Prescribed Time Recovery From State Constraint Violation via Approximation-Free Control Approach

For systems with soft state constraints, initial violation in such constraints is acceptable if no feasible control strategy capable of maintaining such constraints exists or an excessively large amount of energy consumption is required for constraint satisfaction. However, whenever the constraint violation is detected, it is highly desirable that the states be regulated back to satisfy the constraints as soon as possible. In this paper, an approximation-free state feedback control scheme is proposed for unknown second-order nonlinear systems, capable of recovering the states from constraint violation to constraint satisfaction within the prescribed time. Besides, the implicit assumption of compatibility between different constraints in most existing works is removed, and a sufficient condition for compatibility of state constraints is established for unknown second-order systems. The proposed self-recovery control scheme has the following features: 1) the recovery time of the states can be preset by the user regardless of the initial conditions; 2) the proposed controller does not need any explicit information on system model, thus has strong robustness against model uncertainties and disturbances; and 3) no approximation technique (e.g., neural network and fuzzy system) is involved, rendering the proposed control structurally simple and computationally inexpensive.