This note studies the tracking control problem for a class of random pure-feedback nonlinear systems with Markovian switching and unknown parameters. An adaptive tracking controller is constructed by introducing an auxiliary integrator subsystem and using the improved backstepping method such that the closed-loop system has a unique solution that is globally bounded in probability. Meanwhile, the tracking error can converge to an arbitrarily small neighborhood of zero via the parameter regulation technique. The efficiency of the tracking controller designed in this paper is demonstrated by simulation examples.
KEYWORDSbackstepping, Markovian switching, random pure-feedback systems, tracking control 3112
This paper studies a class of random nonlinear systems with time-varying delay, in which the r-order moment (r ≥ 1) of the random disturbance is finite. Firstly, some general conditions are proposed to guarantee the existence and uniqueness of the global solution to random nonlinear timedelay systems. Secondly, some definitions and criteria on noiseto-state stability in the moment sense and in probability sense are given by Lyapunov method respectively. Finally, two regulation controllers are constructed respectively for two corresponding random nonlinear time-delay systems and the effectiveness of two proposed recursive procedures are demonstrated by two simulation examples.
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