Control Of Nonaffine Nonlinear Systems Research Articles

Adaptive robust control of nonaffine nonlinear systems via an improved event‐triggered mechanism

AbstractThis paper aims to address the problem of event‐based adaptive robust control for a class of nonaffine nonlinear systems against actuator faults and unknown deception attacks. Firstly, different from the widely used relative threshold triggering mechanism, an improved event‐triggered mechanism with the time‐varying function threshold is devised for effectively saving more communication costs between controller and actuator. Then, based on a class of modified filter‐based coordinate transformations and the improved event‐triggered mechanism, the intermediate virtual control laws are devised to construct actual controllers, which not only guarantees robust stabilization of the system but also relaxes the universal assumptions on control coefficients and attack weights. Besides, the design challenges resulting from the presence of coupling terms in the nonaffine nonlinear system are successfully overcome by virtue of mean value theorem and the property of fuzzy basis function. Theoretical analysis proves that all signals of the closed‐loop system are semiglobally uniformly ultimately bounded (SUUB) and the Zeno behavior can be averted. Finally, the effectiveness of the proposed strategy is verified via comprehensive simulation results.

Adaptive control of a nonaffine nonlinear system using self-organising kernel extreme learning machine

We propose a self-organising kernel extreme learning machine (KELM) adaptive controller for nonaffine nonlinear systems. Literature survey reveals that neural network (NN) is extensively used to design adaptive controllers for nonlinear systems. When conventional NN, like multilayer feedforward NN and radial basis function NN (RBFNN), is used for controller design, the parameters of these networks converge slowly. Researchers have overcome this shortcoming by using extreme learning machine (ELM). The motivation to use KELM for controller design in our research is to utilise the advantages of ELM and radial basis function kernels. The structure of neural networks is seldom altered during training, resulting in unnecessarily small or large networks. The self-organising nature of our proposed controller caters to solving this problem. The structure of the self-organising KELM updates itself based on a threshold value set for the normalised change in the output weight. In our work, the control input meets three objectives: feedback linearisation, stabilisation of the linearised system and providing immunity to process and measurement noises. The update law for the hidden layer parameters of the KELM is obtained using the Lyapunov technique to ensure the overall stability of the system. A comparative analysis of different performance criteria is performed for trajectory tracking control, in the presence of process and measurement noises, for a numerical example and the Duffing–Holmes chaotic nonlinear system. The simulation results of these analyses demonstrate the superiority of the self-organising KELM compared to ELM and RBFNN based adaptive controllers. The experimental results with a rotary servo system validate the efficacy of the proposed controller in real-time systems. Furthermore, the robustness of the self-organising adaptive controller is verified with the results obtained for the servo system on varying the system parameter and operating condition.

Fuzzy Fixed-Time Control for Nonaffine Nonlinear Systems with Unknown Hysteresis Inputs

Fuzzy Fixed-Time Control for Nonaffine Nonlinear Systems with Unknown Hysteresis Inputs

Finite-time formation control of nonaffine nonlinear systems under directed communication interactions

This paper studies the problem of finite-time formation tracking control for networked nonaffine nonlinear systems with unmeasured dynamics and unknown uncertainties/disturbances under directed topology. A unified distributed control framework is proposed by integrating adaptive backstepping control, dynamic gain control and dynamic surface control based on finite-time theory and consensus theory. Auxiliary dynamics are designed to construct control gains with non-Lipschitz dynamics so as to guarantee finite-time convergence of formation errors. Adaptive control is used to compensate for uncertain control efforts of the transformed systems derived from original nonaffine systems. It is shown that formation tracking is achieved during a finite-time period via the proposed controller, where fractional power terms are only associated with auxiliary dynamics instead of interacted information among the networked nonlinear systems in comparison with most existing finite-time cooperative controllers. Moreover, the continuity of the proposed controller is guaranteed by setting the exponents of fractional powers to an appropriate interval. It is also shown that the improved dynamic surface control method could guarantee finite-time convergence of formation errors, which could not be accomplished by conventional dynamic surface control. Finally, simulation results show the effectiveness of the proposed control scheme.

