On the Connected Safe Number of Some Classes of Graphs

For a connected simple graph G , a nonempty subset S of V G is a connected safe set if the induced subgraph G S is connected and the inequality S ≥ D satisfies for each connected component D of G∖S whenever an edge of G exists between S and D . A connected safe set of a connected graph G with minimum cardinality is called the minimum connected safe set and that minimum cardinality is called the connected safe numbers. We study connected safe sets with minimal cardinality of the ladder, sunlet, and wheel graphs.

Learning constraints from demonstrations with grid and parametric representations

We extend the learning from demonstration paradigm by providing a method for learning unknown constraints shared across tasks, using demonstrations of the tasks, their cost functions, and knowledge of the system dynamics and control constraints. Given safe demonstrations, our method uses hit-and-run sampling to obtain lower cost, and thus unsafe, trajectories. Both safe and unsafe trajectories are used to obtain a consistent representation of the unsafe set via solving an integer program. Our method generalizes across system dynamics and learns a guaranteed subset of the constraint. In addition, by leveraging a known parameterization of the constraint, we modify our method to learn parametric constraints in high dimensions. We also provide theoretical analysis on what subset of the constraint and safe set can be learnable from safe demonstrations. We demonstrate our method on linear and nonlinear system dynamics, show that it can be modified to work with suboptimal demonstrations, and that it can also be used to learn constraints in a feature space.

The maximum taxiing safe set of the wheel-skid aircraft under optimal control of rudder

Directional stability during the roll-out phase is crucial to the safety and reusability of the aircraft. Because of the mechanical properties, the wheel-skid aircraft is more prone to produce course instability. To address this issue, the taxiing safe set of the wheel-skid aircraft is discussed based on the reachability theory. A dynamic model of the on-ground aircraft is established firstly, considering the complex condition of the ground loads. Then, the particular Hamilton–Jacobi partial differential equation is used to obtain the safe set. According to the safe set results, the optimal control of the rudder is built in the state space. Its effectiveness is verified by the comparison with other robust methods. In addition, three structural parameters are selected to analyze the influences on the safe set. Results indicate that the maximum safe yaw angle increases from [Formula: see text] to [Formula: see text] at 70 m/s under the optimal control of the rudder when the steering of nose wheel is locked. The safe boundary in the middle–high-speed region expands by 43.5% under the rudder control. Because of the mechanical properties, uncontrollable deflection will appear due to the asymmetric disturbances when the longitudinal velocity is lower than 42 m/s.

Safe Adaptive Cruise Control with Control Barrier Function and Smith Predictor

This work presents the development of Adaptive Cruise Control (ACC) applied to a vehicle. The ACC tracks a predefined controlled vehicle cruise speed, however when a leading vehicle with lower speed is encountered, the ACC must adapt the controlled vehicle speed to maintain a safe distance between the vehicles. The control strategy applied combines Control Lyapunov Function (CLF), related to performance/stability objectives and Control Barrier Function (CBF), related to safety conditions represented by a safe set. CLF and CBF are integrated with Quadratic Programming (QP) and a relaxation is used to make performance/stability objectives as a soft constraint and safety conditions as a hard constraint. The system model is based on a vehicle available at EPUSP and presents an input time-delay, that can degrade performance and stability. The input delay is compensated with a Smith Predictor. The initial results were obtained through numerical simulations and, in the future, the scheme will be implemented in the vehicle. The numerical simulations indicate that the proposed controller respect the performance/stability objectives and the safety conditions.