Uncertain Discrete-time Nonlinear Systems Research Articles

Simplified algorithm of an adaptive fuzzy backstepping control for MIMO uncertain discrete-time nonlinear systems using a set of noisy measurements

This paper presents a simplified algorithm of an adaptive fuzzy backstepping control (AFBC) for multi-input multi-output uncertain discrete-time nonlinear systems with uncertainties viewed as the modelling errors and the unknown external disturbances, and the observation of the states is taken with measurement noises. The simplified algorithm of the proposed AFBC is designed as follows. The explosion of complexity problem due to repeated computation of nonlinear functions is removed to derive the simplified algorithm at the first stage, secondly the number of the adjustable parameters is reduced by using the fuzzy inference approach based on the proposed simplified extended single input rule modules, and finally the simplified weighted least squares estimator is constructed by reducing the computational burden of the estimation for the un-measurable states and the adjustable parameters. The effectiveness of the proposed approach is indicated through the simulation experiment of a simple numerical system.

Fuzzy Adaptive Control With State Observer for a Class of Nonlinear Discrete-Time Systems With Input Constraint

In this paper, an adaptive fuzzy controller is constructed for a class of nonlinear discrete-time systems with unknown functions and bounded disturbances. The main characteristics of the systems are that they take into account the effect of discrete-time dead zone and the system states are not required to be measurable. The stability problem of this class of systems is for the first time to be addressed in this paper. Due to the unavailability of the states and the presence of the discrete-time dead zone, the controller design becomes more difficult. To stabilize the uncertain nonlinear discrete-time systems, the fuzzy logic systems are used to approximate the unknown functions, a fuzzy state observer is designed to estimate the immeasurable states, and the effect caused by discrete-time dead zone can be solved via establishing an adaptation auxiliary signal. Based on the Lyapunov approach, it is proved that all the signals of the closed-loop system are the semiglobal uniformly ultimately bounded, and the tracking error is made within a small neighborhood around zero. The feasibility of the developed control scheme is verified via two simulation examples.

Modified Chaotic Bat Algorithm Based Counter Propagation Neural Network for Uncertain Nonlinear Discrete Time System

Weight and bias connection are important features of neural networks, which is still challenging for researchers. In this work, we focus on initial weights and bias connection of counter propagation network (CPN) using modified chaotic bat algorithm (MCBA) i.e., MCBA-CPN for uncertain nonlinear systems and compare it with CPN using chaotic bat algorithm (CBA) i.e., CBA-CPN. Chaotic function is used for pulse frequency of bats in MCBA. We have implemented CBA and MCBA, which are based on the consideration of the global solution in the sound intensity adjustment. MCBA-CPN is applied on different uncertain nonlinear systems and Mackey–Glass time series data to test the concert in terms of prediction accuracy. Proposed method is validated through statistical testing like chi-square and [Formula: see text]-test demonstrate that the difference between target and output of proposed method are acceptable. Finally, MCBA-CPN is applied to a real world problem for prediction of milk production data.

Direct adaptive fuzzy backstepping control for uncertain discrete-time nonlinear systems using noisy measurements

ABSTRACTThis paper presents a direct adaptive fuzzy backstepping control (AFBC) for multi-input multi-output uncertain discrete-time nonlinear systems. It is assumed that the systems are described by a discrete-time state equation with uncertainties to be viewed as the modelling errors and the unknown external disturbances, and the observation of the states is taken with independent measurement noises. The proposed direct AFBC is presented as follows. The proposed direct AFBC is assumed to be the fuzzy logic system by removing the explosion of complexity problem due to repeated computation of nonlinear functions at the first stage. Second, the number of the adjustable parameters is reduced by the fuzzy inference approach based on the extended single input rule modules. Third, the simplified weighted least squares estimator is constructed by reducing the computational burden of the estimation for the unmeasurable states and the adjustable parameters. The effectiveness of the proposed direct AFBC is illustrated through the simulation experiment of a simple numerical system.

Robust multiobserver design for discrete uncertain nonlinear systems with time-varying delay

In this paper, a robust multiobserver is proposed for the state estimation of discrete-time uncertain nonlinear systems with time-varying delay. The designed multiobserver is based on the decoupled multimodel approach. Unlike the classically used multimodel structures, the decoupled multimodel provides a flexibility of modelling. Indeed, the partial models’ structures can be adapted to the complexity of the system in each operating regime, thus the partial models can be with different dimensions. Delay-dependent sufficient conditions for the synthesis of a robust multiobserver against norm-bounded parametric uncertainties and in the presence of measurement noise are established in terms of linear matrix inequalities. A simulation example is given to illustrate the effectiveness of the designed multiobserver.

Design of adaptive fuzzy backstepping sliding mode control for MIMO uncertain discrete-time nonlinear systems based on noisy measurements

This paper presents an adaptive fuzzy backstepping sliding mode control for multi-input and multi-output uncertain nonlinear systems in semi-strict feedback form. The systems are described by a discrete-time state equation with uncertainties viewed as the modeling errors and the unknown external disturbances, and the observation of the states is taken with independent measurement noises. Combining the adaptive fuzzy backstepping control with the sliding mode control approach for the comprehensive improvement in the stability and the robustness, the adaptive fuzzy backstepping sliding mode control is approximately designed where the design parameters are selected using an appropriate Lyapunov function. The uncertainities are approximated as fuzzy logic systems using the fuzzy inference approach based on the extended single input rule modules to reduce the number of the fuzzy IF-THEN rules. The estimates for the un-measurable states and the adjustable parameters are taken by the proposed simplified weighted least squares estimator. It is proved that the trajectory of the tracking error and the sliding surface is uniformly ultimately bounded. The effectiveness of the proposed approach is indicated through the simulation experiment of a simple numerical system.

Neural Approximation-Based Adaptive Control for a Class of Nonlinear Nonstrict Feedback Discrete-Time Systems.

In this paper, an adaptive control approach-based neural approximation is developed for a class of uncertain nonlinear discrete-time (DT) systems. The main characteristic of the considered systems is that they can be viewed as a class of multi-input multioutput systems in the nonstrict feedback structure. The similar control problem of this class of systems has been addressed in the past, but it focused on the continuous-time systems. Due to the complicacies of the system structure, it will become more difficult for the controller design and the stability analysis. To stabilize this class of systems, a new recursive procedure is developed, and the effect caused by the noncausal problem in the nonstrict feedback DT structure can be solved using a semirecurrent neural approximation. Based on the Lyapunov difference approach, it is proved that all the signals of the closed-loop system are semiglobal, ultimately uniformly bounded, and a good tracking performance can be guaranteed. The feasibility of the proposed controllers can be validated by setting a simulation example.

Neural estimation using a stable discrete-time MLP observer for a class of discrete-time uncertain MIMO nonlinear systems

This paper has proposed a novel class of the stable discrete-time multilayer perceptron (MLP) neural observer for a class of discrete-time multiple-input multiple-output uncertain nonlinear systems. It is trained online and is used to estimate the states of the system especially when there is no prior knowledge about the dynamics of the system and can be applied as a basis for designing an intelligent control. The weight updating for the MLP is the developed backpropagation algorithm. Online training, convergence of the observer error to neighborhood of origin, robustness against uncertainties and disturbance, low computational expense and fast convergence rate are the main qualities of the suggested method. Lyapunov’s direct method is used to guarantee the stability of the proposed system. To demonstrate the performance of the discrete-time MLP observer, two discrete-time nonlinear dynamic systems are simulated in MATLAB/Simulink. Simulation results confirm the proficiency of the system even at different operating conditions and the presence of disturbance and measurement noise.

FCPN Approach for Uncertain Nonlinear Dynamical System with Unknown Disturbance

In this work, we have used a fuzzy counter-propagation network (FCPN) model to control different discrete-time, uncertain nonlinear dynamic systems with unknown disturbances. Fuzzy competitive learning (FCL) is used to process the weight connection and make adjustments between the instar and the outstar of the network. FCL paradigm adopts the principle of learning, used for calculation of the Best Matched Node (BMN) in the instar–outstar network. FCL provides a control of discrete-time uncertain nonlinear dynamic systems having dead zone and backlash. The errors like mean absolute error (MAE), mean square error (MSE), and best fit rate, etc. of FCPN are compared with networks like dynamic network (DN) and back propagation network (BPN). The FCL foretells that the proposed FCPN method gives better results than DN and BPN. The success and enactments of the proposed FCPN are validated through simulations on different discrete-time uncertain nonlinear dynamic systems and Mackey–Glass univariate time series data with unknown disturbances over BPN and DN.

A modified robust self-tuning controller for Hammerstein nonlinear systems with asymmetric deadzone input nonlinearity

This article presents a novel adaptive control method for a class of uncertain discrete-time Hammerstein nonlinear systems with asymmetric deadzone input nonlinearity and bounded external disturbance. Based on the parameterization model of Hammerstein systems, the unknown parameters are updated by a robust recursive least squares algorithm with a deadzone weighted factor. Then, by introducing an estimate of the unmodeled dynamics as a feedback, the deadzone compensating control law is derived without an adaptive deadzone inverse. Theoretical results show that all the signals in the closed-loop system are bounded and the output tracking error is convergent with a relatively small residue. To show the usefulness of the developed results, simulation examples including an electro-hydraulic servo system and a DC motor subjected to a nonlinear friction are studied.

Reduced-order observer-based fault estimation and fault-tolerant control for a class of discrete Lipschitz nonlinear systems

Summary This paper addresses an issue on reduced-order observer-based robust fault estimation and fault-tolerant control for a class of uncertain nonlinear discrete-time systems. By introducing a nonsingular coordinate transformation, a new nonlinear reduced-order fault estimation observer (RFEO) is proposed with a wide application range in order to achieve an accurate estimation of both states and faults. Next, an improved algorithm is given to obtain the optimal estimation by using a novel iterative linear matrix inequality technique. Furthermore, an RFEO-based output feedback fault-tolerant controller, which is independent of the RFEO, can maintain the stability and performance of the faulty system. Simulation results of an aircraft application show the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.

An Extended Zonotopic and Gaussian Kalman Filter (EZGKF) merging set-membership and stochastic paradigms: Toward non-linear filtering and fault detection

A framework merging the set-membership and the stochastic paradigms is formalized and used to design an Extended Zonotopic and Gaussian Kalman Filter (EZGKF) dealing with the robust state estimation and the fault detection of uncertain discrete-time nonlinear systems. The so-called Set-membership and Gaussian Mergers (SGM) are introduced and particularized to Zonotopes (ZGM). They provide a constructive and computationally efficient solution to propagate random uncertainties with incompletely specified probability distributions combining set-based support enclosures and upper covariance matrix bounds formalized as matrix inequalities. Based on a full time-varying LPV enclosure featuring structured state matrix uncertainties, and given some confidence level expressed in probabilistic terms (maximal false alarm rate), a detection test is developed and shown to merge the usually mutually exclusive benefits granted by set-membership techniques (robustness to the worst-case within specified bounds, domain computations) and stochastic approaches (taking noise distribution into account, probabilistic evaluation of tests). A numerical example illustrates the state estimation capabilities of EZGKF and the improved tradeoff between the sensitivity to faults and the robustness to disturbances/noises.

Adaptive Neural Network-Based Event-Triggered Control of Single-Input Single-Output Nonlinear Discrete-Time Systems.

This paper presents a novel adaptive neural network (NN) control of single-input and single-output uncertain nonlinear discrete-time systems under event sampled NN inputs. In this control scheme, the feedback signals are transmitted, and the NN weights are tuned in an aperiodic manner at the event sampled instants. After reviewing the NN approximation property with event sampled inputs, an adaptive state estimator (SE), consisting of linearly parameterized NNs, is utilized to approximate the unknown system dynamics in an event sampled context. The SE is viewed as a model and its approximated dynamics and the state vector, during any two events, are utilized for the event-triggered controller design. An adaptive event-trigger condition is derived by using both the estimated NN weights and a dead-zone operator to determine the event sampling instants. This condition both facilitates the NN approximation and reduces the transmission of feedback signals. The ultimate boundedness of both the NN weight estimation error and the system state vector is demonstrated through the Lyapunov approach. As expected, during an initial online learning phase, events are observed more frequently. Over time with the convergence of the NN weights, the inter-event times increase, thereby lowering the number of triggered events. These claims are illustrated through the simulation results.

NN-adaptive predictive control for a class of discrete-time nonlinear systems with input-delay

An adaptive neural network (NN) predictive control algorithm is proposed for a class of uncertain discrete-time nonlinear systems with input-delay. For approximate the nonlinear part of the uncertain discrete-time nonlinear system, the recurrent neural network (RNN) is employed. A version of discrete-time NN weight update rule is given. For compensate the reconstructive error of the RNN and the external disturbances, the robust control term is designed. In order to compensate the time-delay in input channel, a predictive control algorithm is proposed. Then the synchronous tracking objective can be realized. An illustrative example is provided to demonstrate the effectiveness of the proposed control strategy.

Near Optimal Event-Triggered Control of Nonlinear Discrete-Time Systems Using Neurodynamic Programming.

This paper presents an event-triggered near optimal control of uncertain nonlinear discrete-time systems. Event-driven neurodynamic programming (NDP) is utilized to design the control policy. A neural network (NN)-based identifier, with event-based state and input vectors, is utilized to learn the system dynamics. An actor-critic framework is used to learn the cost function and the optimal control input. The NN weights of the identifier, the critic, and the actor NNs are tuned aperiodically once every triggered instant. An adaptive event-trigger condition to decide the trigger instants is derived. Thus, a suitable number of events are generated to ensure a desired accuracy of approximation. A near optimal performance is achieved without using value and/or policy iterations. A detailed analysis of nontrivial inter-event times with an explicit formula to show the reduction in computation is also derived. The Lyapunov technique is used in conjunction with the event-trigger condition to guarantee the ultimate boundedness of the closed-loop system. The simulation results are included to verify the performance of the controller. The net result is the development of event-driven NDP.

Observer-based controller for constrained uncertain stochastic nonlinear discrete-time systems

Summary In this paper, an observer-based control approach is proposed for uncertain stochastic nonlinear discrete-time systems with input constraints. The widely used extended Kalman filter (EKF) is well known to be inadequate for estimating the states of uncertain nonlinear dynamical systems with strong nonlinearities especially if the time horizon of the estimation process is relatively long. Instead, a modified version of the EKF with improved stability and robustness is proposed for estimating the states of such systems. A constrained observer-based controller is then developed using the state-dependent Riccati equation approach. Rigorous analysis of the stability of the developed stochastically controlled system is presented. The developed approach is applied to control the performance of a synchronous generator connected to an infinite bus and chaos in permanent magnet synchronous motor. Simulation results of the synchronous generator show that the estimated states resulting from the proposed estimator are stable, whereas those resulting from the EKF diverge. Moreover, satisfactory performance is achieved by applying the developed observer-based control strategy on the two practical problems. Copyright © 2015 John Wiley & Sons, Ltd.

Adaptive single neural network control for a class of uncertain discrete-time nonlinear strict-feedback systems with input saturation

In this paper, a novel adaptive neural network control approach is presented for a class of uncertain discrete-time nonlinear strict-feedback systems with input saturation. By combining single neural network approximation and minimal learning parameter technique, the proposed approach is able to eliminate the complexity growing problem and alleviate the explosion of learning parameters. An auxiliary design system is incorporated into the control scheme to overcome the problem of input saturation constraints. Following this approach, the designed controller contains only one actual control law and one adaptive law, the numbers of input variables and weights of neural network updated online are decreased drastically, and the number of parameter updated online for whole system is reduced to only one. Compared with the existing methods, the adaptive mechanism with much simpler controller structure and minimal learning parameterization is achieved; therefore, the computational burden is lighter. It is shown via Lyapunov theory that all signals in the closed-loop system are uniformly ultimately bounded. Finally, simulation results via two examples are employed to illustrate the effectiveness and merits of the proposed scheme.

Reliable [formula omitted] control for uncertain nonlinear discrete-time systems subject to multiple intermittent faults in sensors and/or actuators

This study focuses on passive fault-tolerant control for a class of uncertain nonlinear discrete-time systems subject to multiple intermittent faults. The considered intermittent faults are assumed to be additive ones in sensors and/or actuators. To achieve fault-tolerant control, a dynamic output-feedback controller is designed such that the closed-loop system remains stable and satisfies acceptable performance, even when there are parameter uncertainties, nonlinearities of specific type, and multiple additive intermittent sensor and/or actuator faults. The linear matrix inequality method is employed to obtain sufficient conditions for achieving fault tolerance and ensuring the prescribed H∞ performance index. Finally, the effectiveness of the proposed method is demonstrated by simulation examples.

Admissibility analysis for discrete-time singular systems with time-varying delays by adopting the state-space Takagi-Sugeno fuzzy model

This paper is pertained with the problem of admissibility analysis of uncertain discrete-time nonlinear singular systems by adopting the state-space Takagi-Sugeno fuzzy model with time-delays and norm-bounded parameter uncertainties. Lyapunov Krasovskii functionals are constructed to obtain delay-dependent stability condition in terms of linear matrix inequalities, which is dependent on the lower and upper delay bounds. Finally, numerical examples are provided to substantiate the theoretical results.

Adaptive neural network tracking design for a class of uncertain nonlinear discrete-time systems with unknown time-delay

In this paper, an adaptive neural network tracking control is studied for a class of uncertain nonlinear systems. The studied systems are in discrete-time form and unknown time-delay is considered here. Up to now, the research works on nonlinear discrete-time main focus on systems without time-delay, so the problem of the unknown time-delay will be solved in this paper. Based on the Lipschitz or norm-boundedness assumption of the unknown nonlinearities, the mean-value theorem is utilized to solve the unknown time-delay problem. In order to overcome the noncausal problem, the strict-feedback systems will be transformed into a special form. The radial basis functions neural networks (RBFNN) are utilized to approximate the unknown functions of the systems, the adaptation laws and the controllers are designed based on the transformed systems. By using the Lyapunov analysis, it is proven that the closed-loop system is stable in the sense that semi-globally uniformly ultimately bounded (SGUUB) and the output tracking errors converge to a bounded compact set. A simulation example is used to illustrate the effectiveness of the proposed algorithm.