Command filter-based adaptive fuzzy switching event-triggered control for non-affine nonlinear systems with actuator faults

This paper considers a problem of command filter-based adaptive fuzzy switching event-triggered control for non-affine nonlinear systems with actuator faults. First, a state observer is given to estimate unmeasurable state. Secondly, an error transformation equation is designed to constrain output tracking error, and the feasibility condition of tracking error is not required. Then, a finite time fault-tolerant control scheme is constructed based on command filter and backstepping technologies, which can compensate completely the effects of actuator faults and trigger errors, and there is no differential explosion, singularity phenomenon and Zeno behavior. Besides, a switching event-triggered algorithm is designed to reduce the triggering number under the premise of ensuring the tracking performance. Finally, the proposed algorithm is applied to an one-link manipulator to verify the availability.

Funnel-based adaptive fuzzy finite-time control for non-affine nonlinear systems preceded by unknown actuators

In this paper, an adaptive finite-time funnel control for non-affine strict-feedback nonlinear systems preceded by unknown non-smooth input nonlinearities is proposed. The input nonlinearities include backlash-like hysteresis and dead-zone. Unknown nonlinear functions are handled using fuzzy logic systems (FLS), based on the universal approximation theorem. An improved funnel error surface is utilized to guarantee the steady-state and transient predetermined performances while the differentiability problem in the controller design is averted. Using the Lyapunov approach, all the adaptive laws are extracted. In addition, an adaptive continuous robust term is added to the control input to relax the assumption of knowing the bounds of uncertainties. All the signals in the closed-loop system are shown to be semi-globally practically finite-time bounded with predetermined performance for output tracking error. Finally, comparative numerical and practical examples are provided to authenticate the efficacy and applicability of the proposed scheme.

Adaptive robust asymptotic tracking control of nonaffine nonlinear systems

AbstractThis article investigates the barrier lyapunov function‐based adaptive robust control scheme for nonaffine nonlinear systems with unknown system dynamics. First, the nonaffine system is converted into affine system via a combination of first‐order filter and coordinate transformation, then a high‐gain observer is utilized to reconstruct the immeasurable states of the derived affine system. Second, a robust integral of the sign of the error (RISE) is incorporated into the control design to reject the unknown dynamics. Third, a barrier lyapunov function based design method is used to ensure that the input vector to the parameter estimation remain within a predefined region. Then, an adaptive robust control scheme with only one adaptive parameter by using the upper bound estimation is developed. Finally, numerical simulations validate the efficacy of the developed control scheme.

Adaptive Finite-Time Fuzzy Funnel Control for Nonaffine Nonlinear Systems

This paper, for the first time, presents an adaptive finite-time fuzzy funnel controller for nonaffine nonlinear systems via backstepping. To ensure the tracking error with prescribed boundedness, a modified transformation for funnel error is developed and embedded in the procedure of control design. The unknown packaged nonlinear functions appeared in the controller design process are approximated by using fuzzy logic systems. It is proved that the proposed method guarantees that the output tracking error falls within a preset funnel and all signals in the closed-loop system are semi-globally practically finite-time bounded (SGPFB). Simulations are carried out to demonstrate the effectiveness of the controller design scheme.

A neuro-observer-based optimal control for nonaffine nonlinear systems with control input saturations

In this study, an adaptive neuro-observer-based optimal control (ANOPC) policy is introduced for unknown nonaffine nonlinear systems with control input constraints. Hamilton–Jacobi–Bellman (HJB) framework is employed to minimize a non-quadratic cost function corresponding to the constrained control input. ANOPC consists of both analytical and algebraic parts. In the analytical part, first, an observer-based neural network (NN) approximates uncertain system dynamics, and then another NN structure solves the HJB equation. In the algebraic part, the optimal control input that does not exceed the saturation bounds is generated. The weights of two NNs associated with observer and controller are simultaneously updated in an online manner. The ultimately uniformly boundedness (UUB) of all signals of the whole closed-loop system is ensured through Lyapunov’s direct method. Finally, two numerical examples are provided to confirm the effectiveness of the proposed control strategy.

