Decentralized output feedback stabilization of large-scale uncertain nonlinear systems

Semi-global finite-time output feedback stabilization for a class of large-scale uncertain nonlinear systems

In this paper, the problem of observer-based adaptive fuzzy decentralized control is studied for uncertain large-scale nonlinear systems with full state constraints, input saturation and unmeasurable state. Compared with the existing literature, the state directly measurable problem is relaxed, and the systems with full state constraints and input saturation problem are further considered. In order to solve the controller design difficulties caused by input saturation and state constraints, the auxiliary design functions and the barrier Lyapunov functions are employed, respectively. By utilizing adaptive backstepping technique and Lyapunov stability theorem, an observer-based adaptive fuzzy decentralized control approach is developed. It is proved that all the signals of the closed-loop systems are semi-globally uniformly ultimately bounded and the observer errors are converged on a small neighborhood of the origin. The tracking errors are remained in the bounded compact set, and the full state constraints are not violated. Two practical examples are given to demonstrate the usefulness of the proposed control scheme.

In this article, a global output feedback stabilization scheme is proposed for a class of time‐delay uncertain nonlinear systems with unknown measurement sensitivity. A new high gain observer is designed with which the sensitivity function can be tackled by only one dynamic gain and the coupled linear‐like controller is fairly simple. By introducing some transformations of the state estimation errors and observer states, and appropriately choosing Lyapunov–Krasovskii functionals, it is proved that the proposed controller can globally stabilize the system.

SummaryIn this paper, we aim at addressing the problem of global output feedback stabilization for a class of uncertain nonlinear systems with quantized input and output. The nonlinear functions of the system are assumed to satisfy high‐order growth condition on the unmeasurable states. Based on the homogeneous domination approach and sector bound approach, a homogeneous quantized controller computed from quantized output is constructed, and a guideline is derived to select the parameters of the quantizers. Further, it is proved that, with the proposed scheme, the closed‐loop system is globally asymptotically stable. Copyright © 2016 John Wiley & Sons, Ltd.

A decentralized adaptive control method is proposed for large-scale systems with unknown time-delayed nonlinear interconnections unmatched in control inputs. It is assumed that the time-delayed interaction terms are bounded by unknown nonlinear bounding functions. The nonlinear bounding functions and uncertain nonlinear functions of large-scale systems are compensated by the function approximation technique using neural networks. The dynamic surface control method is extended to design the proposed memoryless local controller for each subsystem of uncertain nonlinear large-scale time delay systems. Therefore, although the interconnected systems consist of a large number of subsystems, the proposed controller can be designed simply. We prove that all the signals in the total closed-loop system are semiglobally uniformly bounded and the control errors converge to an adjustable neighborhood of the origin. Finally, an example is given to demonstrate the effectiveness and applicability of the proposed scheme.

A novel decentralised indirect adaptive output feedback fuzzy controller with a compensation controller and an H ∞ tracking controller is presented for a class of uncertain large-scale nonlinear systems in this article. The compensator adaptively compensates for interconnections between subsystems as well as mismatched errors, while the H ∞ controller suppresses the effect of external disturbances. Based upon the combination of fuzzy inference systems, a state observer, H ∞ tracking technique and the strictly positive real condition, the proposed overall observer-based decentralised algorithm guarantees not only asymptotical tracking of reference trajectories but also an arbitrary small attenuation level of the unmodelled error dynamics including the disturbances on the tracking control. Simulation results substantiate the effectiveness of the proposed scheme.

This paper investigates the problem of global output feedback stabilisation for a class of high-order nonlinear systems with multiple time-varying delays. By using backstepping recursive technique and the homogeneous domination approach, a continuous output feedback controller is successfully designed, and the global asymptotic stability of the resulting closed-loop system is proven with the help of an appropriate Lyapunov– Krasovskii functional. Two simulation examples are given to illustrate the effectiveness of the proposed approach.

In this paper, asymptotic stabilization for a class of nonlinear large-scale systems with unmatched uncertainties is investigated. Two types of robust control algorithms are proposed to stabilize the uncertain nonlinear large-scale systems asymptotically provided that the nominal systems are asymptotically stable and the unmatched uncertainties are equivalently matched. The decentralized control utilizes the local state of each subsystems as the feedback information. The two-level control uses the local state as well as the states of the state of the connecting subsystems. An example is used to illustrate the proposed control method.

In this article, a novel high gain observer (HGO)-based decentralised indirect adaptive fuzzy controller is developed for a class of uncertain affine large-scale nonlinear systems. By the combination of fuzzy logic systems and an HGO, the state variables are not required to be measurable. The proposed feedback and adaptation mechanisms guarantee that each subsystem is able to adaptively compensate for interconnections and disturbances with unknown bounds. It is ascertained using a singular perturbation method that all the signals of the closed-loop large-scale system stand uniformly ultimately bounded and the tracking errors converge to tunable neighbourhoods of the origin. Simulation results of correlated double inverted pendulums substantiate the effectiveness of the proposed controller.

Adaptive fuzzy fault-tolerant decentralized control for uncertain nonlinear large-scale systems based on dynamic surface control technique

This paper solves the finite-time decentralized control problem for uncertain nonlinear large-scale systems in nonstrict-feedback form. The considered controlled plants are different from the previous results of finite-time control systems, which are the nonstrict-feedback large-scale systems with the unknown functions consisting of all states, interactions, and immeasurable states. Fuzzy logic systems and a filter-based state observer are utilized to model uncertain systems and deal with the immeasurable states, respectively. By combining the backstepping recursive design with Lyapunov function theory, a finite-time adaptive fuzzy decentralized control approach is raised. It is testified that the developed control strategy can guarantee that the closed-loop signals are bounded, and the outputs of systems have satisfactory tracking performance in a finite time. A quadruple-tank process system is given to testify the effectiveness and applicability of the proposed approach.

We present a deterministic design approach for decentralized robust controls of large-scale nonlinear uncertain dynamical systems. Two important types of robust control design are drawn. The local design makes use of the local state of each subsystem as the feedback information. The global design utilizes the local state as well as the neighboring states as the feedback information. Only the set of the possible values of the uncertainties is required for the controls. The decentralized feedback controls are continuous functions of the state.

This paper considers the problem of global stabilization by output feedback for a class of uncertain nonholonomic systems. By combining the output feedback domination design and nonsmooth change of coordinates together, we explicitly construct a simple output feedback controller, which can universally stabilize a whole family of uncertain nonholonomic systems. The effectiveness of the proposed approach is illustrated by solving the output feedback stabilization for wheeled mobile robots.

This paper considers global output feedback stabilization of a class of upper-triangular nonlinear systems with multiple outputs. By coupling a finite-time convergent observer and a saturated homogeneous stabilizer, the global output feedback stabilization can be achieved without the homogeneous growth condition. The proposed techniques are also extended to more general complex nonlinear systems. Various examples, including a ball-and-beam mechanical system and a planar vertical takeoff and landing aircraft, are presented to illustrate the design.

This article focuses on global finite-time output feedback stabilization for uncertain nonlinear systems with unknown measurement sensitivity. The existence of the continuous measurement error resulting from limited accuracy of sensors invalidates the existing design strategies depending on the use of the precise output in the construction of an observer, which highlights the contribution of this article. Essentially, different from related works, we propose a new finite-time convergent observer by avoiding the use of the information on nonlinearities. By combining the homogeneous domination with the addition of a power integrator method, an output feedback controller composed of multiple nested sign functions is successfully developed. Finally, the effectiveness of the presented scheme is exhibited by a numerical example.