Feedforward Nonlinear Systems Research Articles

State-Feedback Stabilization for a Class of Stochastic Feedforward Nonlinear Time-Delay Systems

We investigate the state-feedback stabilization problem for a class of stochastic feedforward nonlinear time-delay systems. By using the homogeneous domination approach and choosing an appropriate Lyapunov-Krasovskii functional, the delay-independent state-feedback controller is explicitly constructed such that the closed-loop system is globally asymptotically stable in probability. A simulation example is provided to demonstrate the effectiveness of the proposed design method.

State Feedback Control for Stochastic Feedforward Nonlinear Systems

This paper considers the state feedback stabilization problem for a class of stochastic feedforward nonlinear systems. By using the homogeneous domination approach, a state feedback controller is constructed to render the closed-loop system globally asymptotically stable in probability. A simulation example is provided to show the effectiveness of the designed controller.

Simple saturated designs for ANCBC systems and extension to feedforward nonlinear systems

This article re-examines the robust stabilisation of the asymptotically null-controllable with bounded controls (ANCBC) systems, and extends the established algorithm to a wide class of feedforward nonlinear systems whose nominal dynamics contains both multiple integrators and multiple oscillators. Based on the notion of ‘converging-input bounded-state’ (CIBS) rather than ‘small-input small-state’ (SISS), the computation burden in Sussmann et al. (Sussmann, H.J., Sontag, E.D., and Yang, Y. (1994), ‘A General Result on the Stabilization of Linear Systems using Bounded Controls’, IEEE Transactions on Automatic Control, 39, 2411–2425) is reduced and a class of simple saturated control laws is presented for the CIBS stabilisation of ANCBC systems. Then, by combining the technique of dealing with higher-order terms, the algorithm for ANCBC systems is extended to feedforward nonlinear systems.

Global adaptive stabilisation of feedforward systems by smooth output feedback

The authors address the problem of global output-feedback stabilisation for a class of feedforward nonlinear systems. The system satisfies linear growth condition with an unknown growth rate. Using the dynamic gain scaling technique and introducing a new adaptive law, it is proved that global adaptive stabilisation of the feedforward systems can be achieved by smooth output feedback. The gain matrices are only required to satisfy the Hurwitz condition, which makes the control law very easy to implement. Moreover, the authors show that for feedforward systems and low triangular systems with unknown linear growth rate, global adaptive stabilisation can be handled in a unifying framework, that is, the observer and the controller can be designed in a same structure just with two different adaptive laws for the dynamic gain, respectively.

Using a single bit to stabilise an n-dimensional quantised non-linear feedforward system

This study investigates the global asmptotic stabilisability of an n-dimensional quantised feedforward non-linear system. The system’s dynamics are assumed to be locally Lipschitz. So the ranges of the state variables are tightly related to the parameters of the quantisation procedure, that is, there exists coupling between quantisation and control. To save network transmission bandwidth, less quantisation bits (per sample) are preferred. In De Persis’ paper, n bits (per sample) are shown to be enough to stabilise the n-dimensional system by taking a time-invariant quantiser, which assigns 1 bit to each state variable (dimension). We design a time-varying quantiser and can globally stabilise the system with only 1 bit, instead of n bits. That single bit is assigned to the most ‘important’ state variable at each sampling instant, which yields the time-varying coupling among the quantisation errors of state variables besides the coupling between quantisation and control. Owing to the well-designed structure of our quantiser, we can place exponentially converging upper bounds on the quantisation errors of state variables and well handle both types of couplings, so that the global stability of the system is guaranteed with 1 bit. An example is used to demonstrate the effectiveness of the proposed quantiser.

