Adaptive multiple model control for nonlinear constrained systems with a novel barrier Lyapunov function

Abstract

AbstractThis paper investigates the problem of the multiple model control of nonlinear full state constrained systems with a novel barrier Lyapunov function. To handle the problem of unknown parameters, the identification model set containing identification models is established. The novel barrier Lyapunov functions (BLFs) are employed to guarantee that all system states do not violate their boundaries and can remove the restricted condition associated with traditional BLFs. By using the first order filter technique, the "explosion of complexity" difficulty caused by the repeated differential from the backstepping technique is removed. In addition, the estimation of unknown parameters is obtained by using the convex hull property. Based on the second level adaptation technique, the convex hull parameters are designed by using the identification error dynamics, and this algorithm has better convergence property than other algorithms. Then, a multiple model control strategy is developed, which not only guarantees that the requirement of all state constraints is realized, but also ensures that the boundedness of all signals of closed‐loop systems are not violated. The key advantage is that the proposed strategy does not require enormous identification models, that is, the number of identification model is reduced significantly. Finally, the effectiveness of the presented scheme is illustrated through the simulation results.