Safety critical systems involve the tight coupling between potentially conflicting control objectives and safety constraints. As a means of creating a formal framework for controlling systems of this form, and with a view toward automotive applications, this paper develops a methodology that allows safety conditions—expressed as control barrier functions —to be unified with performance objectives—expressed as control Lyapunov functions—in the context of real-time optimization-based controllers. Safety conditions are specified in terms of forward invariance of a set, and are verified via two novel generalizations of barrier functions; in each case, the existence of a barrier function satisfying Lyapunov-like conditions implies forward invariance of the set, and the relationship between these two classes of barrier functions is characterized. In addition, each of these formulations yields a notion of control barrier function (CBF), providing inequality constraints in the control input that, when satisfied, again imply forward invariance of the set. Through these constructions, CBFs can naturally be unified with control Lyapunov functions (CLFs) in the context of a quadratic program (QP); this allows for the achievement of control objectives (represented by CLFs) subject to conditions on the admissible states of the system (represented by CBFs). The mediation of safety and performance through a QP is demonstrated on adaptive cruise control and lane keeping, two automotive control problems that present both safety and performance considerations coupled with actuator bounds.

https://ieeexplore.ieee.org/ielaam/9/7993115/7782377-aam.pdf

Control Barrier Function Based Quadratic Programs for Safety Critical Systems

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L2 Gain And Passivity Techniques In Nonlinear Control

This paper provides an introduction and overview of recent work on control barrier functions and their use to verify and enforce safety properties in the context of (optimization based) safety-critical controllers. We survey the main technical results and discuss applications to several domains including robotic systems.

/pdf/control-barrier-functions-theory-and-applications-2et3txgks8.pdf

Control Barrier Functions: Theory and Applications

We introduce Exponential Control Barrier Functions as means to enforce strict state-dependent high relative degree safety constraints for nonlinear systems. We also develop a systematic design method that enables creating the Exponential CBFs for nonlinear systems making use of tools from linear control theory. The proposed control design is numerically validated on a relative degree 6 linear system (the serial cart-spring system) and on a relative degree 4 nonlinear system (the two-link pendulum with elastic actuators.)

Exponential Control Barrier Functions for enforcing high relative-degree safety-critical constraints

In this paper, we propose a nonlinear control design for solving the problem of stabilization with guaranteed safety. The design is based on the merging of a Control Lyapunov Function and a Control Barrier Function. The proposed control method allows us to combine the design of a stabilizer based on CLF and the design of safety control based on CBF. The efficacy of the proposed approach is shown in the simulation results.

Uniting Control Lyapunov and Control Barrier Functions

In this paper, we study robustness analysis of systems' safety with respect to external input (or disturbance) signals. To this end, we introduce a new notion of input-to-state safety (ISSf) which allows us to quantify the systems' safety robustness, in the same way as the application of input-to-state stability (ISS) notion for analyzing robustness of systems' stability. In particular, ISSf prescribes the relationship between the evolution of state distance to the unsafe set with the initial conditions and the bounded external input signals. Finally, we discuss how to combine this notion with ISS for analyzing the robustness of both systems' stability and safety.

/pdf/on-the-new-notion-of-input-to-state-safety-2jb644by8f.pdf

On the new notion of input-to-state safety

In this paper, we propose a new robustness notion that is applicable for certifying systems' safety with respect to external disturbance signals. The proposed input-to-state safety (ISSf) notion allows us to certify systems' safety in the presence of the disturbances which is analogous to the notion of input-to-state stability (ISS) for analyzing systems' stability.

/pdf/robustness-analysis-of-systems-safety-through-a-new-notion-3dwusloo5j.pdf

Robustness Analysis of Systems' Safety through a New Notion of Input-to-State Safety

/pdf/passivity-based-control-with-guaranteed-safety-via-5xrfqfazar.pdf

Passivity-Based Control with Guaranteed Safety via Interconnection and Damping Assignment

In this paper, we present a novel notion of input-to-state safety (ISSf) for general nonlinear systems which can be useful for certifying system's safety under the influence of external bounded input (or disturbance) signals. We provide sufficient conditions for ISSf using barrier function/certificate which are analogous to the input-to-state stability Lyapunov function.

/pdf/on-the-sufficient-conditions-for-input-to-state-safety-55fkkhn4mc.pdf

Muhammad Zakiyullah Romdlony

Papers

Uniting Control Lyapunov and Control Barrier Functions

On the new notion of input-to-state safety

Robustness Analysis of Systems' Safety through a New Notion of Input-to-State Safety

Passivity-Based Control with Guaranteed Safety via Interconnection and Damping Assignment

On the sufficient conditions for input-to-state safety