Optimal Safety for Constrained Differential Inclusions Using Nonsmooth Control Barrier Functions
- Resource Type
- Periodical
- Authors
- Ghanbarpour, M.; Isaly, A.; Sanfelice, R.G.; Dixon, W.E.
- Source
- IEEE Control Systems Letters IEEE Control Syst. Lett. Control Systems Letters, IEEE. 7:1303-1308 2023
- Subject
- Robotics and Control Systems
Computing and Processing
Components, Circuits, Devices and Systems
Safety
Sufficient conditions
Cost function
Optimal control
Finite element analysis
Uncertainty
Numerical stability
Constrained systems
differential inclusions
nonsmooth control barrier functions
optimal control
safe control
- Language
- ISSN
- 2475-1456
For a broad class of nonlinear systems, we formulate the problem of guaranteeing safety with optimality under constraints. Specifically, we define controlled safety for differential inclusions with constraints on the states and the inputs. Through the use of nonsmooth analysis tools, we show that a continuous optimal control law can be selected from a set-valued constraint capturing the system constraints and conditions guaranteeing safety using control barrier functions. Our results guarantee optimality and safety via a continuous state-feedback law designed using nonsmooth control barrier functions. An example pertaining to obstacle avoidance with a target illustrates our results and the associated benefits of using nonsmooth control barrier functions.