Nonaffine Systems Research Articles

Fuzzy Adaptive DSC Design for an Extended Class of MIMO Pure-Feedback Non-Affine Nonlinear Systems in the Presence of Input Constraints

A novel adaptive fuzzy dynamic surface control (DSC) scheme is for the first time constructed for a larger class of (multi-input multi-output) MIMO non-affine pure-feedback systems in the presence of input saturation nonlinearity. First of all, the restrictive differentiability assumption on non-affine functions has been canceled after using the piecewise functions to reconstruct the model for non-affine nonlinear functions. Then, a novel auxiliary system with bounded compensation term is firstly introduced to deal with input saturation, and the dynamic system employed in this work designs a bounded compensation term of tangent function. Thus, we successfully relax the strictly bounded assumption of the dynamic system. Additionally, the fuzzy logic systems (FLSs) are used to approximate unknown continuous systems functions, and the minimal learning parameter (MLP) technique is exploited to simplify control design and reduce the number of adaptive parameters. Finally, two simulation examples with input saturation are given to validate the effectiveness of the developed method.

Actor-Critic Reinforcement Learning Control of Non-Strict Feedback Nonaffine Dynamic Systems

The most focuses of the existing actor-critic reinforcement learning control (ARLC) are on dealing with continuous affine systems or discrete nonaffine systems. In this paper, I propose a new ARLC method for continuous nonaffine dynamic systems subject to unknown dynamics and external disturbances. A new input-to-state stable system is developed to establish an augmented dynamic system, from which I further get a strict-feedback affine model that is convenient for control designing based on a model transformation approach. The Nussbaum function is connected with a fuzzy approximation to devise an actor network whose tracking performance is further enhanced via strengthening signals generated by a fuzzy critic network. The stability of the closed-loop control system is guaranteed by the Lyapunov synthesis. Finally, the comparison simulation results are presented to verify the design.

Neural network based adaptive tracking control for a class of pure feedback nonlinear systems with input saturation

In this paper, an adaptive neural networks &#x0028 NNs &#x0029 tracking controller is proposed for a class of single-input &#x002F single-output &#x0028 SISO &#x0029 non-affine pure-feedback non-linear systems with input saturation. In the proposed approach, the original input saturated nonlinear system is augmented by a low pass filter. Then, new system states are introduced to implement states transformation of the augmented model. The resulting new model in affine Brunovsky form permits direct and simpler controller design by avoiding back-stepping technique and its complexity growing as done in existing methods in the literature. In controller design of the proposed approach, a state observer, based on the strictly positive real &#x0028 SPR &#x0029 theory, is introduced and designed to estimate the new system states, and only two neural networks are used to approximate the uncertain nonlinearities and compensate for the saturation nonlinearity of actuator. The proposed approach can not only provide a simple and effective way for construction of the controller in adaptive neural networks control of non-affine systems with input saturation, but also guarantee the tracking performance and the boundedness of all the signals in the closed-loop system. The stability of the control system is investigated by using the Lyapunov theory. Simulation examples are presented to show the effectiveness of the proposed controller.

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.

Performance guaranteed fault control of uncertain constrained nonaffine systems under input quantization and actuation failures

SummaryThis paper investigates the tracking control problem for a class of uncertain nonaffine system in the presence of input quantization and saturation yet possibly faulty actuators. A quantized robust adaptive fault‐tolerant control scheme capable of guaranteeing performance specifications is developed. By injecting quantizer parameters into the control design and using performance transformation, a constrained robust adaptive fault‐tolerant control scheme is developed to cope with modeling uncertainties, actuation saturation, and actuation faults, ensuring uniformly ultimately bounded stable tracking with the prescribed performance. The effectiveness of the proposed control strategy is confirmed by systematic stability analysis and simulation.

