Approximation-based control of nonlinear MIMO time-delay systems

Approximation-based control is presented for a class of multi-input multi-output (MIMO) nonlinear systems in block-triangular form with unknown state delays. Neural networks (NNs) are utilized to approximate and compensate for unknown functions in the system dynamics, including the unknown bounds of the functions of delayed states. The use of a separation technique removes the need for any assumption on the function of delayed states, and allows the handling of multiple delays in each function of delayed states. By combining the use of Lyapunov–Krasovskii functionals and adaptive NN backstepping, the proposed control guarantees that all closed-loop signals remain bounded, while the outputs converge to a neighborhood of the desired trajectories. Simulation results demonstrate the effectiveness of the proposed scheme.