High Order Control Lyapunov-Barrier Functions for Temporal Logic Specifications

Abstract

Recent work has shown that stabilizing an affine control system to a desired state while optimizing a quadratic cost subject to state and control constraints can be reduced to a sequence of Quadratic Programs (QPs) by using Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs). In our own recent work, we defined High Order CBFs (HOCBFs) for systems and constraints with arbitrary relative degrees. In this paper, in order to accommodate initial states that do not satisfy the state constraints and constraints with arbitrary relative degree, we generalize HOCBFs to High Order Control Lyapunov-Barrier Functions (HOCLBFs). We also show that the proposed HOCLBFs can be used to guarantee the Boolean satisfaction of Signal Temporal Logic (STL) formulae over the state of the system. We illustrate our approach on a safety-critical optimal control problem (OCP) for a unicycle.

Sequential Cooperative Energy and Time-Optimal Lane Change Maneuvers for Highway Traffic

“…We use Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs) to map the safety constraints and goal constraints (see [8] for details). Our objective is to ensure that system (1) remains within a safety set S S := {x|h S (x) ≥ 0}.…”

“…To ensure the safety of cooperative maneuvers, approximate solutions using Control Barrier Functions (CBFs) [7], [8] have been employed in [9] and [10]. In the context of automated lane-changing maneuvers, [11] proposed a rule-based lane-changing strategy without cooperation using CBFs.…”

Recurrent Neural Network Controllers for Signal Temporal Logic Specifications Subject to Safety Constraints

“…Input: System dynamics (1) and STL formula ϕ Output: Robust and correct controller π(x 0:t , θ * ) 1 Construct HOCBFs from ϕ using (10), (11); 2 Set up constraints on ω using ( 13), ( 15), (17); 3 Set up constraints on p i,j using (8); 4 Initialize controller π(x 0:t , θ) including Q(x 0:t , θ q ), F(x 0:t , θ f ), InitNet (18) and the dQP (9); 5 repeat 6 Sample V initial conditions x v 0 ;…”

“…The controller was obtained via a quadratic program (QP), which can be solved efficiently. In [18], high order control Lyapunov-barrier functions were defined and used to satisfy STL tasks for systems with arbitrary relative degrees. The methods in [17], [18] require manual design of the CBFs corresponding to the STL and the parameters in the constraints.…”

“…In [18], high order control Lyapunov-barrier functions were defined and used to satisfy STL tasks for systems with arbitrary relative degrees. The methods in [17], [18] require manual design of the CBFs corresponding to the STL and the parameters in the constraints. A bad design may result in increased conservativeness or even infeasibility.…”