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 Stabilization of Uncertain Non-Affine Systems with Nonlinear Parameterization

This paper investigates the problem of adaptive control for non-affine systems with nonlinear parameterization. Under the controllability-like conditions characterized by the Lie brackets of affine vector fields, we show that there is LgV-type adaptive controllers that globally asymptotically regulate the state of the nonlinearly parameterized system with stable free dynamics while maintaining global stability of the closed-loop system. LgV-type adaptive controllers are designed and their effectiveness is demonstrated by two interesting examples.

RBF Neural Control Design for SISO Nonaffine Nonlinear Systems

In the present paper, an RBF neural control scheme is designed for regulatory control of SISO nonaffine systems facing unknown nonlinearities. Using Taylor series expansion, the nonaffine part of the system is converted into affine form. RBF network is utilized to estimate the equivalent affine system. The parameters of RBF network are updated online based on Lyapunov stability theory. To avoid the requirement of measurement of the states of the system, an observer is designed, which provides the estimated values of the system’s states. Using Lyapunov theory, the signals of the system are shown to be asymptotically stable. To validate the effectiveness of the presented scheme, numerical simulation study has been performed.

Continuous Asymptotically Tracking Control for a Class of Nonaffine-in-Input System With Nonvanishing Disturbance

In this paper, we explore the possibility of designing a continuous controller for a class of nonaffine system to achieve asymptotically tracking results with robustness to system uncertainties, unvanishing disturbances, and unknown control effectiveness. A robust integral of the sign of the error design is formulated to search a robust control for the nonaffine dynamics, while a time-varying gain of Nussbaum-type-function (NTF) is augmented to estimate the unknown direction and magnitude for control effectiveness. A second-order filter is employed to proceed the design when the NTF gain is involved without using any unmeasurable signals. Rigorous analysis shows that the proposed controller can asymptotically stabilizes the closed-loop system and the output tracking error. Simulation results on a Duffing–Holmes chaotic system demonstrate the effectiveness of the proposed approach.

Adaptive dynamic surface control for unknown pure feedback non-affine systems with multiple constraints

In this study, an adaptive dynamic surface control scheme is developed for a class of nonlinear systems. The considered systems can be viewed as a class of unknown pure feedback non-affine systems with multiple constraints. One remarked advantage is that not only less adjustable parameters are used in the design but also the design structure is universal for different systems. The characteristics of the considered systems will lead to a difficult task for design a low-complexity and stable controller. To this end, the mean value theorem is employed to transform the pure feedback systems into a linear structure, but non-affine terms still exist. Then, a novel recursive design procedure is constructed to remove the difficulties of unknown model, pure feedback non-affine characteristic and multiple constraints by integrating two auxiliary elementary functions with a novel bounded estimation approach. Furthermore, based on Lyapunov stability theorem and decoupled back-stepping method, it is proved that all the signals in the close-loop system are global uniformly bounded and the tracking error satisfies prescribed transient and steady state performance indexes constraints. Finally, simulation studies clarify and verify the approach.

Robust control of large-scale nonlinear systems by a hybrid adaptive fuzzy observer design with input saturation

In this paper a robust hybrid observer-based hybrid adaptive fuzzy controller for large-scale multiple-input multiple-output (MIMO) systems with affine and nonaffine form in the presence of input saturation is presented. Based on an arbitrary control gain matrix, a hybrid control scheme is designed to avoid the possible singularity problem. The proposed control method is very simple, effective and robust. The states of the system and the mathematical model of the system under control do not need to be well known. An observer-based adaptive fuzzy system based on strictly positive real (SPR) theory is applied to approximate the system states, but it does not require SPR conditions to be known identified. A robust control term is utilized to compensate the both uncertainties and observer errors and attenuate the residual error to the desired level. Finally, to display the applicability and efficiency of the proposed control method, a MIMO affine system and a MIMO nonaffine system with input saturation are applied in simulations.

