Abstract
The article proposes a robust control approach based on self-organizing Hermite-polynomial-based neural network disturbance observer for a class of non-affine nonlinear systems with input saturation, state constraint, and unknown compound disturbance. Using Taylor series expansion, a hyperbolic tangent function, the non-affine nonlinear system with input saturation is transformed into time-varying affine system without input saturation, which can reduce step n + 1 of the backstepping technique compared with conventional method. Next, a self-organizing Hermite-polynomial-based neural network disturbance observer is proposed to estimate the compound disturbance online. Then, the auxiliary systems are designed to solve state constraint for subsystems, and hyperbolic tangent function is used to approximate the saturated control input. Simulation results proved the effectiveness of the proposed control scheme.
Highlights
Besides traditional proportional–integral/proportional–integral–derivative (PI/ PID) control, many control approaches of nonlinear system have been proposed, including feedback linearization method,[1,2,3] backstepping control,[4,5,6,7] and the method based on neural network.[8,9,10,11]
The non-affine nonlinear system with input saturation and state constraint is transformed into affine nonlinear system by Taylor series expansion and hyperbolic tangent function, which simplifies the calculation of auxiliary systems and backstepping scheme compared with Chen et al.[21]
Aiming at system (equation (9)), we propose the backstepping scheme based on the self-organizing Hermite-polynomial-based neural network disturbance observer (SHNNDO)
Summary
Besides traditional proportional–integral/proportional–integral–derivative (PI/ PID) control, many control approaches of nonlinear system have been proposed, including feedback linearization method,[1,2,3] backstepping control,[4,5,6,7] and the method based on neural network.[8,9,10,11] In Bidram et al.,[1] an input–output feedback linearization control method is proposed for multi-agent systems with nonlinear and heterogeneous dynamics via which nonlinear dynamics of agents is transformed to linear dynamics. The non-affine nonlinear system with input saturation and state constraint is transformed into affine nonlinear system by Taylor series expansion and hyperbolic tangent function, which simplifies the calculation of auxiliary systems and backstepping scheme compared with Chen et al.[21] SHNNDO is proposed to estimate the unknown compound disturbance, which is of minor calculation and better approximation performance. To ensure that the output y tracks the desired signal yd in the non-affine system with input saturation, we first proposed SHNNDO to estimate the unknown disturbance and design auxiliary systems to handle the influence of input saturation.
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