Uncertain Multi-input Multi-output Nonlinear Systems Research Articles

Adaptive Fuzzy Fault Tolerant Control of Uncertain MIMO Nonlinear Systems With Output Constraints and Unknown Control Directions

This article studies the adaptive fuzzy fault tolerant control (FTC) problem for a class of uncertain multi-input multi-output (MIMO) nonlinear systems with unknown control directions in the presence of time-varying asymmetric output constraints. Our contribution includes a step forward beyond usual FTC results to exhibit that the system output of nonsquare and square MIMO systems is uniformly bounded against actuator faults by a novel FTC methodology without the fault detection unit, as well as stay in the preselected constraints. To obtain new results, an equivalent unconstrained system is established by employing an error transformation technique. Furthermore, a learning-based switching function scheme is proposed to automatically activate different groups of actuators without human intervention for attenuating the influence of faulty actuators. By this means, no explicit fault detection and isolation units are needed to result in reducing the risk of false alarm or missed detections and expediting the responsiveness of the controller. Moreover, the obstacle caused by unknown control directions is circumvented by a novel technique combining the matrix decomposition technique and Nussbaum-type function. It is proved that the desired tracking performance with prescribed output bounds and the boundedness of all the signals in the closed-loop system can be guaranteed via an improved average dwell time approach. Finally, simulation results demonstrate the merits of the proposed controller.

Output-Constrained Robust Adaptive Control for Uncertain Nonlinear MIMO Systems With Unknown Control Directions

This letter proposes a new output-constrained robust adaptive controller for a class of uncertain multi-input multi-output nonlinear systems. In the adaptive control synthesis, Nussbaum gain is introduced, which not only ensures the closed-loop stability of the system in presence of unknown control directions but also enforces the asymptotic tracking of the reference signal under non-parametric plant uncertainties. The output constraints are enforced by carrying out a novel transformation, which transforms the constrained system into an equivalent unconstrained system. It is proven that the closed-loop system is asymptotic stable in the sense of Lyapunov and the output of the system will remain bounded by the imposed output constraints. The effectiveness of the proposed control design is demonstrated through extensive simulations.

Type-2 fuzzy cerebellar model articulation control system design for MIMO uncertain nonlinear systems

This paper aims to propose a more efficient neural network and applies it as an adaptive controller for the multi-input multi-output (MIMO) uncertain nonlinear systems. First, a more efficient fuzzy neural network named as fuzzy cerebellar model articulation controller (CMAC) is introduced, then an adaptive controller is proposed using a novel interval type-2 fuzzy CMAC (T2FCMAC). The T2FCMAC realizes an interval type-2 fuzzy logic system based on the structure of the CMAC. Due to the better ability of handling uncertainties provided by type-2 fuzzy sets, it can solve some complicated problems with outstanding effectiveness than type-1 fuzzy sets. In addition, an intelligent control system is proposed; this control system is comprised of a T2FCMAC and an auxiliary compensation controller. The T2FCMAC is utilized to approximate a perfect controller and the parameters of T2FCMAC are on-line tuned by the derived adaptive laws based on a Lyapunov function. The auxiliary compensation controller is designed to suppress the influence of residual approximation error between the perfect controller and the T2FCMAC. Finally, two MIMO uncertain nonlinear systems, a Chua’s chaotic circuit and a mass-spring-damper mechanical system, are performed to verify the effectiveness of the proposed control scheme. The simulation results confirm that the proposed intelligent adaptive control system can achieve favorable tracking performance with desired robustness.

