Uncertain Discrete-time Nonlinear Systems Research Articles

Multiple U-model control of uncertain discrete-time nonlinear systems

Multiple U-model control of uncertain discrete-time nonlinear systems

Multiple U-model control of uncertain discrete-time nonlinear systems

Based on U-model concept and multiple model methodology, this paper presents a weighted multiple U-model control scheme to address the control problem of some classes of discrete-time nonlinear systems with large parameter uncertainties including parameter jumps, which is a difficult problem without a unified solution up to now. Simulation results on two types of non-linear systems with large parameter uncertainties verified the effectiveness of the proposed scheme.

Similar Fault Isolation of Discrete-Time Nonlinear Uncertain Systems: An Adaptive Threshold Based Approach

In this paper, a new concept of “similar fault” is introduced to the field of fault isolation (FI) of discrete-time nonlinear uncertain systems, which defines a new and important class of faults that have small mutual differences in fault magnitude and fault-induced system trajectories. Effective isolation of such similar faults is rather challenging as their small mutual differences could be easily concealed by other system uncertainties (e.g., modeling uncertainty/disturbances). To this end, a novel similar fault isolation (sFI) scheme is proposed based on an adaptive threshold mechanism. Specifically, an adaptive dynamics learning approach based on the deterministic learning theory is first introduced to locally accurately learn/identify the uncertain system dynamics under each faulty mode using radial basis function neural networks (RBF NNs). Based on this, a bank of sFI estimators are then developed using a novel mechanism of absolute measurement of fault dynamics differences. The resulting residual signals can be used to effectively capture the small mutual differences of similar faults and distinguish them from other system uncertainties. Finally, an adaptive threshold is designed for real-time sFI decision making. One important feature of the proposed sFI scheme is that: it is capable of not only isolating similar faults that belong to a pre-defined fault set (used in the training/learning process), but also identifying new faults that do not match any pre-defined faults. Rigorous analysis on isolatability conditions and isolation time is conducted to characterize the performance of the proposed sFI scheme. Simulation results on a practical application example of a single-link flexible joint robot arm are used to show the effectiveness and advantages of the proposed scheme over existing approaches.

Small fault detection from discrete-time closed-loop control using fault dynamics residuals

This paper addresses the problem of small fault detection from closed-loop control for discrete-time nonlinear uncertain systems. The problem is challenging due to (i) the considered system is subject to unstructured nonlinear uncertain dynamics; (ii) the faults are considered to be “small” in the sense that system states and control inputs in faulty mode remain close to those in normal mode; and (iii) fault detection needs to be accomplished during closed-loop control which might counteract the fault effects and thus diminish fault information for detection use. To overcome these challenges, a novel adaptive dynamics learning based fault detection scheme is proposed. Specifically, a new concept of fault dynamics residual is first developed to extract and represent enhanced fault information from closed-loop control. Then, an ideal estimator is constructed by using absolute measures of the proposed fault dynamics residuals. To make the ideal estimator implementable for systems with nonlinear uncertain dynamics, an adaptive dynamics learning approach is subsequently proposed to achieve the locally-accurate approximation of the uncertain fault dynamics. Finally, an adaptive threshold is developed based on the actual estimation system for real-time decision making, i.e., the fault is claimed to be detected when the associated residual signal becomes larger than the adaptive threshold. Rigorous analysis is performed to deduce the small fault detectability condition, which is shown to be significantly relaxed compared to those of existing fault detection methods. Extensive simulations have also been conducted to demonstrate the effectiveness and advantages of the proposed approach.

Fuzzy-Model-Based Output Feedback Sliding-Mode Control for Discrete-Time Uncertain Nonlinear Systems

This paper addresses the output feedback sliding-mode control (SMC) problem for discrete-time uncertain nonlinear systems through Takagi-Sugeno fuzzy dynamic models. Combining with the sliding surface, a descriptor system is constructed to characterize the sliding motion dynamics. Sufficient conditions for asymptotic stability analysis of the sliding motion are attained by the piecewise quadratic Lyapunov functions within a convex optimization setup. Two SMC design approaches are proposed to ensure the finite-time convergence of the sliding surface. Two simulation examples are presented to show the effectiveness of the proposed approaches.

