Class Of Minimum-phase Nonlinear Systems Research Articles

Robust Nonlinear Regulation: Continuous Internal Models and Hybrid Identifiers

We consider the problem of output regulation for the class of minimum-phase nonlinear systems described in normal form. We assume that the ideal steady state control input fulfills a nonlinear regression law that is linearly parametrized in the uncertain parameters and we propose an internal model-based design that combines high-gain and identification tools. The identification tool by which the internal model is updated, is discrete-time by thus obtaining a hybrid internal model. The present paper is part of a wider research activity of the authors in which the attempt is to combine high-gain tools typically used in the context of nonlinear output regulation with identification tools that are here used to estimate the optimal regression law by best fitting the friend and its time derivatives.

Semi-global robust output regulation of minimum-phase nonlinear systems based on high-gain nonlinear internal model

We consider the assumption of existence of the general nonlinear internal model that is introduced in the design of robust output regulators for a class of minimum-phase nonlinear systems with rth degree (r ≥ 2). The robust output regulation problem can be converted into a robust stabilisation problem of an augmented system consisting of the given plant and a high-gain nonlinear internal model, perfectly reproducing the bounded including not only periodic but also nonperiodic exogenous signal from a nonlinear system, which satisfies some general immersion assumption. The state feedback controller is designed to guarantee the asymptotic convergence of system errors to zero manifold. Furthermore, the proposed scheme makes use of output feedback dynamic controller that only processes information from the regulated output error by using high-gain observer to robustly estimate the derivatives of the regulated output error. The stabilisation analysis of the resulting closed-loop systems leads to regional as well as semi-global robust output regulation achieved for some appointed initial condition in the state space, for all possible values of the uncertain parameter vector and the exogenous signal, ranging over an arbitrary compact set.

New Results on the Global Stabilization of Minimum-Phase Nonlinear Systems

The problem of global stabilization for a class of minimum-phase nonlinear systems in normal form is addressed using Lyapunov-based techniques. The proposed method extends early semi-global stabilization results. The key point in designing global stabilizers is the use of full-state feedback control laws which do not preserve the triangularity of the system.

Global robust stabilization of minimum-phase nonlinear systems with uncertainty

The problem of global stabilization via state feedback is studied for a class of minimum-phase nonlinear systems with unknown unmodelled time-varying parameters or disturbances belonging to a given compact set. Sufficient conditions are presented for the existence of a robust stabilizing state-feedback controller. The controller is constructed explicitly by using a Lyapunov-based recursive design procedure. The proposed feedback control law is a smooth function of the state, and requires information of bounding functions on the size of uncertainties. In the case where the disturbance signals represent only an unknown constant vector parameter and appear linearly in the system, an adaptive controller is developed based on similar arguments, achieving global stability with state regulation. The main results of this paper incorporate and generalize a number of robust and adaptive control schemes for global stabilization of uncertain feedback linearizable systems without zero dynamics.