To bring complex systems into real world environments in a safe manner, they will have to be robust to uncertainties-both in the environment and the system. This paper investigates the safety of control systems under input disturbances, wherein the disturbances can capture uncertainties in the system. Safety, framed as forward invariance of sets in the state space, is ensured with the framework of control barrier functions (CBFs). Concretely, the definition of input to state safety (ISSf) is generalized to allow the synthesis of non-conservative, tunable controllers that are provably safe under varying disturbances. This is achieved by formulating the concept of tunable input to state safe control barrier functions (TISSf-CBFs) which guarantee safety for disturbances that vary with state and, therefore, provide less conservative means of accommodating uncertainty. The theoretical results are demonstrated with a simple control system with input disturbance and also applied to design a safe connected cruise controller for a heavy duty truck.
In this paper, we establish a mathematical framework that allows us to optimize the speed profile and select the optimal gears for heavy-duty vehicles (HDVs) traveling on highways while varying parameters. The key idea is to solve the analogous boundary value problem (BVP) analytically for a simple scenario (linear damped system with quadratic elevation profile) and use this result to initialize a numerical continuation algorithm. Then, the numerical algorithm is used to investigate how the optimal solution changes with parameters. In particular, we gradually introduce nonlinearities (air resistance and engine saturation), implement different elevation profiles, and incorporate external perturbations (headwind and traffic). This approach enables real-time optimization in dynamic traffic conditions, therefore may be implemented on-board.
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