher": "arXiv", "publication_date": "2022-04-06" }, { "id": "authors:jz2q3-n3386", "collection": "authors", "collection_id": "jz2q3-n3386", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220714-194252464", "type": "monograph", "title": "Safe Backstepping with Control Barrier Functions", "author": [ { "family_name": "Taylor", "given_name": "Andrew J.", "orcid": "0000-0002-5990-590X", "clpid": "Taylor-Andrew-J" }, { "family_name": "Ong", "given_name": "Pio", "orcid": "0000-0002-9665-1320", "clpid": "Ong-Pio" }, { "family_name": "Moln\u00e1r", "given_name": "Tam\u00e1s G.", "orcid": "0000-0002-9379-7121", "clpid": "Moln\u00e1r-Tam\u00e1s-G" }, { "family_name": "Ames", "given_name": "Aaron D.", "orcid": "0000-0003-0848-3177", "clpid": "Ames-A-D" } ], "abstract": "Complex control systems are often described in a layered fashion, represented as higher-order systems where the inputs appear after a chain of integrators. While Control Barrier Functions (CBFs) have proven to be powerful tools for safety-critical controller design of nonlinear systems, their application to higher-order systems adds complexity to the controller synthesis process -- it necessitates dynamically extending the CBF to include higher order terms, which consequently modifies the safe set in complex ways. We propose an alternative approach for addressing safety of higher-order systems through Control Barrier Function Backstepping. Drawing inspiration from the method of Lyapunov backstepping, we provide a constructive framework for synthesizing safety-critical controllers and CBFs for higher-order systems from a top-level dynamics safety specification and controller design. Furthermore, we integrate the proposed method with Lyapunov backstepping, allowing the tasks of stability and safety to be expressed individually but achieved jointly. We demonstrate the efficacy of this approach in simulation.", "doi": "10.48550/arXiv.arXiv.2204.00653", "publisher": "arXiv", "publication_date": "2022-04-01" }, { "id": "authors:6k18b-jpa21", "collection": "authors", "collection_id": "6k18b-jpa21", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200706-084348576", "type": "article", "title": "Safety-Critical Event Triggered Control via Input-to-State Safe Barrier Functions", "author": [ { "family_name": "Taylor", "given_name": "Andrew J.", "orcid": "0000-0002-5990-590X", "clpid": "Taylor-Andrew-J" }, { "family_name": "Ong", "given_name": "Pio", "orcid": "0000-0002-9665-1320", "clpid": "Ong-Pio" }, { "family_name": "Cort\u00e9s", "given_name": "Jorge", "orcid": "0000-0001-9582-5184", "clpid": "Cort\u00e9s-J" }, { "family_name": "Ames", "given_name": "Aaron D.", "orcid": "0000-0003-0848-3177", "clpid": "Ames-A-D" } ], "abstract": "The efficient utilization of available resources while simultaneously achieving control objectives is a primary motivation in the event-triggered control paradigm. In many modern control applications, one such objective is enforcing the safety of a system. The goal of this paper is to carry out this vision by combining event-triggered and safety-critical control design. We discuss how a direct transcription, in the context of safety, of event-triggered methods for stabilization may result in designs that are not implementable on real hardware due to the lack of a minimum interevent time. We provide an example showing this phenomena and, building on the insight gained, propose an event-triggered control approach via Input-to-State Safe Barrier Functions that achieves safety while ensuring that interevent times are uniformly lower bounded.", "doi": "10.1109/lcsys.2020.3005101", "issn": "2475-1456", "publisher": "IEEE", "publication": "IEEE Control Systems Letters", "publication_date": "2021-07", "series_number": "3", "volume": "5", "issue": "3", "pages": "749-754" } ]