Disturbance-observer-based fuzzy terminal sliding mode control for MIMO uncertain nonlinear systems

• Modelling and simulation of a novel five-rotor unmanned aerial vehicle with an extra rotor. • Proposing a disturbance-observer-based fuzzy terminal sliding mode controller . • Considering MIMO uncertain nonlinear systems with unmeasured external disturbance . • Unknown non-symmetric input saturation and control singularity are investigated. • Closed-loop stability and convergence of the state estimations in finite time are proved. This study is concerned with the design of a disturbance-observer-based fuzzy terminal sliding mode controller (FTSMC) for multi-input multi-output (MIMO) uncertain nonlinear systems by considering unknown non-symmetric input saturation and control singularity. The disturbance observer is proposed for the unmeasured external disturbance and guarantees the convergence of the disturbance estimation error to zero in a finite time. The terminal sliding mode controller (TSMC) is designed for MIMO uncertain nonlinear systems by utilizing the output of the proposed disturbance observer. This control scheme combines the disturbance-observer-based TSMC with a fuzzy logic system in the presence of unknown non-symmetric input saturation and control singularity in order to reduce chattering phenomena. Finite time asymptotic stability, convergence of the disturbance observer, and convergence of the closed-loop system are proved via Lyapunov stability theorem. In addition, a five-rotor unmanned aerial vehicle (UAV) is employed in the numerical simulations to demonstrate the effectiveness and performance of the proposed control scheme. Disturbance observer estimates the payload and flight endurance of the five-rotor UAV. Genetic algorithm (GA) optimization is used to specify the parameters of the disturbance-observer-based TSMC (GATSMC) to decrease chattering. Finally, the superior performance of FTSMC is investigated over TSMC and GATSMC.

Active disturbance rejection control to MIMO nonlinear systems with stochastic uncertainties: approximate decoupling and output-feedback stabilisation

ABSTRACTIn this paper, we apply the active disturbance rejection control, an emerging control technology, to output-feedback stabilisation for a class of uncertain multi-input multi-output nonlinear systems with vast stochastic uncertainties. Two types of extended state observers (ESO) are designed to estimate both unmeasured states and stochastic total disturbance which includes unknown system dynamics, unknown stochastic inverse dynamics, external stochastic disturbance without requiring the statistical characteristics, uncertain nonlinear interactions between subsystems, and uncertainties caused by the deviation of control parameters from their nominal values. The estimations decouple approximately the system after cancelling stochastic total disturbance in the feedback loop. As a result, we are able to design an ESO-based stabilising output-feedback and prove the practical mean square stability for the closed-loop system with constant gain ESO and the asymptotic mean square stability with time-varying gain ESO, respectively. Some numerical simulations are presented to demonstrate the effectiveness of the proposed output-feedback control scheme.

Fuzzy adaptive control of nonlinear MIMO systems with unknown dead zone outputs

This paper addresses a novel fuzzy adaptive control method for a class of uncertain nonlinear multi-input multi-output (MIMO) systems with unknown dead-zone outputs and immeasurable states. The immeasurable states under consideration are estimated by designing a fuzzy state observer. Based on the properties of the Nussbaum-type function, the difficulty of fuzzy adaptive control caused by the unknown dead zone outputs of MIMO nonlinear uncertain systems is overcome. The presented design algorithm not only guarantees that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded, but also ensures that the outputs of the MIMO system converge to a small neighborhood of the desired outputs. The main contributions of this research lie in that the developed MIMO systems are more general, and an efficient design method of output-feedback controller is investigated for the studied MIMO systems, which is more applicable in practical environment. Simulation results illustrate the effectiveness of the proposed scheme.

Synthetic adaptive fuzzy tracking control for MIMO uncertain nonlinear systems with disturbance observer

In this paper, a synthetic adaptive fuzzy tracking control method is studied for a class of multi-input multi-output (MIMO) uncertain nonlinear systems with time-varying disturbances. The unknown nonlinear functions are approximated by employing generalized fuzzy hyperbolic model. A synthetic adaptive fuzzy control is designed by dynamic surface control, serial-parallel estimation model and the disturbance observer. Then by using Lyapunov stability theory, it is guaranteed that all the variables of the closed-loop systems are semi-globally uniformly ultimately bounded (SGUUB). Finally, a satisfactory tracking performance with faster and higher accuracy can be obtained by adjusting the parameters appropriately. A practical example simulation can demonstrate the effectiveness and applicability of the proposed control approach.

