Family Of Uncertain Nonlinear Systems Research Articles

Practical tracking control of a class of uncertain nonlinear systems and unknown output function

SummaryThis paper investigates the problem of global practical tracking control via dynamic output‐feedback for a family of uncertain nonlinear systems with unknown output function. The nonlinear terms of the system under consideration are assumed to be bounded by an unknown parameter multiplied by a function of unmeasured states. Furthermore, contrary to the previous works, the system output is presented with a multiplicative unknown measurement noise. Based on a high‐gain observer to reconstruct the unmeasured system states and handle the unknown output function, an adaptive output feedback controller is designed to guarantee the reference trajectory tracking. The boundedness of all the closed‐loop signals is verified by Lyapunov analysis and the tracking errors are proved to be sufficiently small prescribed after a finite time. A practical example is given to illustrate the effectiveness of the proposed design scheme.

Sampled-Data Delayed Output Feedback Control of a Class of Nonlinear Systems

This letter presents a sampled-data control strategy for robust stabilization of a family of uncertain nonlinear systems via delayed output signals. Instead of building dynamic observers,we use an output signal sampled at the current time and delayed outputmeasurements at the previous n -1 sampling points to design sampleddata controllers, which are easier for implementation by computer. Under a linear growth condition, it is proved that global robust stabilization is achievable by sampleddata delayed output feedback. The robust stability analysis of the hybrid closed-loop system with delays is conducted by the Lyapunov-Krasovskii functional method.

Adaptive Contraction-based Control of Uncertain Nonlinear Processes using Neural Networks

Driven by the flexible manufacturing trend in the process control industry and the uncertain nature of chemical process models, this article aims to achieve offset-free tracking for a family of uncertain nonlinear systems (e.g., using process models with parametric uncertainties) with adaptable performance. The proposed adaptive control approach incorporates into the control loop an adaptive neural network embedded contraction-based controller (to ensure convergence to time-varying references) and an online parameter identification module coupled with reference generation (to ensure modelled parameters converge those of the physical system). The integrated learning and control approach involves training a state and parameter dependent neural network to learn a contraction metric parameterized by the uncertain parameter and a differential feedback gain. This neural network is then embedded in an adaptive contraction-based control law which is updated by parameter estimates online. As uncertain parameter estimates converge to the corresponding physical values, offset-free tracking, simultaneously with improved convergence rates, can be achieved, resulting in a flexible, efficient and less conservative approach to the reference tracking control of uncertain nonlinear processes. An illustrative example is included to demonstrate the overall approach.

Robust output feedback control of polynomial growth nonlinear systems with measurement uncertainty

SummaryEven in the presence of uncertainty in both state and output equations, we prove that global asymptotic stabilization is still possible by output feedback for a family of uncertain nonlinear systems dominated by a triangular system with a polynomial output‐dependent growth rate. In contrast to the linear growth requirement in the recent work the nonlinear perturbations in this paper are allowed to satisfy a linear growth condition with a polynomial output‐dependent rate. To handle simultaneously the polynomial nonlinearities and unknown parameter in the system output, we propose a high‐gain estimator with a dynamic gain that is updated online through a Riccati‐type dynamic equation. Then, an estimator‐based controller is designed by a recursive algorithm that makes it possible to assign the controller gains step by step. The globally stabilizing output‐feedback controller developed in this paper is robust with respect to uncertainties in the system dynamics and output equations.

Prescribed Performance Fault-Tolerant Control of Uncertain Nonlinear Systems With Unknown Control Directions

A low-complexity state feedback fault-tolerant control scheme guaranteeing prescribed tracking performance is proposed for a family of uncertain nonlinear systems with unknown control directions. Contrary to the current state-of-the-art, novel error transformation functions and new update laws related to performance functions are introduced to the control design such that no compensators or approximation structures are needed, in spite of actuation faults, component faults, and unknown nonlinearities. The proposed method is verified via a simulation on an inverted pendulum.

On observer for a class of uncertain nonlinear systems

This paper considers the problem of estimating the unmeasurable states for a family of uncertain nonlinear systems. For systems with bounded trajectories, we propose a weak practical observer (see Definition 1). When the trajectories are unbounded, under the assumption that the nonlinearity is bounded, we construct a global time-varying observer. Finally, an example is provided to verify the effectiveness of the observer.

Global adaptive output stabilization of uncertain nonlinear systems with polynomial output depending growth rate

SUMMARYThis paper investigates the problem of global output stabilization for a family of uncertain nonlinear systems, which are dominated by a triangular‐type condition. The distinguishing feature of such a class of systems is the presence of unmeasured states growth with growth rate polynomial of output‐input multiplying an unknown constant. We show by an example that the power of the input in the growth rate seems to be optimal.Copyright © 2013 John Wiley & Sons, Ltd.

Semi-Global Robust Stabilization of a Family of Uncertain Nonlinear Systems by Non-Smooth Output Feedback: the Planar Case

We present a preliminary result on robust semi-global stabilization via output feedback for a family of uncertain nonlinear systems which represent a generalized normal form of affine systems in the plane. The main contribution of this paper is to show that with only the knowledge of the bounding system of the uncertain planar system, it is possible to establish the semi-global stabilization result by nonsmooth output feedback, although the uncertain controlled plant is not in a triangular form, non-smoothly stabilizable and non-uniformly observable.

