Neural-network-based adaptive tracking control for Markovian jump nonlinear systems with unmodeled dynamics

• Complex nonlinear Markovian jump systems with unmodeled dynamics are considered.
• Adaptive neural control scheme is extended to complex nonlinear Markovian jump systems.
• Assumption about the sign of unknown control gains is abandoned.
• The proposed scheme is also effective for Markovian jump systems with known control gains.
• Only one parameter is required to be adjusted online.

An adaptive control scheme is investigated for a class of strict-feedback Markovian jump nonlinear systems with unknown control gains and unmodeled dynamics. To deal with the unmodeled dynamics, an available dynamic signal is employed to construct appropriate Lyapunov functions. RBF neural networks are used to approximate the unknown nonlinear functions with Markovian switching. The approximation capability of neural networks is combined with the backstepping technique to avoid the inherent problem of controller complexity in traditional backstepping design method. It is proved that all the signals in the closed-loop system are uniformly ultimately bounded in probability and that the tracking errors signal converges to a small neighborhood of origin by choosing suitable design parameters. Simulation results illustrate the effectiveness of the proposed scheme.