Design of Adaptive Sliding Mode Controllers for Perturbed Nonlinear Systems with Partial Unmeasurable States and State Constraints

A sliding mode control (SMC) strategy is proposed in this paper for a class of perturbed nonlinear systems with unmeasurable states and state constraints to deal with the state tracking problems. First of all, a partial states observer is designed for solving the problems due to unmeasurable states. The estimation errors will approach zero in a finite time. Secondly, based on a designed barrier Lyapunov function, one designs the sliding surface function and an adaptive sliding mode tracking controller to ensure that the states have the ability to track the desired signals. Moreover, the tracking error is capable of converging to zero in a finite time without violating the given state's constraints. Perturbation estimator and adaptive mechanisms are also utilized so that there is no need to know the upper bounds of perturbations and perturbation estimation errors. Finally, a numerical example is provided to demonstrate the feasibility of the proposed control strategy.

Hall Effects on Unsteady Magneto Hydrodynamic Convection Flow of Nanofluids Past a Rotating Porous Plate

The effects of Hall current are considered for the convective rotational current free of nanofluid magnetohydrodynamics (copper and alumina) in a permeable medium with a vertical porous flat plate, semi-infinite rotation with stable state of the heat source and convection limit. The slip rate is expected to oscillate over time with a constant frequency so that the boundary layer solutions are of the equivalent oscillating type. The equations to regulate the flow are analytically solved by perturbation estimation. The effects of different parameters on the flow are investigated by means of diagrams and tables