Adaptive Control for a Class of Partially Unknown Non-Affine Systems: Applied to Autonomous Surface Vessels

In this paper, a neural network-based adaptive control algorithm is proposed for a class of non-affine systems where the nonlinear influence of the system input on the states is unknown. The algorithm transforms the problem of controlling non-affine systems to control of nonlinear affine systems and then, by approximating the inverse of the input function, calculates feasible control input. Lyapunov technique, Uniform Ultimate Boundedness and Matrix Singular Values are used for stability analysis and design of the controller. In order to investigate the performance of the algorithm, it is applied to an autonomous vessel where the dynamics of the propeller is unknown.

Barrier Function-Based Neural Adaptive Control With Locally Weighted Learning and Finite Neuron Self-Growing Strategy.

This paper presents a new approach to construct neural adaptive control for uncertain nonaffine systems. By integrating locally weighted learning with barrier Lyapunov function (BLF), a novel control design method is presented to systematically address the two critical issues in neural network (NN) control field: one is how to fulfill the compact set precondition for NN approximation, and the other is how to use varying rather than a fixed NN structure to improve the functionality of NN control. A BLF is exploited to ensure the NN inputs to remain bounded during the entire system operation. To account for system nonlinearities, a neuron self-growing strategy is proposed to guide the process for adding new neurons to the system, resulting in a self-adjustable NN structure for better learning capabilities. It is shown that the number of neurons needed to accomplish the control task is finite, and better performance can be obtained with less number of neurons as compared with traditional methods. The salient feature of the proposed method also lies in the continuity of the control action everywhere. Furthermore, the resulting control action is smooth almost everywhere except for a few time instants at which new neurons are added. Numerical example illustrates the effectiveness of the proposed approach.

Constrained data-driven optimal iterative learning control

A constrained optimal ILC for a class of nonlinear and non-affine systems, without requiring any explicit model information except for the input and output data, is proposed in this work. In order to address the nonlinearities, an iterative dynamic linearization method without omitting any information of the original plant is introduced in the iteration direction. The derived linearized data model is equivalent to the original nonlinear system and reflects the real-time dynamics of the controlled plant, rather than a static approximate model. By transferring all the constraints on the system output, control input, and the change rate of input signals into a linear matrix inequality, a novel constrained data-driven optimal ILC is developed by minimizing a predesigned objective function. The optimal learning gain is unfixed and updated iteratively according to the input and output measurements, which enhances the flexibility regarding modifications and expansions of the controlled plant. The results are further extended to the point-to-point control tasks where the exact tracking performance is required only at certain points and a constrained data-driven optimal point-to-point ILC is proposed by only utilizing the error measurements at the specified points only.

Global finite time stabilization of pure-feedback systems with input dead-zone nonlinearity

This paper is concerned with finite-time stabilization of a class of pure-feedback systems with dead-zone input. A systematic design procedure is established to derive the finite-time controller. Firstly, to circumvent the difficulties arising from the nonaffine properties, through a change of coordinates and incorporating mean value theorem, a system transformation technique is introduced to convert the original nonaffine system into an affine one. Then, based on the strengthened finite-time Lyapunov stability theorem as well as utilizing the bounds of dead-zone parameters, the finite-time stabilizer is explicitly constructed via backstepping design approach. It is proven that the designed controller can ensure all the states of the closed-loop system converge to zero in a finite time and maintain at zero afterwards. The proposed design framework is also extended to finite-time stabilization of uncertain pure-feedback systems and finite-time tracking control of pure-feedback systems. The effectiveness of the theoretical results are finally demonstrated by a numerical example and a realistic example.

A novel integrated approach for path following and directional stability control of road vehicles after a tire blow-out

The path following and directional stability are two crucial problems when a road vehicle experiences a tire blow-out or sudden tire failure. Considering the requirement of rapid road vehicle motion control during a tire blow-out, this article proposes a novel linearized decoupling control procedure with three design steps for a class of second order multi-input-multi-output non-affine system. The evaluating indicators for controller performance are presented and a performance related control parameter distribution map is obtained based on the stochastic algorithm which is an innovation for non-blind parameter adjustment in engineering implementation. The analysis on the robustness of the proposed integrated controller is also performed. The simulation studies for a range of driving conditions are conducted, to demonstrate the effectiveness of the proposed controller.

