In this article, an innovative backstepping controller for hydraulic systems is proposed to handle system uncertainties and accomplish specified performance tracking without violating the full-state constraints. To deal with uncertainties, extended state observers ESOs and an adaptive law are integrated. ESOs are structured to estimate disturbances, whereas adaptive law is applied to approximate unknown parameters. The estimated uncertainties are then incorporated into a constrained controller, ensuring that both the prescribed transient tracking performance and the nonviolation of full-state constraints can be guaranteed. A prescribed performance function (PPF) and the barrier Lyapunov function (BLF) are synthesized to guarantee the transient behavior of the tracking error and all state errors within desirable boundaries. Then, an adaptive prescribed performance controller with uncertainty compensation is constructed by merging the BLF and PPF through back-stepping design to stabilize the closed-loop system. Finally, abundant comparative experimental results validate the proposed controller's tracking performance.

In this article, an adaptive output feedback prescribed performance controller is proposed for a hydraulic system with matched and mismatched uncertainties (including parametric uncertainties and uncertain nonlinearities), which always exist in physical hydraulic systems, and degrade the internal state stability and tracking response performance. By integrating the adaptive control and disturbance observer into the extended state observer, the matched and mismatched uncertainties can be feedforward compensated in the output feedback control. Then, based on the fusion of prescribed performance function and barrier Lyapunov function, the proposed practical method is designed via backstepping method for hydraulic systems, all states are maintained within a preset range by constraining the upper bound of the control errors and the output tracking error is kept within a predetermined boundary that decreases with time. Moreover, the stability of closed-loop system is analyzed by Lyapunov theory. Finally, comparative experimental results are obtained to verify the control performance of the proposed control strategy.

In this study, an output-feedback prescribed performance technique with disturbance compensation is performed for full-state constrained nonlinear systems. A prominent characteristic of this technique is that not only the prescribed tracking performance is achieved when the partial states are measurable but the associated disturbances and full-state constraints are also considered, which makes the design of a high-performance controller extremely difficult. To this end, extended state observer (ESO) and nonlinear disturbance observer (NDO) are integrated to estimate unknown disturbances and unmeasurable states. Moreover, the barrier Lyapunov function (BLF) and prescribed performance function (PPF) are associated to keep the tracking errors within specified ranges and constrain all system states at all times. Then, an output-feedback prescribed performance control (PPC) algorithm with state estimation and disturbance compensation is developed. Furthermore, the stability of the closed-loop controller–observer system is certificated by utilizing the Lyapunov theory. Finally, the effectiveness of the algorithm is verified by its application to the dc motor system.