Adaptive Control for Nonlinear Systems With Both Tracking Error Constraints and Full-State Constraints: A Universal Constraint Approach

This paper studies the adaptive control problem for a class of uncertain strict-feedback nonlinear systems, where both tracking error and full states need to be directly constrained. First, a novel universal constraint approach is introduced, which combines a universal composite barrier function (UCBF) that depends on the tracking error and the output, with universal barrier functions (UBFs) that depend on the remaining states. Compared with existing research, it displays the following appealing features: 1) both tracking error constraints and full-state constraints are ensured simultaneously without encountering the “feasibility conditions”. The constraints on the tracking error and the output are decoupled, and the constraining functions on both the tracking error and full states, especially including the output, can be directly determined by the user. 2) the proposed approach provides a universal solution that can handle both constrained and unconstrained cases uniformly without changing the control structure. Then, through a new coordinate transformation, the nonlinear system subject to the two constraints is converted into an equivalent “unconstrained” system. Further, by designing a modified filter and utilizing the adaptive backstepping design, an adaptive dynamic surface asymptotic controller is proposed to stabilize the “unconstrained” system. It is theoretically proved that the tracking error converges to zero asymptotically without “explosion of complexity”, and the features of the universal constraint approach are achieved. The effectiveness of the proposed control is also illustrated by simulation verification.