Robust practical output tracking by dynamic output feedback for uncertain non-linear systems with unstabilisable and undetectable linearisation

This paper studies the global robust practical output tracking problem using a dynamic output feedback controller (i.e., an output compensator) for a family of uncertain non-linear systems whose Jacobian linearisation may be unstabilisable and/or undetectable. It is shown that under some mild conditions on a given system, there is an output compensator achieving global robust practical output tracking and such a compensator is explicitly constructed by the 'coupled controller-observer method' recently proposed. The usefulness of our result is illustrated by some simple numerical examples.

Universal adaptive control of nonlinear systems with unknown growth rate by output feedback

This paper investigates the problem of global stabilization by output feedback, for a family of uncertain nonlinear systems without zero dynamics. These nonlinear systems are dominated by a triangular system satisfying linear growth condition. In contrast to the previous work in the literature, the growth rate here is a positive constant but not known a priori, and therefore the problem becomes more involved and difficult. Using the idea of universal control combined with the output feedback design method developed in Qian and Lin (2002, 2003), we explicitly construct a universal-type adaptive output feedback controller which globally regulates all the states of the uncertain systems without knowing the growth rate.

Output feedback control for a class of nonlinear systems

This paper studies the global stabilization problem by an output controller for a family of uncertain nonlinear systems satisfying some relaxed triangular-type conditions and with dynamics which may not be exactly known. Using a feedback domination design method, we explicitly construct a dynamic output compensator which globally stabilizes such an uncertain nonlinear system. The usefulness of our result is illustrated with an example.

Robust output feedback stabilization of uncertain nonlinear systems with uncontrollable and unobservable linearization

This paper investigates the problem of robust output feedback stabilization for a family of uncertain nonlinear systems with uncontrollable/unobservable linearization. To achieve global robust stabilization via smooth output feedback, we introduce a rescaling transformation with an appropriate dilation, which turns out to be very effective in dealing with uncertainty of the system. Using this rescaling technique combined with the nonseparation principle based design method, we develop a robust output feedback control scheme for uncertain nonlinear systems in the p-normal form, under a homogeneous growth condition. The construction of smooth state feedback controllers and homogeneous observers uses only the knowledge of the bounding homogeneous system rather than the uncertain system itself. The robust output feedback design approach is then extended to a class of uncertain cascade systems beyond a strict-triangular structure. Examples are provided to illustrate the results of the paper.

Further results on global stabilization of uncertain nonlinear systems by output feedback

AbstractFor a family of uncertain nonlinear systems dominated by a triangular system that satisfies linear growth condition with an output dependent growth rate, we prove that global robust stabilization can be achieved by smooth output feedback. This conclusion has incorporated and generalized the recent output feedback stabilization results, for instance, the work (IEEE Trans. Automat. Control 2002; 47:2068–2073) where the same conclusion was already shown to be true for planar systems, and the work (Proceedings of the 42nd IEEE, CDC, 2003; 1544–1549) where the growth rate is required to be a polynomial function of the system output. There are two key ingredients in the present contribution. One of them is the introduction of a rescaling transformation with a dynamic factor that is tuned on‐line through a Riccati‐like differential equation, which turns out to be extremely effective in dealing with the system uncertainty. The other one is the development of a recursive observer design algorithm making it possible to assign the robust observer gains in a step‐by‐step fashion. Both a smooth state feedback controller and a robust observer are explicitly constructed for the rescaled system using only the knowledge of the bounding system. Copyright © 2005 John Wiley & Sons, Ltd.

UNIVERSAL OUTPUT FEEDBACK CONTROL OF NONLINEAR SYSTEMS WITH UNKNOWN GROWTH RATE

This paper investigates the problem of global stabilization by output feedback for a family of uncertain nonlinear systems dominated by a triangular system satisfying linear growth condition. In contrast to the previous work in the literature, the growth rate here is a positive constant but not known a priori, and therefore the problem cannot be addressed by the existing output feedback control schemes. Using the idea of universal control integrated with the recent output feedback design method that is not based on the separation principle, we construct a universal-type output feedback controller which globally regulates all the states of the uncertain systems without knowing the growth rate. We also discuss briefly how this result can be extended to a larger class of nonlinear systems with unknown parameters.

Robust stabilization of uncertain high order systems via smooth output feedback

We investigate the robust stabilization problem for a family of uncertain nonlinear systems with uncontrollable/unobservable linearization. To achieve global robust stabilization using a single output feedback controller, we introduce a rescaling transformation with an appropriate dilation, which turns out to be very effective in dealing with uncertainty of the system. Using this rescaling technique combined with the non-separation principle based design methods (Qian and Lin, 2002a; Yang and Lin, 2003), we develop a robust output feedback control scheme for uncertain nonlinear systems satisfying a homogeneous growth condition. Both a smooth state feedback controller and a homogeneous observer are designed for the rescaled system using only the knowledge of the bounding system rather than the uncertain system itself.

A further result on global stabilization of uncertain nonlinear systems by output feedback

For a family of uncertain nonlinear systems dominated by a triangular system that satisfies linear growth condition with an output dependent growth rate, we prove that global robust stabilization can be achieved by smooth output feedback. This conclusion has incorporated and generalized the recent output feedback stabilization results, for instance, the work (Qian and Lin, 2002b) where the same conclusion was already shown to be true for planar systems, and the work (Praly and Jiang, 2003) where the growth rate is required to be a polynomial function of the system output. There are two key ingredients in the present contribution. One of them is the introduction of a rescaling transformation with a dynamic factor that is tuned on-line through a Riccati-like differential equation, which turns out to be extremely effective in dealing with the system uncertainty. The other one is the development of a recursive observer design algorithm making it possible to assign the robust observer gains in a step-by-step fashion. Both a smooth state feedback controller and a robust observer are explicitly constructed for the rescaled system using only the knowledge of the bounding system.