Uncertain Exosystems Research Articles

Adaptive regulation for minimum phase systems with unknown relative degree and uncertain exosystems

This paper investigates the adaptive error feedback regulation problem for unknown minimum phase, single-input, single-output linear systems with uncertain exosystems. The design problem of a feedback control which is capable of driving the output tracking error exponentially to zero, on the basis of the output tracking error only, is locally solved by an adaptive controller which continuously updates the frequency estimates and requires only two informations on the uncertain linear system: (i) an upper bound for the relative degree; (ii) the sign of the high-frequency gain. The proposed adaptive controller contains two gains to be tuned: an adaptation gain which should be chosen sufficiently small and a control gain which should be chosen sufficiently large. Extensions to single-input single-output nonlinear systems affected by uncertain biased multisinusoidal disturbances are outlined.

Constructive Nonlinear Internal Models for Global Robust Output Regulation and Application

This technical note focuses on an internal model construction approach. Several novel types of parameterized nonlinear internal models with certain output are proposed to be useful for achieving nonadaptive control based global robust output regulation with uncertain exosystems. That is, the globally stabilizing control for the augmented system can be done independent of adaptive stabilization control law. We also solve a cooperative global robust output regulation problem as an interesting application of the proposed internal models. In this way, we note that the hurdles can be circumvented arising in the same problem if the canonical linear internal model were used.

A Framework for Global Robust Output Regulation of Nonlinear Lower Triangular Systems With Uncertain Exosystems

This technical note considers global robust output regulation for nonlinear lower triangular systems with uncertain exosystems. The problem, under standing minimum phase and solvability of regulator equations conditions, has not been well solved in the literature. It has attracted many researchers to contribute efforts to build solutions, however only partially from different aspects, mostly utilizing adaptive internal models. The bottleneck is that the usual adaptive approach is not suitable for recursive implementation due to the so-called “propagation of uncertainties” while recursion is usually indispensable for global control of lower triangular systems. This motivates the present development of an expanded and “nonadaptive” internal model based design framework. As a major consequence, we are able to avoid propagation of uncertainties and establish a constructive solution for the problem.

Adaptive nonlinear ship tracking control with unknown control direction

SummaryThis paper is to suggest a novel design for ship tracking control of the benchmark Norrbin nonlinear ship model under relaxed conditions. The challenges of the problem under investigation include the uncertain or absent information of the model time constant, the uncertain reference course, and the intrinsic environmental disturbances. We formulate the ship tracking control problem in terms of a nonlinear output regulation problem with unknown control direction and uncertain exosystems. To solve the problem, we first adopt a novel internal model candidate to convert the output regulation problem into a stabilization problem for an augmented system. Then, a Nussbaum‐gain‐based stabilizer is developed for the augmented system to complete the design. Simulation results are presented to show the effectiveness of the proposed controller.

Output regulation of nonlinear output feedback systems with exponential parameter convergence

This paper revisits the global robust output regulation (GROR) problem of nonlinear output feedback systems with uncertain exosystems by error output feedback control. The problem was conventionally tackled by employing a linear canonical internal model and as a result, suitable adaptive stabilization has to be done for the augmented system to achieve output regulation. Distinguished from that, a novel nonlinear internal model approach is developed in the present study that successfully converts the GROR problem into a robust non-adaptive stabilization problem for the augmented system. The feature of the new approach is two-fold. On one hand, stabilization of augmented system is disentangled from any extra adaptive control law and thus the procedure is simplified. On the other hand, it leads to explicit strict Lyapunov characterization for the closed-loop system and consequently assures exponential parameter convergence.

Attitude stabilization of rigid spacecraft with disturbance generated by time varying uncertain exosystems

This paper is concerned with the problem of attitude stabilization of rigid spacecraft in the presence of parameter uncertainty and external disturbance generated by some time varying uncertain exosystems. A time varying internal model that is free of the uncertain parameter is proposed to compensate the disturbance. An adaptive attitude controller is presented by incorporating time varying dynamic coordinate transformation, semi-tensor product and adaptive control method. Especially, the parameter uncertainties caused by the inertia matrix and uncertain exosystems are tackled by combining the semi-tensor product and adaptive control method. Finally, a simulation example is presented to illustrate the effectiveness of the proposed method.

Robust output regulation for a class of MIMO nonlinear systems with uncertain exosystems

The robust output regulation problem is considered for a class of multi-input multi-output (MIMO) nonlinear systems with uncertain exosystems. Under a mild assumption that the uncertainties of the controlled plant and exosystem have known boundary functions, a new design method of dynamic variable structure controller is proposed. It is proven that the tracking error of the closed-loop system can reach a specified manifold in a finite time and converge to zero asymptotically while all states involved are bounded. Simulation results of a permanent magnet synchronous motor servo system are given to validate the proposed approach.

Robust design of nonlinear internal models without adaptation

We propose a solution to the problem of semiglobal output regulation for nonlinear minimum-phase systems driven by uncertain exosystems that does not rely upon conventional adaptation schemes to estimate the frequency of the exogenous signals. Rather, the proposed approach relies upon regression-like arguments used to derive a nonlinear internal model able to offset the presence of an unknown number of harmonic exogenous inputs of uncertain amplitude, phase and frequency. The design methodology guarantees asymptotic regulation if the dimension of the regulator exceeds a lower bound determined by the actual number of harmonic components of the exogenous input. If this is not the case, a bounded steady-state regulation error is ensured whose amplitude, though, can be arbitrarily decreased by acting on a design parameter of the regulator.