Adaptive iterative learning controller with input learning technique for a class of uncertain MIMO nonlinear systems

In this paper, an adaptive iterative learning controller (AILC) with input learning technique is presented for uncertain multi-input multi-output (MIMO) nonlinear systems in the normal form. The proposed AILC learns the internal parameter of the state equation as well as the input gain parameter, and also estimates the desired input using an input learning rule to track the whole history of command trajectory. The features of the proposed control scheme can be briefly summarized as follows: 1) To the best of authors’ knowledge, the AILC with input learning is first developed for uncertain MIMO nonlinear systems in the normal form; 2) The convergence of learning input error is ensured; 3) The input learning rule is simple; therefore, it can be easily implemented in industrial applications. With the proposed AILC scheme, the tracking error and desired input error converge to zero as the repetition of the learning operation increases. Single-link and two-link manipulators are presented as simulation examples to confirm the feasibility and performance of the proposed AILC.

Indirect neuroadaptive control of unknown MIMO systems tracking uncertain target under sensor failures

The problem of tracking a moving target with unknown trajectory is interesting and nontrivial. The underlying problem becomes even more challenging if uncertain dynamics and sensor failures are involved. This work presents an indirect adaptive neural network control strategy capable of making uncertain multi-input multi-output nonlinear systems track a moving target with uncertain trajectory closely despite sensor faults. An analytical model is proposed to allow the estimated (predicted) target trajectory to be linked mathematically with the actual disguised (polluted) target trajectory, thus facilitating the control design and stability analysis. A barrier Lyapunov function based design technique is employed to ensure that the inputs to the neural network remain within the compact set such that the neural network unit maintains its learning/approximating functionality during the entire process of system operation. The proposed control scheme guarantees the boundedness of all the closed-loop signals and the uniformly ultimately bounded stable tracking. Numerical simulation results also confirm the effectiveness of the proposed neuroadaptive tracking control method.

Robust stability of MIMO nonlinear uncertain systems using operator-based right coprime factorisation

ABSTRACTIn this paper, a class of multi-input–multi-output (MIMO) nonlinear systems with uncertainties is considered by using operator-based right coprime factorisation. First, based on proposed quotient operators, coupling effect of the MIMO nonlinear systems is discussed. Second, based on the operator-based right coprime factorisation approach, sufficient conditions for guaranteeing robust stability of the MIMO nonlinear systems with uncertainties are proposed by using a new unimodular operator. Finally, a simulation example is shown to illustrate the proposed design scheme for the MIMO nonlinear systems with uncertainties.

Global Finite Time Stabilization of a Class of Uncertain MIMO Nonlinear Systems

It is aimed to obtain global finite time stabilization of a class of uncertain multi-input–multi-output (MIMO) nonlinear systems in the presence of bounded disturbances by applying nonsingular terminal sliding mode controllers. The considered nonlinear systems consist of double integrator subsystems which interact with each other. In the proposed methods, new terminal sliding surfaces are introduced along with design of proper control inputs. The terminal sliding surfaces are defined such that the global finite time stability of sliding mode dynamic is attained. The control inputs are designed to steer the states into sliding motion within finite time and retain them on the terminal sliding surfaces. The presented approaches guarantee the finite time convergence of states with low sensitivity to their initial values. The convergence rate could be adjusted by proper choice of existing arbitrary parameters in the suggested control schemes. Three numerical simulation examples including van de Pol system and two robotic manipulators are provided to confirm the applicability and effectiveness of the proposed control schemes.