Measurement feedback control for a class of feedforward nonlinear systems

SUMMARYWe propose a measurement feedback controller for a class of feedforward nonlinear systems under sensor noise. The sensor noise has unknown magnitude, frequency, and phase. Our proposed controller is coupled with a low‐pass filter in such a way that the sensor noise is attenuated. We show that the controlled system results in bounded states whose ultimate bounds are inversely proportional to the minimum frequency of the sensor noise. Our result is further generalized to work in a case where the sensor noise is only required to have a Fourier transform with finite energy. Moreover, if the sensor noise enters only at partial states, depending on the location of the sensor noise, the ultimate bounds of the particular states can be made arbitrarily small via the gain factor of the controller. Copyright © 2012 John Wiley & Sons, Ltd.

Open-Loop Reference System for Nonlinear Control Applied to Unmanned Helicopters

A novel way to design a nonlinear feedforward controller is presented. Contrary to input-output linearization and pseudo-control hedging techniques, the new formulation proposed is based on the states of the reference system instead of the plant’s states. By reshaping a commonly-used structure, the resulting scheme is used to produce a pure nonlinear feedforward system which is completely independent from system outputs. This permits the application of the presented control law when knowledge of the system states is not available. Due to the strict separation of plant and reference dynamics, stability of the reference system is no longer affected by the feedback of plant states. Results of flight tests of an unmanned helicopter, which are presented in this paper, demonstrate the applicability of this control concept.

Decentralized stabilization of large-scale feedforward systems using saturated delayed controls

This paper investigates the problem of decentralized stabilization via saturated delayed feedback. First, a new class of saturated delayed feedback controllers is proposed for a class of single-input feedforward nonlinear systems. Then, this design scheme is generalized for the setting of decentralized feedforward systems using saturated time-delayed feedback. The stability analysis for the closed-loop decentralized systems is rather simple based on the proposed feedback structure.

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

Over the past several years, triangular or feedforward nonlinear systems have received considerable attention and there are many independent results for stabilization or regulation problems. These results are often specifically targeted for only one of these systems and they are applicable when the system nonlinearity is known a priori. In this paper, we propose an adaptive output feedback controller coupled with switching logic to universally regulate both triangular and feedforward systems without recognizing the system nonlinearity. Moreover, with our control scheme, the linear growth rate is not required to be known.

Global finite-time stabilisation of a class of feedforward non-linear systems

In this study, the problem of global finite-time stabilisation for a class of feedforward non-linear systems is considered. Based on state transformation and Lyapunov method, a state feedback controller with a dynamic gain is derived. The finite-time stability of the closed-loop system and the boundedness of the control signal are proved by the finite-time Lyapunov stability theory. Different from many other existing control designs for feedforward non-linear systems, neither saturation nor recursive computation is applied in our approach, and thus the designed controllers have a very simple structure which can be easily implemented. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.

Global stabilization for a class of switched nonlinear feedforward systems

The problem of global stabilization for a class of switched nonlinear feedforward systems under arbitrary switchings is investigated in this paper. Based on the integrator forwarding technique and the common Lyapunov function method, we design bounded state feedback controllers of individual subsystems to guarantee asymptotic stability of the closed-loop system. A common coordinate transformation of all subsystems is exploited to avoid individual coordinate transformations for subsystems that are required when applying the forwarding recursive design scheme. An example is provided to demonstrate the effectiveness of the proposed design method.

Feedback stabilization for high order feedforward nonlinear time-delay systems

This paper investigates the problem of global strong stabilization by state feedback, for a family of high order feedforward nonlinear time-delay systems. The uncertain nonlinearities are assumed to satisfy a polynomial growth assumption with an input or delayed input dependent rate. With the help of the appropriate Lyapunov–Krasovskii functionals, and a rescaling transformation with a gain to be tuned online by a dynamic equation, we propose a dynamic low gain state feedback control scheme. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.

Adaptive stabilization of time-delay feedforward nonlinear systems

In this paper, we consider the adaptive stabilization problem for feedforward nonlinear systems with time delays. An adaptive stabilizer is proposed. Our stabilizer takes a nested saturation feedback, and a set of switching logics is designed to tune online the saturation levels in a piecewise constant or switching manner. It has been shown that under our proposed control, all closed-loop states are bounded and asymptotic regulation is achieved.