Tube model predictive control for a class of nonlinear discrete-time systems

This paper signifies a tube model predictive control for discrete time uncertain nonlinear systems in the presence of bounded disturbances. The problem of obtaining robustness against parametric un...

Networked iterative learning control for systems with packet dropout and communication delay

In this paper, we consider networked iterative learning control (NILC) design for a class of uncertain discrete-time nonlinear systems with random packet dropout and communication delay, where the input-output coupling parameter (IOCP) is assumed to be unknown. Firstly, we present a learning scheme for the unknown IOCP. Then a simple NILC scheme is developed. It is strictly proved that under certain conditions the developed scheme can guarantee zero-error convergence. Finally, an example is given to validate the findings.

Computational method for estimating the domain of attraction of discrete-time uncertain rational systems

Using linear matrix inequality (LMI) conditions, we propose a computational method to generate Lyapunov functions and to estimate the domain of attraction (DOA) of uncertain nonlinear (rational) discrete-time systems. The presented method is a discrete-time extension of the approach first presented in [39], where the authors used Finsler’s lemma and affine annihilators to give sufficient LMI conditions for stability. The system representation required for DOA computation is generated systematically by using the linear fractional transformation (LFT). Then a model simplification step not affecting the computed Lyapunov function (LF) is executed on the obtained linear fractional representation (LFR). The LF is computed in a general quadratic form of a state and parameter dependent vector of rational functions, which are generated from the obtained LFR model. The proposed method is compared to the numeric n-dimensional order reduction technique proposed in [11]. Finally, additional tuning knobs are proposed to obtain more degrees of freedom in the LMI conditions. The method is illustrated on two benchmark examples.

Robust Preview Control for a Class of Uncertain Discrete-Time Lipschitz Nonlinear Systems

This paper considers the design of the robust preview controller for a class of uncertain discrete-time Lipschitz nonlinear systems. According to the preview control theory, an augmented error system including the tracking error and the known future information on the reference signal is constructed. To avoid static error, a discrete integrator is introduced. Using the linear matrix inequality (LMI) approach, a state feedback controller is developed to guarantee that the closed-loop system of the augmented error system is asymptotically stable with H∞ performance. Based on this, the robust preview tracking controller of the original system is obtained. Finally, two numerical examples are included to show the effectiveness of the proposed controller.

H∞ observer-based event-triggered sliding mode control for a class of discrete-time nonlinear networked systems with quantizations

This paper investigates the problem of H∞ observer-based event-triggered sliding mode control (SMC) for a class of uncertain discrete-time Lipschitz nonlinear networked systems with quantizations occurring in both input and output channels. The event-triggered strategy is used to save the limited network bandwidth. Then, based on the zero-order-hold (ZOH) measurement, a state observer is designed to reconstruct the system state, which facilitates the design of the discrete-time sliding surface. Considering the effects of quantizations, networked-induced constraints and event-triggered scheme, the nonlinear state error dynamics and sliding mode dynamics are converted into a unified linear parameter varying (LPV) time-delay system with the aid of a reformulated Lipschitz property. By using the Lyapunov-Krasovskii functional and free weighting matrix, a new sufficient condition is derived to guarantee the robust asymptotic stability of the resulting closed-loop system with prescribed H∞ performance. And then the observer gain, event-triggering parameter and sliding mode parameter are co-designed. Furthermore, a novel SMC law is synthesized to force the trajectories of the observer system onto a pre-specified sliding mode region in a finite time. Finally, a single-link flexible joint robot example is utilized to demonstrate the effectiveness of the proposed method.

Discrete Time Sliding Mode Controller Using a Disturbance Compensator for Nonlinear Uncertain Systems

In this paper, we propose a new sliding mode control for discrete time nonlinear uncertain systems. The uncertainties include both parametric uncertainties in the state model and external disturbances. To recover the lost invariance and robustness properties of discrete sliding mode control, we develop a disturbance estimation scheme to compensate the system uncertainties without affecting the control law. This control approach ensures the stability of the closed loop system as well as chattering reduction. The performance of the proposed controller is applied to control the motion of a cart-inverted pendulum used as a typical benchmark of nonlinear systems. The stabilization problem of the inverted pendulum system is to design a controller to keep the pendulum in its unstable equilibrium point in the presence of disturbances and parameters variation. The simulation result shows the effectiveness of the control design.

