Adaptive robust control (ARC) has been applied to pneumatic systems successfully for its excellent performance and strong robustness. Although many researchers are already working on studying of the ARC, the stability analyses of these works are performed by the Lyapunov method. The contraction theory is a new proposed “differential” Lyapunov-like analytic tool for the nonautonomous nonlinear system. It can provide a more convenient analysis and richer design toolbox of the nonlinear system than Lyapunov method. This article intelligently brings the philosophy of contraction theory into the ARC design framework to form a contraction theory-based ARC (CT-ARC) for a pneumatic servo system. The proposed method offers more design choices than the traditional ARC. In addition, a command filter is employed to acquire the differential signal of the virtual control law. The stability analysis of the whole system is presented elegantly by the contraction theorem with consideration of the estimation error of the command filter. Furthermore, exponential convergence of the closed-loop system can be derived under specific conditions. Finally, various experiments for the trajectory tracking control of a pneumatic cylinder demonstrate the efficiency of CT-ARC.

Indomethacin micro-crystals sized ∼2 µm have been encapsulated with polyelectrolyte multi-layers for the purpose of controlled release. Charged linear poly (dimethyldiallyl ammonium chloride) (PDDA) and poly (styrene sulphonate) (PSS) were alternatively deposited on ∼2 µm drug micro-crystals. The release of indomethacin from coated micro-crystals was measured in aqueous solutions of pH 1.4 and 6.8. The polyelectrolyte multi-layer capsule thickness was proved to control. The results provided a method of achieving prolonged drug release through self-assembly of polymeric shells on drug microcrystals.

In this paper, an adaptive robust neural network controller (ARNNC) is synthesized for a single-rod pneumatic actuator to achieve high tracking accuracy without knowing the bounds of the parameters and disturbances. The ARNNC control framework integrates adaptive control, robust control, and neural network control intelligently. Adaptive control improves the precision of dynamic compensation with parametric estimation, and robust control attenuates the effect of unmodeled dynamics and unknown disturbances. In reality, the unmodeled dynamics of the complicated pneumatic systems and unpredictable disturbances in working conditions affect the tracking precision. However, these cannot be expressed as an exact formula. Therefore, the real-time learning radial basis function (RBF) neural network component is considered for better compensation of unmodeled dynamics, random disturbances, and estimation errors of the adaptive control. Although the bounds of the parameters and disturbances for the pneumatic systems are unknown, the prescribed transient performance and final tracking accuracy of the proposed method can be still achieved with fictitious bounds. Asymptotic tracking performance can be acquired under the provided circumstance. The comparative experiments with a pneumatic cylinder driven by proportional direction valve illustrate the effectiveness of the proposed ARNNC as shown by a high tracking accuracy is achieved.

Nonlinear tracking differentiator (NTD) is a powerful tool for achieving differential signals. Although numerous studies considering NTD have been carried out, the convergence analysis of NTD in these works is accomplished by the Lyapunov method, which is quite complex and needs unrealistic assumptions. Contraction theory, a newly proposed system analysis tool, is particularly effective in analyzing nonlinear non-autonomous systems. Motivated by these considerations, this paper proposed an NTD with variable damping (VD-NTD) based on contraction theory. Firstly, the convergence of NTD is performed with contraction theory, which is much simpler than the traditional Lyapunov-based method. Secondly, the optimization of NTD is done based on its characteristics. Also, the convergence of the proposed VD-NTD is verified elegantly by contraction theory. Finally, simulations on sinusoidal signals, filtered square waves, and complex signals with sudden changes have been carried out, the proposed method not only acquires better performance but is more robust to unpredictable disturbances.

Stabilization and learning are imperative to the high-performance feedback control of nonlinear systems. A dual adaptive robust control (DARC) scheme is proposed for nonlinear systems with model uncertainties to achieve a desired level of performance. Only the output of the nonlinear system is accessible in this work, all the states and parameters are learned online. Firstly, the DARC uses the prior physical bounds of systems to design a discontinuous projection with update rate limits which confines the bounds of parameter and state estimation. Then robustness of the nonlinear system can be guaranteed by the deterministic robust control (DRC) method. Secondly, a dual adaptive estimation mechanism (DAEM) is developed to learn the unknown parameters and states of systems. One part of the DAEM is the bounded gain forgetting (BGF) estimator, which is developed to handle inaccurate parameters and parametric variations. The other is the adaptive unscented Kalman filter (AUKF) synthesized for state estimation. The AUKF contains a statistic estimator based on the maximum a posterior (MAP) rule to estimate the unknown covariance matrix. Finally, simulation results illustrate the effectiveness of the suggested method.