Technology Category
Constraint Satisfaction and Optimization: Satisfiability Modulo TheoriesNatural Language Processing: Safety and RobustnessSearch and Optimization: Mixed Discrete/Continuous Search
Safety-Critical Control with Bounded Inputs: A Closed-Form Solution for Backup Control Barrier Functions
🤖 AI Summary
Real-time safety-critical control of input-constrained systems—particularly for resource-limited aerospace platforms—remains challenging due to the high computational cost of conventional backup Control Barrier Functions (bCBFs), which require online solution of high-dimensional quadratic programs.
Method: This paper proposes a closed-loop solvable bCBF framework. We derive, for the first time, an analytical closed-form solution to the bCBF optimization problem by optimally interpolating between a nominal controller and a backup controller, thereby jointly ensuring system safety and input boundedness without runtime numerical optimization.
Contribution/Results: The proposed method drastically reduces computational complexity while rigorously enforcing nonlinear safety constraints. Experimental validation on a double-integrator system and a nonlinear fixed-wing aircraft model demonstrates both theoretical safety guarantees and real-time feasibility. This work provides a provably safe, lightweight control solution tailored for computationally constrained platforms.
Technology Category
Application Category
📝 Abstract
Verifying the safety of controllers is critical for many applications, but is especially challenging for systems with bounded inputs. Backup control barrier functions (bCBFs) offer a structured approach to synthesizing safe controllers that are guaranteed to satisfy input bounds by leveraging the knowledge of a backup controller. While powerful, bCBFs require solving a high-dimensional quadratic program at run-time, which may be too costly for computationally-constrained systems such as aerospace vehicles. We propose an approach that optimally interpolates between a nominal controller and the backup controller, and we derive the solution to this optimization problem in closed form. We prove that this closed-form controller is guaranteed to be safe while obeying input bounds. We demonstrate the effectiveness of the approach on a double integrator and a nonlinear fixed-wing aircraft example.
Problem
Research questions and friction points this paper is trying to address.
Developing safe controllers for systems with bounded inputs
Eliminating computational costs of high-dimensional quadratic programs
Ensuring safety guarantees while obeying input constraints
Innovation
Methods, ideas, or system contributions that make the work stand out.
Closed-form solution for backup control barrier functions
Optimal interpolation between nominal and backup controllers
Guaranteed safety with bounded input constraints
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