Discrete time quasi-sliding mode control of nonlinear uncertain systems

The control of nonlinear uncertain systems is still an open area of research, and sliding mode control (SMC) is one of the robust and effective methods to cope with uncertain conditions. In this paper, a new sliding mode control algorithm for a class of discrete-time nonlinear uncertain systems is proposed. By using an estimator of uncertainties and external disturbances, the proposed algorithm ensures the stability of the closed loop system as well as the reference tracking. The controller designed using the above technique is completely insensitive to the parametric uncertainty and the external disturbances. Simulations are carried out on a numerical example and a bioreactor benchmark, and the results confirm the effectiveness of our proposition.

Guaranteed cost control for uncertain nonlinear systems with mixed time-delays: The discrete-time case

In this paper, the guaranteed cost control problem is investigated for a general class of discrete-time uncertain nonlinear systems with mixed time-delays. The mixed time-delays under consideration comprise both the discrete and the distributed delays. By using the completing-the-square technique, the discrete and distributed time-delays are handled in a unified framework. Then, by constructing an appropriate Lyapunov functional, a sufficient condition is established under which the closed-loop control system is stable and an adequate performance index is guaranteed over all admissible uncertainties as well as mixed time-delays. Based on the sufficient condition, the nonlinear cost-guaranteed controller is designed and an explicit expression of the controller parameter is obtained. Finally, a numerical simulation example is presented to demonstrate the effectiveness and applicability of the results derived.

Adaptive fuzzy dynamic surface control for uncertain discrete-time non-linear pure-feedback MIMO systems with network-induced time-delay based on state observer

ABSTRACTIn this paper, a state observer-based adaptive fuzzy dynamic surface control is developed for uncertain discrete-time non-linear pure-feedback multiple-input-multiple-output (MIMO) systems with network-induced time-delay. The uncertainties are approximated by a set of adaptive fuzzy logic systems, with the adjusted parameters updated by a simplified recursive least squares estimation algorithm, combined with a state observer. For a constant known network-induced time-delay, the proposed modified dynamic surface control utilising the predicted system states, expands the acceptable network-induced time-delay and stable operating range for a discrete-time non-linear pure-feedback MIMO system in the network. The simulation results indicate that the presented method is effective.

RHONN identifier-control scheme for nonlinear discrete-time systems with unknown time-delays

This work presents a neural identifier-control scheme for uncertain nonlinear discrete-time systems with unknown time-delays. This scheme is based on a neural identifier to get a model of the system and a discrete-time block control technique based on sliding modes to generate the control law. The neural identifier is based on a Recurrent High Order Neural Network (RHONN) trained with an Extended Kalman Filter (EKF) based algorithm. Applicability is shown using real-time test results for linear induction motors. Also, a Lyapunov analysis is added in order to prove the semi-globally uniformly ultimately boundedness (SGUUB) of the proposed neural identifier-control scheme.

Robust Global Adaptive Exponential Stabilization of Discrete-Time Systems With Application to Freeway Traffic Control

This paper is devoted to the development of adaptive control schemes for uncertain discrete-time systems, which guarantee robust global exponential convergence to the desired equilibrium point of the system. The proposed control scheme consists of a nominal feedback law, which achieves robust global exponential stability properties when the vector of the parameters is known, in conjunction with a nonlinear dead-beat observer. The proposed adaptive control scheme depends on certain parameter observability assumptions. The obtained results are applicable to highly nonlinear uncertain discrete-time systems with unknown constant parameters. The successful applicability of the obtained results to real control problems is demonstrated by the rigorous application of the proposed adaptive control scheme to uncertain freeway models. A provided example demonstrates the efficiency of the approach.

