Abstract
A novel differentiator-based approximation-free output-feedback controller for uncertain nonautonomous nonlinear pure-feedback systems is proposed. Using high-order sliding mode observer, which is a finite-time exact differentiator, the time-derivatives of the signal generated using tracking error and filtered input are directly estimated. As a result, the proposed non-backstepping control law and stability analysis are drastically simple. The tracking error vector is guaranteed to be exponentially stable in finite time regardless of the nonautonomous property in the considered system. It does not require neural networks or fuzzy logic systems, which are typically adopted to capture unstructured uncertainties intrinsic in the controlled system. As far as the authors know, there are no research results on the output-feedback controller for the uncertain nonautonomous pure-feedback nonlinear systems. The results of the simulation show clearly the performance and compactness of the control scheme proposed.
Highlights
Designing a controller for nonlinear systems containing unstructured uncertainties has been considerably advanced and performed in recent years
Adaptive backstepping with universal approximators (UAs) or dynamic surface control (DSC) algorithm is typically adopted to induce control laws that deal with unstructured uncertainties and unmatched disturbances [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]
The pure-feedback nonlinear systems are more general than strict-feedback systems [8,25,26,27,28] because they have the nonaffine appearance of the states which are chosen as virtual controls in each intermediate design steps
Summary
Designing a controller for nonlinear systems containing unstructured uncertainties has been considerably advanced and performed in recent years. Adaptive backstepping with UAs or dynamic surface control (DSC) algorithm is typically adopted to induce control laws that deal with unstructured uncertainties and unmatched disturbances [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]. Proposed adaptive controllers are typically combining UAs with backstepping or DSC In these control algorithms, unstructured uncertainties in the system are estimated by NNs or FLSs. The outputs of the approximators are used by the controller to compensate or cancel the effect of the unmatched or unstructured uncertainties. The complexity of the control law grows significantly as the dynamic order of the controlled system increases To evade this problem, in the DSC-based controllers, the time-derivatives of virtual controls are replaced by some filtered values of them. To show the compactness and performance of the controller that is proposed, simulations have been performed
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