An adaptive disturbance rejection control scheme for multivariable nonlinear systems

ABSTRACTAn adaptive disturbance rejection control scheme is developed for uncertain multi-input multi-output nonlinear systems in the presence of unmatched input disturbances. The nominal output rejection scheme is first developed, for which the relative degree characterisation of the control and disturbance system models from multivariable nonlinear systems is specified as a key design condition for this disturbance output rejection design. The adaptive disturbance rejection control design is then completed by deriving an error model in terms of parameter errors and tracking error, and constructing adaptive parameter-updated laws and adaptive parameter projection algorithms. All closed-loop signals are guaranteed to be bounded and the plant output tracks a given reference output asymptotically despite the uncertainties of system and disturbance parameters. The developed adaptive disturbance rejection scheme is applied to turbulence compensation for aircraft fight control. Simulation results from a benchmark aircraft model verify the desired system performance.

Adaptive neural network control of uncertain MIMO nonlinear systems with input saturation

In this paper, an adaptive neural network (NN) tracking controller is developed for a class of uncertain multi-input multi-output (MIMO) nonlinear systems with input saturation. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions in the MIMO system. A novel auxiliary system is developed to compensate the effects induced by input saturation (in both magnitude and rate) during tracking control. Endowed with a switching structure that integrates two existing representative auxiliary system designs, this novel auxiliary system improves control performance by preserving their advantages. It provides a comprehensive design structure in which parameters can be adjusted to meet the required control performance. The auxiliary system signal is utilized in both the control law and the neural network weight-update laws. The performance of the resultant closed-loop system is analyzed, and the bound of the transient error is established. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive neural network control.

Adaptive Fuzzy Control for MIMO Nonlinear Systems With Nonsymmetric Control Gain Matrix and Unknown Control Direction

In this paper, an indirect adaptive fuzzy control scheme is developed for a class of uncertain multi-input multi-output nonlinear systems with nonsymmetric control gain matrix and unknown control direction. The nonsymmetric control gain matrix is expressed as the sum of a symmetric matrix and a skew symmetric matrix, and the symmetric matrix, as well as the skew symmetric matrix, is approximated by fuzzy systems. By using the symmetric matrix decomposition technique, the estimated symmetric matrix is decomposed into the product of one diagonal matrix and two orthogonal matrixes. Based on the decomposition results, the adaptive fuzzy controller is developed to avoid the possible singularity problem and the parameter initialization problem. A robust control term is employed to compensate for the lumped errors, and a Nussbaum-type function is incorporated in the robust control term to deal with the unknown control direction. The proposed scheme guarantees that all the signals in the resulting closed-loop system are bounded and that the tracking errors converge asymptotically to zero. Two simulation examples are used to demonstrate the effectiveness of the proposed scheme.

Intelligent adaptive backstepping control for MIMO uncertain non-linear quadrotor helicopter systems

Designing a controller for multi-input–multi-output (MIMO) uncertain non-linear systems is one of the most important challenging works. In this paper, the contribution is focused on the design and analysis of an intelligent adaptive backstepping control for a MIMO quadrotor helicopter perturbed by unknown parameter uncertainties and external disturbances. The design approach is based on the backstepping technique and uses a radial basis function neural network (RBFNN) as a perturbation approximator. First, a backstepping controller optimized by the particle swarm optimization is developed for a nominal helicopter dynamic model. Then, the unknown perturbations are approximated based on the universal approximation property of the RBFNN. The parameters of the RBFNN are adjusted through online learning. To improve the control design performance further, a fuzzy compensator is introduced to eliminate the approximation error produced by the neural approximator. Asymptotical stability of the closed-loop control system is analytically proven via the Lyapunov theorem. The main advantage of the proposed methodology is that no prior knowledge of parameter uncertainties and disturbances is required. Simulations of hovering and trajectory tracking missions of a quadrotor helicopter are conducted. The results demonstrate the effectiveness and feasibility of the proposed approach.