Dissipativity-Based Reliable Interval Type-2 Fuzzy Filter Design for Uncertain Nonlinear Systems

The problem of dissipativity-based reliable fuzzy filter design for a category of uncertain nonlinear discrete-time systems is investigated based on the interval type-2 (IT2) T–S fuzzy approach. Uncertainties, which exist in considered systems, are described via adopting both lower membership functions and upper membership functions with corresponding weighting coefficients. In the design process, a vital problem, sensor failure, is taken into consideration. To improve the flexibility of filter design, an IT2 fuzzy filter model is employed, in which membership functions are different from those of the system model. Firstly, sufficient criteria are proposed to ensure the asymptotic stability with strict dissipativity of filtering error system. Following the proposed sufficient conditions, sufficient criteria for dissipative IT2 fuzzy filter design are proposed to estimate unknown system dynamics, where cone complementary linear algorithm is introduced to solve the bilinear problem. Secondly, both $$\mathcal{H}_{\infty }$$ and passive IT2 fuzzy filter design algorithms are presented as extensions. Finally, simulation results are given to illustrate the effectiveness of the IT2 fuzzy reliable filtering approach proposed in this paper.

Adaptive Control via Neural Output Feedback for a Class of Nonlinear Discrete-Time Systems in a Nested Interconnected Form.

In this paper, an adaptive output feedback control is framed for uncertain nonlinear discrete-time systems. The considered systems are a class of multi-input multioutput nonaffine nonlinear systems, and they are in the nested lower triangular form. Furthermore, the unknown dead-zone inputs are nonlinearly embedded into the systems. These properties of the systems will make it very difficult and challenging to construct a stable controller. By introducing a new diffeomorphism coordinate transformation, the controlled system is first transformed into a state-output model. By introducing a group of new variables, an input-output model is finally obtained. Based on the transformed model, the implicit function theorem is used to determine the existence of the ideal controllers and the approximators are employed to approximate the ideal controllers. By using the mean value theorem, the nonaffine functions of systems can become an affine structure but nonaffine terms still exist. The adaptation auxiliary terms are skillfully designed to cancel the effect of the dead-zone input. Based on the Lyapunov difference theorem, the boundedness of all the signals in the closed-loop system can be ensured and the tracking errors are kept in a bounded compact set. The effectiveness of the proposed technique is checked by a simulation study.

Adaptive fuzzy dynamic surface control for uncertain discrete-time nonlinear systems in pure-feedback form using a set of noisy measurements

This paper is concerned with the design of an adaptive fuzzy dynamic surface control for multi-input multi-output uncertain discrete-time nonlinear systems in pure-feedback form. The states of the systems are observed with independent measurement noises. The design approach of the proposed adaptive fuzzy dynamic surface control is described as follows. By applying the theory of the adaptive fuzzy dynamic surface control, the problem of the explosion of complexity due to the repeated differentials of nonlinear functions is removed so that the controller is simplified in a structure at the first stage; second, the number of the adjustable parameters is reduced by using the simplified extended single-input rule modules; and, finally, the simplified weighted least squares estimator is designed to take the estimates for the unmeasurable states and the adjustable parameters. The simulation experiment for a simple numerical system provides the effectiveness of the proposed approach.

Resilient and robust finite-time H∞ control for uncertain discrete-time jump nonlinear systems

• Investigating the resilient and robust finite-time H ∞ control for DMJNSs. • Designing a controller to ensure that DMJNSs are SFTS, SFTB or SH ∞ FTB for DMJNSs. • Presentation of LMI-based conditions to deal with the feasibility issues. • The effectiveness of proposed approaches is illustrated by numerical examples. This paper studies the robust and resilient finite-time H ∞ control problem for uncertain discrete-time nonlinear systems with Markovian jump parameters. With the help of linear matrix inequalities and stochastic analysis techniques, the criteria concerning stochastic finite-time boundedness and stochastic H ∞ finite-time boundedness are initially established for the nonlinear stochastic model. We then turn to stochastic finite-time controller analysis and design to guarantee that the stochastic model is stochastically H ∞ finite-time bounded by employing matrix decomposition method. Applying resilient control schemes, the resilient and robust finite-time controllers are further designed to ensure stochastic H ∞ finite-time boundedness of the derived stochastic nonlinear systems. Moreover, the results concerning stochastic finite-time stability and stochastic finite-time boundedness are addressed. All derived criteria are expressed in terms of linear matrix inequalities, which can be solved by utilizing the available convex optimal method. Finally, the validity of obtained methods is illustrated by numerical examples.