Search

This paper investigates the problem of adaptive finite-time tracking control for strict-feedback nonlinear continuous-time systems subject to full state constraints and dead-zone. By utilizing the finite-time stability theory, barrier Lyapunov functions and the adaptive backstepping method, a novel adaptive tracking control strategy is proposed. On the basis of the presented method, the finite-time control problem of the nonlinear system with dead-zone is solved. The finite-time controller is designed such that all the signals in the closed-loop system are bounded, the output is driven to track the reference signal to a small neighborhood and all states are ensured to remain in the predefined compact sets. Finally, the effectiveness of the proposed scheme is verified via some simulation results.

A continuous, low-complexity, static, state-feedback controller is proposed for strict-feedback systems with deadzone input nonlinearity and disturbances, utilizing the Prescribed Performance Control methodology. The scheme achieves preselected bounds on the transient and steady state output error performance despite the uncertainty in system nonlinearities and deadzone characteristics. Regarding the latter, a general class of admissible deadzones is considered compared to the current state-of-the-art, permitting nonsmooth and even locally decreasing behavior outside the dead-band. Furthermore, approximating structures, i.e.,?neural networks, fuzzy systems, etc., are not utilized and, moreover, the backstepping "explosion of complexity" issue is eliminated without residing in filtering, thus deriving a low-complexity design. The proposed controller evades the construction of a deadzone inverse and does not employ a special analytical deadzone representation. Simulations are performed to verify the theoretical findings.

This note develops a new recursive estimator with a dead zone. By using the estimator, a robust adaptive regulator for a class of simple discrete time nonlinear systems with bounded disturbance is presented. A global stability result of the closed-loop system is obtained through Lyapunov analysis without assuming any growth conditions on the nonlinearities. The regulation performance is also presented through a simulation example.

This paper deals with the adaptive output feedback control problem of a class of uncertain nonlinear systems with an unknown non-symmetric dead-zone nonlinearity. The nonlinear system considered here is dominated by a triangular system without zero dynamics satisfying polynomial growth in the unmeasurable states. An adaptive control scheme is developed without constructing the dead-zone inverse. The proposed adaptive control scheme requires only the information of bounds of the slopes and the breakpoint of dead-zone nonlinearity. The novelty of this paper is that a universal-type adaptive output feedback controller is numerically constructed by using a sum of squares (SOS) optimization algorithm, which ensures the boundedness of all the signals in the adaptive closed-loop without knowing the growth rate of the uncertainties. An example is presented to show the effectiveness of the proposed approach.

In this paper, we present an LMI-based synthesis approach on output feedback design for input saturated linear systems by using deadzone loops. Algorithms are developed for minimizing the upper bound on the regional L"2 gain for exogenous inputs with L"2 norm bounded by a given value, and for minimizing this upper bound with a guaranteed reachable set or domain of attraction. The proposed synthesis approach will always lead to regionally stabilizing controllers if the plant is exponentially unstable, to semi-global results if the plant is non-exponentially unstable, and to global results if the plant is already exponentially stable, where the only requirement on the linear plant is detectability and stabilizability. The effectiveness of the proposed techniques is illustrated with one example.

Despite the well-known conservatism of sector-based results for systems consisting of an interconnection of a linear-time-invariant (LTI) system and a static, sector-bounded nonlinearity, they are widely used in control system analysis and synthesis. This paper shows how, when the sector-bounded nonlinearity is a dead-zone, standard sector based results can be modified to allow the synthesis of a nonlinear controller which can deliver improved performance over standard results. The appealing feature of the method is that, as the main part of the design proceeds using standard sector results, the computation associated with the improved controller is essentially the same as with the standard controller.

Based on a recent description of deadzone nonlinearities via local sector conditions, a new LMI characterization is proposed to compute full-order continuous-time anti-windup controllers with pole constraints. More precisely, an upper bound is introduced on the real part of the controller poles to avoid slow dynamics, which often leads to poor time-domain performance. As is demonstrated in a short applicative part, the introduction of such a bound allows us to efficiently handle the trade-off between stability domain enlargement and time-domain response relevance.

In this paper, a decentralized adaptive control scheme is proposed to address output tracking of a class of interconnected time-delay subsystems with the input of each loop preceded by an unknown dead-zone. Each local controller is designed using the backstepping technique and consists of a new robust control law and new updating laws. Unknown time-varying delays are compensated by using appropriate Lyapunov-Krasovskii functionals. Furthermore, by introducing a new smooth dead-zone inverse, the proposed backstepping design is able to eliminate the effects resulting from dead-zone nonlinearities in the input. It is shown that the proposed controller can guarantee not only stability, but also good transient performance.

