Safety-Critical Control via Invariance Theory

(2019.10 – 2021.09, HR-Recycler Project)

Research Focus

This research investigates safety-critical control of nonlinear dynamic systems through forward invariance and Lyapunov-based stability theory.

The central question is:

How can safety constraints be enforced directly at the control layer, independent of planning assumptions and without relying on perfect trajectory execution?

Conventional map–plan–track architectures decouple planning and control, implicitly assuming ideal execution across layers. In practice, deviations in trajectory tracking, infeasible plans, and hardware limitations introduce cascading errors that may violate safety constraints. This research addresses safety at the dynamical level rather than at the planning level.

Technical Challenges

Safety-critical control for nonlinear dynamical systems faces several structural challenges:

• Execution-level safety violations: Planning layers may generate feasible trajectories, yet tracking errors and actuation limits can cause deviations that violate safety constraints during execution.

• Lack of safety guarantees in conventional control design: Classical stabilization methods focus on asymptotic stability but do not explicitly guarantee constraint satisfaction.

• Coupling between stability and safety objectives: Enforcing safety constraints may conflict with control objectives such as tracking or task execution.

Addressing these challenges requires control synthesis methods that guarantee forward invariance of safety sets while maintaining system stability.

Methodological Contributions

This research develops invariance-based control methods that guarantee safety and stability through Lyapunov and forward-invariance theory.

Two complementary approaches are explored to address safety-critical control in different system settings.

1. Switch-Based Invariance Control

For safety-critical manipulation tasks, this work develops switch-based safe tracking controllers that enforce safety constraints within predefined safe regions.

The approach enforces a switch-based safety filter to the nominal controller to ensure that:

• System trajectories remain inside safe sets during motion

• Tracking objectives are achieved without violating safety boundaries

An adaptive super-twisting control strategy is introduced to handle model uncertainties and disturbances, enabling robust safe tracking for robotic manipulators operating within constrained workspaces. [1]

2. Safety-Critical Control via Control Barrier Functions

This work investigates Control Barrier Function (CBF)–based control synthesis for multi-agent systems with global and local safety constraints.

The method constructs barrier functions that guarantee collision avoidance and constraint satisfaction while enabling cooperative task execution.

Key developments include:

• CBF-based distributed coverage control for constrained unicycle agents [2][3].

• Safety-preserving coordination under constant-speed and nonholonomic dynamics [2].

• Online learning–assisted local barrier construction for collision avoidance [3].

This framework enables distributed multi-agent coordination while preserving forward invariance of safety sets.

Outcomes and Implications

This research demonstrates that safety guarantees can be embedded directly into the control layer through invariance-based design, independent of high-level planning assumptions.

The results show that:

• Safety constraints can be enforced at the dynamical level through forward-invariance principles.

• Stability and safety objectives can be jointly satisfied via Lyapunov-based control synthesis.

• Distributed multi-agent systems can maintain safety using decentralized control laws and local information.

More broadly, the work establishes invariance theory as a rigorous foundation for safety-critical control, enabling controllers that remain safe under execution uncertainty, disturbances, and decentralized coordination.

These ideas later informed subsequent research on formal safety verification and risk-aware control frameworks for autonomous systems.

Publications

1. Z. Zhang, Y. Wang, and Dirk Wollherr, "Safe Tracking Control of Euler-Lagrangian Systems Based on A Novel Adaptive Super-twisting Algorithm", 21st IFAC World Congress, Berlin, Germany, 11-17 July 2020. [ScienceDirect][ResearchGate][presentation]

2. Q. Liu*, Z. Zhang*, N. K. Le, J. Qin, F. Liu, and S. Hirche, "Distributed Coverage Control of Constrained Constant-Speed Unicycle Multi-Agent Systems", in IEEE Transactions on Automation Science and Engineering, vol. 22, pp. 2225 - 2240, Mar 2024, DOI: 10.1109/TASE.2024.3377131. [IEEE Xplore] [ArXiv]

3. C. Li, Z. Zhang, A. Nesrin, Q. Liu, F. Liu, M. Buss, "Instantaneous local control barrier function: An online learning approach for collision avoidance", in Journal of Intelligent and Robotic Systems, vol. 109, no.2, pp. 40, Oct 2023, DOI: 10.1007/s10846-023-01962-8. [Springer] [ResearchGate]