Design of Stabilizing Controllers With a Dynamic Gain for Feedforward Nonlinear Time-Delay Systems

In this technical note, constructive control techniques have been proposed for controlling feedforward nonlinear time-delay systems. The nonlinear terms admit an incremental rate depending on the input or delayed input. Based on the Lyapunov-Razumikhin theorem and Lyapunov-Krasovskii theorem, the delay-independent feedback controllers are explicitly constructed such that the closed-loop systems are globally asymptotically stable. An example is given to demonstrate the effectiveness of the proposed design procedure.

Stabilization of a Class of Feedforward and Non-feedforward Nonlinear Systems with a Large Delay in the Input via LMI Approach

We consider a stabilization problem of a class of input-delayed nonlinear systems that have not only feedforward, but also some non-feedforward nonlinearity. While there are some existing results that deal with input-delayed non-feedforward nonlinear systems, they often assume a small input delay. It has been often the case that for a large input delay, the results are limited to only feedforward systems. In this letter, combined with the LMI approach in [3] and the reduction method in [5], we show that some feedforward and non-feedforward systems with a large delay in the input can be stabilized via the proposed controller.

Asymptotic stabilization of high‐order feedforward systems with delays in the input

AbstractThis paper deals with the state feedback controller design for a class of high‐order feedforward (upper‐triangular) nonlinear systems with delayed inputs. The uncertainties in the systems are assumed to be dominated by higher‐order nonlinearities multiplying by a constant growth rate. The designed controller, which is a continuous but not smooth feedback, could achieve global asymptotical stability. Based on the appropriate state transformation of time‐delay systems, the problem of controller design can be converted into the problem of finding a parameter, which can be obtained by appraising the nonlinear terms of the systems. The nonlinear systems considered here are more general than conventional feedforward systems and they could be viewed as generalized feedforward systems. Two examples are given to show the effectiveness of the proposed design procedure. Copyright © 2009 John Wiley & Sons, Ltd.

Stabilisation of non-linear systems with unknown growth rate by adaptive output feedback

In recent years, several results have been proposed on the global stabilisation of non-linear systems with unknown linear growth rate. However, these works are limited in the sense that they consider only one particular form of non-linear systems–mostly either triangular or feedforward form. We propose an adaptive output feedback control scheme which can deal with both triangular or feedforward non-linear systems with unknown linear growth rate in a unified framework. Thus, our result broadens the class of non-linear systems under consideration over the existing results.

A small gain approach to global stabilization of nonlinear feedforward systems with input unmodeled dynamics

In this paper, we study the global robust stabilization problem of strict feedforward systems subject to input unmodeled dynamics. We present a recursive design method for a nested saturation controller which globally stabilizes the closed-loop system in the presence of input unmodeled dynamics. One of the difficulties of the problem is that the Jacobian linearization of our system at the origin may not be stabilizable. We overcome this difficulty by employing a special version of the small gain theorem to address the local stability, and, respectively, the asymptotic small gain theorem to establish the global convergence property, of the closed-loop system. An example is given to show that a redesign of the controller is required to guarantee the global robust asymptotic stability in the presence of the input unmodeled dynamics.

Global Stabilization of Feedforward Nonlinear System Based on Nested Saturated Control

Abstract In this paper, we discuss global stabilization procedure for convergence of a more general feedforward nonlinear systems. Our stabilizer consists of a nested saturation function, which is a nonlinear combination of saturation functions. We extend the existing stabilization results and prove that our stabilizer is exponential convergent.

Pseudo-decentralized adaptive stabilization of large-scale feedforward nonlinear systems

In this paper, we propose a pseudo-decentralized adaptive control scheme for a class of large-scale feedforward nonlinear systems with unknown nonlinear effects within subsystems and unknown nonlinear interactions among subsystems. The local controller of each subsystem takes a nested saturation feedback, using the state of its own subsystem, and the saturation levels are tuned online in a switching manner via a set of switching logics, which requires some binary flag communication among subsystems. Global asymptotic regulation of the closed-loop states is achieved.