Ensuring safe robust control design through optimal control with switching strategy

Abstract This paper presents the design of a safe‐ robust control law for a class of nonlinear systems subjected to model and input uncertainties. Safety is addressed by means of control barrier functions. The design method involves defining an over‐approximate region of the safe set and using it as a constraint. We then convert this safe‐ robust control problem into a constrained‐optimal control problem for a nominal system with a modified cost‐functional. Subsequently, this constrained‐optimal control problem is reformulated as a minimization of a Hamilton‐Jacobi‐Bellman equation subjected to safety constraints, which is solved using the Karush‐Kuhn‐Tucker multiplier method. The design of the control law is facilitated by the use of a switching function when moving from safe to unsafe regions. This approach is termed the modular design approach, which maintains the system's robustness while preserving safety. Finally, numerical simulations are carried out to validate the proposed controller and test its efficacy on nonlinear systems with uncertainties.