Tracking Control of Unknown Non‐Linear Systems Using Dynamic Event‐Triggered Adaptive Bernstein Polynomial Approximation

ABSTRACT In this paper, an adaptive tracking control method based on the approximation of dynamic event‐triggered (DET) Bernstein polynomials is proposed for unknown non‐linear dynamic systems. Bernstein polynomials can be used to approximate complex non‐linear functions, but the computational complexity increases with the increase of function complexity and order. In order to save the communication resources of the system and reduce the computational amount, we consider the ET method to reduce the number of controller updates by designing the static event‐triggered (SET) condition and the DET condition, respectively, and comparing the simulation results, we find that the DET further reduces the frequency of the controller update on the basis of SET. In addition, if the Bernstein theorem is used to compensate for the unknown non‐linear function directly, we need to derive the coefficients of the Bernstein polynomials through mathematical derivation, but we believe that the non‐linear dynamic function is unknown, so we cannot directly use the Bernstein polynomials to approximate the unknown non‐linear dynamic function, in order to solve the problem that the coefficients of the Bernstein polynomials are uncertain, we deal with the uncertain parameters in the Bernstein polynomials by an adaptive strategy to ensure that the Bernstein polynomials approximate the unknown non‐linear dynamical system and guarantee that all signals in the closed‐loop non‐linear dynamical system are semi‐global uniform ultimately bounded (SGUUB). Finally, the reliability of the proposed method is verified by numerical simulations and Zeno behavior is avoided.