This brief proposes a robust control algorithm for stabilization of a three-axis stabilized flexible spacecraft in the presence of parametric uncertainty, external disturbances and control input nonlinearity/dead-zone. The designed controller based on adaptive variable structure output feedback control satisfies the global reaching condition of sliding mode and ensures that the system state globally converges to the sliding mode. A modified version of the proposed control law is also designed for adapting the unknown upper bounds of the lumped uncertainties and perturbations. The stability of the system under the modified control law is established. Numerical simulations show that the precise attitude pointing and vibration suppression can be accomplished using the derived robust or adaptive controller.

We present a general formulation of the problem of multi-variable anti-windup bumpless transfer (AWBT) controller synthesis which provides sufficient conditions for stability covering a large class of typical input nonlinearities such as saturation, deadzone, and switching/override nonlinearities. The resulting synthesis method demonstrates graceful performance degradation whenever input nonlinearities are active through minimization of a weighted L"2 gain. The main contribution of the paper is that the AWBT controller synthesis, using static compensation, is cast as a convex optimization over linear matrix inequalities.

The paper deals with the parameter identification of Hammerstein systems having discontinuous asymmetric nonlinearities (two-segment piecewise-linear with preload and dead zone). Application of a simple decomposition technique provides a special form of Hammerstein model with a minimum number of parameters. The identification is carried out with only one record of measured input/output data despite the dead zone. To demonstrate the feasibility of the identification method, some illustrative examples are included.

An exact method for evaluating the periods and stability of limit cycles in decentralized relay systems is presented. The method can cope with relays having dead zones and hystereses. The underlying idea is to convert the continuous decentralized relay system under a limit cycle to an equivalent fictitious sampled-data system with synchronous samplers. Consequently, regular sampled-data tools can be applied in a straightforward manner to derive closed-form necessary conditions as well as stability conditions and other properties of such systems. This paper extends and generalises recent results obtained by the authors.

For discrete-time plants with unknown dead-zones at the output we propose a new controller structure with an adaptive dead-zone inverse. We consider two control problems; one when only the dead-zone is unknown, and the other when the whole plant is unknown. We allow the dead-zone to be with unequal slopes. The proposed controller structure results in a linear parametrization which is crucial for developing adaptive update laws. We prove the signal boundedness for the closed-loop system, and for a special case we establish asymptotic tracking. Simulation results show that our adaptive control schemes improve system performance.

In this paper we deal with robust control of a class of nonlinear systems which contain uncertainties. It can be viewed as an extension of the work in Corless and Leitmann [IEEE Trans, Autom. Control, AC-26, 1139–1144 (1981)] for the cases where the vector of uncertainties is only partially known. To cope with the uncertainties, an adaptive controller using a dead-zone and a hysteresis function is proposed and both the uniform boundedness of all the closed-loop signals and uniform ultimate boundedness of the system state are guaranteed. In contrast with some previous attempts to relax the a priori knowledge on the uncertainties bounds by using a discontinuous control law, we propose continuous control laws in this paper. Hence, chattering problems (which have practical importance) can be avoided.

This paper presents stability analysis for discrete time pole placement control system with input saturation constraints. It is shown that the adaptive closed-loop system for a class of stable type-m plants is globally stable in the sense that all the signals in the loop remain bounded. It is also shown that certain degree of robustness with respect to modelling uncertainties and disturbances can be achieved for the adaptive control system by implementing a simple fixed dead zone in the parameter estimator. If the plant is free from modelling uncertainties and disturbances and the control input is not saturated for a finite period of time, then the closed-loop adaptive control system will asymptotically be characterized by the desired closed-loop poles within this time period.

In this paper, we propose an adaptive controller for a class of first order nonlinear systems: x = − θ∗Tf(x) − b∗u, subject to bounded input and output disturbances. Unmodelled dynamics are also considered in the stability analysis. A dead zone in the parameters update law is used. The dead zone size does not depend neither on the disturbances upperbounds nor on the magnitude of the unmodelled dynamics. Moreover, the disturbances and parameters upperbounds are not assumed to be a priori known.

A rigorous approach is presented for determining the forced or free oscillations of an on-off system whose linear part is of arbitrary order and whose non-linear part may have a dead zone, hysteresis and dissymetry. A graphical representation yields the solution as the intersections of a circle and a locus @? consisting of two portions which depend respectively on the characteristics of the non-linear component and on the transfer function of the linear part. Examples illustrate the procedure and show the influence of system parameters.