An active disturbance rejection control for hysteresis compensation based on Neural Networks adaptive control

In the present paper, an active disturbance rejection control(ADRC) scheme via radial basis function(RBF) neural networks is designed for adaptive control of non-affine nonlinear systems facing hysteresis disturbance in which RBF neural network approximation is utilized to tackle the system uncertainties and ADRC is designed to real-time estimate and compensate disturbance with unknown backlash-like hysteresis. Combining the adaptive neural networks design with ADRC design techniques, a new dual-channel composite controller scheme is developed herein whereby adaptive neural networks are used as feed-forward inverse control and ADRC as closed-loop feedback control. Furthermore, as compared to adaptive neural networks control algorithm, the proposed RBF-ADRC dual-channel composite controller can guarantee that the desired signal can be tracked with a small domain of the origin and it is confirmed to be effective under Lyapunov stability theory and MATLAB simulations.

Observer‐based finite time adaptive fault tolerant control for nonaffine nonlinear systems with actuator faults and disturbances

SummaryThis paper studies the problem of observer‐based finite time adaptive fault tolerant control for nonaffine nonlinear systems with actuator faults and disturbances. Based on mean value theorem and convex combination method, a adaptive neural observer with virtual control coefficients is designed to estimate the systems states. Then, by using funnel Lyapunov function and backstepping method, a finite time control scheme is designed in the presence of disturbances and actuator faults. The stability analysis proves that tracking errors can converge to the prescribed performance bound in a finite time and all signals are uniformly ultimately bounded. Finally, simulation results verify efficiency of the studied approach.

Adaptive control for non-affine nonlinear systems with input saturation and output dead zone

This paper disposes of the problem of adaptive dynamic surface control for non-affine nonlinear systems. The full state constraints, output dead zone and input saturation are fully considered in the controlled system. Invariant sets are used for a continuous and semi-bounded condition of non-affine functions. The “complexity explosion” issue caused by backstepping procedure is avoided via the dynamic surface control method. A Nussbaum function is used to handle the unknown control coefficient derived from the output dead zone, and barrier Lyapunov functions are employed to handle full state constraints. To counteract the effects of disturbance and uncertainty, the robust compensator is constructed. In addition, it is proved that all signals in the system are bounded and all states satisfy their constraints. Finally, the simulation results show the effectiveness of the proposed method.

Adaptive neural tracking control for non-affine nonlinear systems with finite-time output constraint

In this paper, an adaptive neural tracking control approach is presented for a class of non-affine nonlinear systems with finite-time output constraint. The non-affine form of the original system is converted to the affine form by means of the mean value theorem. To constraint the output tracking error within a predefined boundary in finite time, a modified performance function, i.e., finite-time performance function, is introduced. During the process of controller design, the dynamic surface control is employed to handle the ‘explosion of complexity’ problem occurred in the conventional backstepping method. According to the approximation of radial basis functions neural networks, an adaptive neural control scheme is developed which guarantees that the output tracking error is preserved within a specified prescribed performance and all the signals in closed-loop system are bounded by appropriately choosing the design parameters. The stability of the closed-loop system is proved by Lyapunov stability analysis and the simulation results are proposed to demonstrate the effectiveness of the developed control approach.

Adaptive finite-time dynamic surface tracking control of nonaffine nonlinear systems with dead zone

An adaptive finite-time dynamic surface tracking control scheme is concentrated for a class of nonaffine nonlinear systems with dead zone. By virtue of Lyapunov theory of finite time stability and backstepping technology, an adaptive fuzzy finite-time dynamic surface tracking controller is correctly devised, in which fuzzy logic systems (FLSs) are adopted to approximate the unknown terms. Different from the usual dynamic surface control strategy, the presented approach combines the finite-time control with this scheme by using backstepping technique, which not only eliminates the problem of explosion of complexity, but also ensures that all the signals of the closed-loop system are semi-globally practically finite-time stable, meanwhile, the tracking error can be confined to a small region near the equilibrium point. At last, a numerical example is given to demonstrate the effectiveness of the proposed method.

Neural network based adaptive dynamic surface control of nonaffine nonlinear systems with time delay and input hysteresis nonlinearities

In this paper, neural networks (NNs)-based adaptive dynamic surface control is investigated for a class of pure-feedback nonlinear systems with unknown time delay and input hysteresis nonlinearities. The design difficulty appeared in this paper due to time delay is handled by combining neural networks with finite covering lemma instead of using Krasovskii functionals, and the assumptions on the time-delay functions are removed based the finite covering lemma and NNs. Meanwhile, completely unknown backlash-like hysteresis control input that frequently exists in practice is also considered. By combining the adaptive backstepping recursive design technique with the universal approximation ability of neural networks, an adaptive neural control algorithm is systemically designed for the system under consideration, and the explosion of complexity exists in traditional backstepping design is avoided by using dynamic surface technique. It is shown that the designed adaptive controller can guarantee that all the signals are ultimately uniformly bounded and the desired signal can be tracked with a small domain of the origin. A numerical example and an example of a real plant for adjustable metal cutting system are provided to show the feasibility of the proposed method.