Observer-based fuzzy adaptive control for multi-input multi-output nonlinear systems with a nonsymmetric control gain matrix and unknown control direction

In this study, we present an observer-based fuzzy adaptive control scheme for a class of uncertain multi-input multi-output nonlinear systems with a nonsymmetric control gain matrix, unknown control direction, and unmeasured states. In this scheme, fuzzy systems are used to approximate the unknown nonlinear functions and an adaptive fuzzy state observer is designed to estimate the unmeasured states. The parameter adaptive laws are designed by fuzzy basis functions rather than by its filtering and a robust control term is used to compensate for the lumped errors. The proposed method solves the problem of the nonsymmetric control gain matrix and it requires no a priori knowledge of the control direction for the states that are unmeasured. We prove that all of the signals in the resulting closed-loop systems are bounded and that the tracking errors converge asymptotically to zero. Two simulation examples are used to demonstrate the effectiveness of the proposed scheme.

ELM-based adaptive backstepping neural control for a class of uncertain MIMO nonlinear systems with predefined tracking accuracy

In this work, the adaptive backstepping neural control technique is proposed for a class of uncertain multi-input multi-output nonlinear systems in block-triangular form with the ultimate tracking accuracy assumed to be known a priori. The stability analysis of the closed-loop control system is derived based on Barbalat's Lemma instead of Lyapunov stability theory. Semi-global uniform ultimate boundedness of all the signals in the closed-loop system is achieved and after a sufficiently large interval of time, the outputs of the system are proven to converge to the predefined value. A single hidden layer feed-forward neural network based on the extreme learning machine is used in this work to approximate the unknown nonlinear functions in the control laws. Two simulation examples, including a mathematical one and a practical one, are given to verify the effectiveness of the proposed controller and its superiority over the existing techniques.

Robust adaptive neural control for a class of uncertain MIMO nonlinear systems

In this paper, a novel robust adaptive neural control scheme is proposed for a class of uncertain multi-input multi-output nonlinear systems. The proposed scheme has the following main features: (1) a kind of Hurwitz condition is introduced to handle the state-dependent control gain matrix and some assumptions in existing schemes are relaxed; (2) by introducing a novel matrix normalisation technique, it is shown that all bound restrictions imposed on the control gain matrix in existing schemes can be removed; (3) the singularity problem is avoided without any extra effort, which makes the control law quite simple. Besides, with the aid of the minimal learning parameter technique, only one parameter needs to be updated online regardless of the system input–output dimension and the number of neural network nodes. Simulation results are presented to illustrate the effectiveness of the proposed scheme.

Robust‐decentralized tracking control for a class of uncertain MIMO nonlinear systems with time‐varying delays

SUMMARYA new control design method based on signal compensation is proposed for a class of uncertain multi‐input multi‐output (MIMO) nonlinear systems in block‐triangular form with nonlinear uncertainties, unknown virtual control coefficients, strongly coupled interconnections, time‐varying delays, and external disturbances. By this method, the controller design is performed in a backstepping manner. At each step of backstepping procedure, a nominal virtual controller is first designed to get desired output tracking for the nominal disturbance‐free subsystem, and then a robust virtual compensator is designed to restrain the effect of the uncertainties, delays involved in the subsystem, and the couplings among the subsystems. The designed controller is linear and time‐invariant, so the explosion of complexity in the control law is avoid. It is proved that robust stability and robust practical tracking property of the closed‐loop system can be ensured, and the tracking errors can be made as small as desired. Copyright © 2013 John Wiley & Sons, Ltd.

Adaptive Tracking Control of Uncertain MIMO Nonlinear Systems with Time- varying Delays and Unmodeled Dynamics

In this paper, adaptive neural tracking control is proposed based on radial basis function neural networks (RBFNNs) for a class of multi-input multi-output (MIMO) nonlinear systems with completely unknown control directions, unknown dynamic disturbances, unmodeled dynamics, and uncertainties with time-varying delay. Using the Nussbaum function properties, the unknown control directions are dealt with. By constructing appropriate Lyapunov-Krasovskii functionals, the unknown upper bound functions of the time-varying delay uncertainties are compensated. The proposed control scheme does not need to calculate the integral of the delayed state functions. Using Young’s inequality and RBFNNs, the assumption of unmodeled dynamics is relaxed. By theoretical analysis, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded.