Safety-Critical Control

Overview

Safety-critical control addresses the problem of designing controllers for nonlinear systems that are guaranteed to remain within safe operating regions, even under bounded disturbances and input constraints. My research uses Barrier Lyapunov functions (BLF) and Control Barrier Functions (CBF) to design provably safe controllers that simultaneously achieve control objectives without violating safety constraints.

Applications include autonomous vehicles with velocity and attitude constraints, systems with bounded actuators, and multi-constraint scenarios where multiple safety conditions must be satisfied simultaneously.

Control Architecture

Consider a strict-feedback nonlinear system

\[ \dot x_i = f_i(\bar x_i)+g_i(\bar x_i)x_{i+1},\ \ i=1,\dots,n-1, \qquad \dot x_n=f_n(\bar x_n)+g_n(\bar x_n)u,\qquad y=x_1 \]

whose physical actuator output must always remain inside a prescribed, possibly asymmetric, admissible set \(\mathbb U=\{u\mid u_{min}<u<u_{max}\}\). Rather than saturating the commanded input after the controller is designed — which destroys differentiability exactly where it matters most — admissibility is embedded directly into the closed-loop dynamics through an Admissibility-Preserving Input Realization (APIR):

\[ \dot u = p_1\left[\rho\left\{1-\left(\frac{u}{u_{max}}\right)^{\gamma}\right\}+(1-\rho)\left\{1-\left(\frac{u}{u_{min}}\right)^{\gamma}\right\}\right]u_c - p_1p_2u \]

a continuously differentiable dynamic state whose vector field points strictly inward as \(u\) approaches either bound, making the admissible set forward-invariant by construction and directly compatible with recursive backstepping design.

Figure not yet added — save apc_architecture.png to images/research/

Key Contributions

• BLF-based controllers for state-constrained trajectory tracking of UAVs.

• Provably safe control for constrained nonlinear systems with bounded inputs.

• CBF-based approaches for simultaneous satisfaction of multiple safety constraints.

• Formal safety certificates with convergence guarantees under uncertainty.

• Admissibility-preserving control for strict-feedback systems under asymmetric actuator and rate constraints, via a continuously differentiable input realization integrated with backstepping.

Relevant Publications