Learning from neural control for non-affine systems with full state constraints using command filtering

ABSTRACT This paper focusses on learning from command filtering-based adaptive neural control for non-affine nonlinear systems with full state constraints. This paper utilises a novel transformed function to convert the origin full-state constrained problem into an equivalent unconstrained one. By combining command-filtered backstepping, a novel adaptive neural control scheme is proposed to guarantee that all closed-loop signals are uniformly ultimately bounded and all states stay in the predefined bounded regions. Subsequently, by verifying the partial persistent excitation condition of the radial basis function neural network, neural weight estimates are proven to converge to the ideal weights and the convergent weights are stored in the constant values. Using the stored knowledge, a neural learning control scheme is developed for similar control tasks, which can improve control performances without the violation of full state constraints. Simulation studies are performed to illustrate the validity of the proposed scheme.

Observer-based terminal sliding mode control of non-affine nonlinear systems: Finite-time approach

This paper studies the problem of observer based fast nonsingular terminal sliding mode control schemes for nonlinear non-affine systems with actuator faults, unknown states, and external disturbances. A hyperbolic tangent function based extended state observer is considered to estimate unknown states, which enhances robustness by estimating external disturbance. Then, Taylor series expansion is employed for the non-affine nonlinear system with actuator faults, which transforms it to an affine form system to simplify disturbance observer and controller design. A finite time disturbance observer is designed to address unknown compound disturbances, which includes external disturbances and system uncertainties. A fast nonsingular terminal sliding mode with exponential function sliding mode is proposed to address output tracking. Simulation results show the proposed scheme is effective.

Adaptive tracking control for non-affine nonlinear systems with non-affine function possibly being discontinuous

ABSTRACTA novel adaptive control scheme is presented for a class of non-affine nonlinear systems with non-affine nonlinear function possibly being discontinuous. A discontinuous condition for non-affine nonlinear systems is present to guarantee the controllability of system. The non-affine nonlinear function is modelled appropriately by using piecewise functions. Based on Lyapunov analysis method, the basic idea of invariant set theory is constructively introduced to prove the boundedness of all the signals in the closed-loop system. Finally, simulation example is provided to demonstrate the effectiveness of the proposed approach.

Adaptive Neural Control of Nonaffine Nonlinear Systems without Differential Condition for Nonaffine Function

An adaptive neural control scheme is proposed for nonaffine nonlinear system without using the implicit function theorem or mean value theorem. The differential conditions on nonaffine nonlinear functions are removed. The control-gain function is modeled with the nonaffine function probably being indifferentiable. Furthermore, only a semibounded condition for nonaffine nonlinear function is required in the proposed method, and the basic idea of invariant set theory is then constructively introduced to cope with the difficulty in the control design for nonaffine nonlinear systems. It is rigorously proved that all the closed-loop signals are bounded and the tracking error converges to a small residual set asymptotically. Finally, simulation examples are provided to demonstrate the effectiveness of the designed method.

Global robust tracking control of non-affine nonlinear systems with application to yaw control of UAV helicopter

In this paper, a novel robust nonlinear tracking control scheme is proposed for the yaw channel of an unmanned-aerial-vehicle helicopter that is non-affine in the control input. By a novel dynamic modeling technique, the non-affine nonlinear systems are approximated to facilitate the desired control design. In the controller design procedure, the terminal sliding model control method is introduced to deal with the unknown uncertainties/disturbances. Moreover, filter and disturbance estimator are combined to further reduce the chattering. A systematic procedure is developed and related theoretical and practical issues are discussed. The proposed nonlinear tracking control scheme can guarantee the asymptotic output tracking of the closed-loop control systems in spite of unknown uncertainties/disturbances. Finally, the simulation results on the dynamic model of a real helicopter-on-arm are provided to demonstrate the effectiveness of the proposed new control techniques.