Harmonic Control Lyapunov Barrier Functions for Constrained Optimal Control with Reach-Avoid Specifications
This addresses control problems for systems requiring safety and goal achievement, but it is incremental as it builds on existing control Lyapunov barrier functions.
The paper tackles constrained optimal control with reach-avoid specifications by introducing harmonic control Lyapunov barrier functions, which show a significantly low risk of entering unsafe regions and a high probability of reaching the goal region in numerical experiments.
This paper introduces harmonic control Lyapunov barrier functions (harmonic CLBF) that aid in constrained control problems such as reach-avoid problems. Harmonic CLBFs exploit the maximum principle that harmonic functions satisfy to encode the properties of control Lyapunov barrier functions (CLBFs). As a result, they can be initiated at the start of an experiment rather than trained based on sample trajectories. The control inputs are selected to maximize the inner product of the system dynamics with the steepest descent direction of the harmonic CLBF. Numerical results are presented with four different systems under different reach-avoid environments. Harmonic CLBFs show a significantly low risk of entering unsafe regions and a high probability of entering the goal region.