Secure state constraints control design for uncertain nonlinear systems via a unified boundary modification approach

Abstract

This paper investigates the tracking control problem of uncertain nonlinear systems under secure full-state constraints. Existing results implicitly assume that the constraints are reasonable and feasible control strategy capable of maintaining such constraints exists, which is unrealistic, especially for uncertain nonlinear systems, pre-determining the controllable attractor domain poses a challenge. In this paper, we present a unified boundary modification approach, which addresses the incompatibility problem between state constraints and ensures the secure operation of the system. First, we complete the direct constraints on the states using nonlinear state-dependent functions, where constraints comprise two components: (1) user-specified boundaries and (2) dynamic modification part. Then, we construct detection variables to determine whether the system loses control due to incompatible constraints. When the system enters the collision avoidance region, the dynamic adjustment function automatically corrects the constraints to ensure controllability and stability. The dynamic adjustment function remains inactive when the system operates within the safe region. Thus, existing state constraint results are a special case of ours. Moreover, we introduce a novel transformation so that the initial conditions of virtual controller are not restricted by the barrier function. The solution is more flexible in design and implementation, and the tracking error is confined within the specified performance envelope. Finally, numerical simulations validate the effectiveness of the approach.