Performance recovery of a class of uncertain non-affine systems with unmodelled dynamics: an indirect dynamic inversion method

ABSTRACTThis paper presents an output feedback indirect dynamic inversion (IDI) approach for a class of uncertain nonaffine systems with input unmodelled dynamics. Compared with previous approaches to achieve performance recovery, the proposed method aims at dealing with a broader class of nonaffine-in-control systems with triangular structure. An IDI state feedback law is designed first, in which less knowledge of the model plant is needed compared to earlier approximate dynamic inversion methods, thus yielding more robust performance. After that, an extended high-gain observer is designed to accomplish the task with output feedback. Finally, we prove that the designed IDI controller is equivalent to an adaptive proportional-integral (PI) controller, with respect to both time response equivalence and robustness equivalence. The conclusion implies that for the studied strict-feedback non-affine systems with unmodelled dynamics, there always exits a PI controller to stabilise the systems. The effectiveness and benefits of the designed approach are verified by three examples.

Tracking control of nonaffine systems using bio-inspired networks with auto-tuning activation functions and self-growing neurons

This paper presents a bio-inspired artificial neural network (Bio-ANN) to tackle the tracking control of complex dynamic systems. The proposed Bio-ANN is motivated by the operant conditioning of biological systems, in which we not only adaptively tune the weights but also adjust the structural parameter of basis functions automatically, significantly enhancing the learning capability of the proposed control. Furthermore, the size of the dataset needed for online ANN training is small and the overall computational cost is low. With the help of such Bio-ANN, we develop a control scheme for a class of single-input single-output non-affine systems, where the operant conditioning bionic model (OCBM) is utilized. By comparing the proposed method with existing self-organizing approaches via numerical simulations, we verify that a faster convergent rate is achieved with better control precision by using the proposed OCBM based control approach.

Robust output tracking of a class of non-affine systems

ABSTRACTThis paper considers the robust output tracking problem for a class of uncertain non-affine systems. The state-space equations of these systems have a non-affine quadratic polynomial structure. In order to design the output tracking controller, first the error dynamical equations are constructed. Then, a novel sliding mode controller is designed for robust stabilization of the error dynamical equations. For this purpose, a proper sliding manifold which is a function of error vector is suggested. According to upper and lower bounds of uncertainties, two quadratic polynomials are built and with respect to the location of the roots of the given polynomials, the new sliding mode control law is obtained. The proposed controller can conquer the uncertainties and guarantees the asymptotic convergence of the system output toward the wanted time-varying reference signal. Finally, in order to verify the theoretical results, the proposed method is applied to the magnetic ball levitation system. Computer simulations demonstrate the efficiency of the proposed method.

Prescribed Performance Adaptive Control for a Class of Non-affine Uncertain Systems with State and Input Constraints

AbstractFor a class of non-affine nonlinear systems with state constraints, input constraint, uncertain parameters and unknown external disturbance, a back-stepping control scheme is proposed based on mean value theorem, nonlinear mapping and prescribed performance bounds (PPB). The non-affine system is first transformed into a time-varying system with a linear structure by using the mean value theorem, and the intervals of the time-varying uncertain parameters are calculated. The bounded time-varying parameters and external disturbance are estimated by adaptive algorithms with projection; the estimation error is compensated by employing nonlinear damping technology. To handle the state and input constraints, the nonlinear mapping technique (NMT), hyperbolic tangent function and Nussbaum function are employed. The prescribed performance control method improves the performance of the system. It is proved that the proposed control scheme can guarantee that all signals of the closed-loop system are bounded through the Lyapunov analysis. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.