LAUSR

This letter addresses the state safety constraint problems for a class of discrete-time nonlinear systems based on discrete time barrier Lyapunov functions (BLFs). Unlike traditional log and tan BLFs, a discrete-time BLF is developed for guaranteeing that all system states do not violate their constraint boundaries. In order to estimate uncertain parameters, a multiple model set consisting of $q+1$ identification models is constructed. Then, a convex hull makes better use of the information of all identification models. One of the main advantages of this convex hull scheme is that it not only solves the convergence problem of the estimation algorithm of parameters, but also improves the cooperativity of the multiple model control method. At the same time, discrete-time BLFs and discrete-time filter techniques are employed to construct the actual controller in a unified framework. It has been demonstrated conclusively that all signals are bounded and all states can be limited in a prescribed region. Finally, one simulation example is provided to validate the theoretical findings mentioned above.