Robust Adaptive Control Design Research Articles

Design of robust adaptive controller and feedback error learning for rehabilitation in Parkinson's disease: a simulation study.

Deep brain stimulation (DBS) is an efficient therapy to control movement disorders of Parkinson's tremor. Stimulation of one area of basal ganglia (BG) by DBS with no feedback is the prevalent opinion. Reduction of additional stimulatory signal delivered to the brain is the advantage of using feedback. This results in reduction of side effects caused by the excessive stimulation intensity. In fact, the stimulatory intensity of controllers is decreased proportional to reduction of hand tremor. The objective of this study is to design a new controller structure to decrease three indicators: (i) the hand tremor; (ii) the level of delivered stimulation in disease condition; and (iii) the ratio of the level of delivered stimulation in health condition to disease condition. For this purpose, the authors offer a new closed-loop control structure to stimulate two areas of BG simultaneously. One area (STN: subthalamic nucleus) is stimulated by an adaptive controller with feedback error learning. The other area (GPi: globus pallidus internal) is stimulated by a partial state feedback (PSF) controller. Considering the three indicators, the results show that, stimulating two areas simultaneously leads to better performance compared with stimulating one area only. It is shown that both PSF and adaptive controllers are robust regarding system parameter uncertainties. In addition, a method is proposed to update the parameters of the BG model in real time. As a result, the parameters of the controllers can be updated based on the new parameters of the BG model.

Neural Networks Approximator Based Robust Adaptive Controller Design of Hypersonic Flight Vehicles Systems Coupled with Stochastic Disturbance and Dynamic Uncertainties

A neural network robust control is proposed for a class of generic hypersonic flight vehicles with uncertain dynamics and stochastic disturbance. Compared with the present schemes of dealing with dynamic uncertainties and stochastic disturbance, the outstanding feature of the proposed scheme is that only one parameter needs to be estimated at each design step, so that the computational burden can be greatly reduced and the designed controller is much simpler. Moreover, by introducing a performance function in controller design, the prespecified transient and performance of tracking error can be guaranteed. It is proved that all signals of closed-loop system are uniformly ultimately bounded. The simulation results are carried out to illustrate effectiveness of the proposed control algorithm.

Design of fractional robust adaptive intelligent controller for uncertain fractional-order chaotic systems based on active control technique

In this paper, a robust fractional-order adaptive intelligent controller is proposed for stabilization of uncertain fractional-order chaotic systems. The intelligent neuro-fuzzy network is used to estimate unknown dynamics of system, while the neuro-fuzzy network parameters as well as the upper bounds of the model uncertainties, disturbances and approximation errors are adaptively estimated via separate adaptive rules. An SMC scheme, with a fractional-order sliding surface, is employed, as the controller to improve the velocity and performance of the proposed control system and to eliminate the unknown but bounded uncertainties, external disturbances and approximation errors. The Lyapunov stability theorem has been also employed to show the stability of the closed-loop system, robustness against uncertainties, external disturbances and approximation errors, while the control signal remains bounded. Explanatory examples and simulation results are given to confirm the effectiveness of the proposed procedure, which consent well with the analytical results.

Robust nonlinear adaptive backstepping excitation controller design for rejecting external disturbances in multimachine power systems

This paper proposes a new approach to design a robust adaptive backstepping excitation controller for multimachine power systems in order to reject external disturbances. The parameters which significantly affect the stability of power systems (also called stability sensitive parameters) are considered as unknown and the external disturbances are incorporated into the power system model. The proposed excitation controller is designed in such a way that it is adaptive to the unknown parameters and robust to external disturbances. The stability sensitive parameters are estimated through the adaptation laws and the convergences of these adaptation laws are obtained through the negative semi-definiteness of control Lyapunov functions (CLFs). The proposed controller not only provides robustness property against external disturbances but also overcomes the over-parameterization problem of stability sensitive parameters which usually appears in some conventional adaptive methods. Finally, the performance of the proposed controller is tested on a two-area four machine 11-bus power system by considering external disturbances under different scenarios and is compared to that of an existing nonlinear adaptive backstepping controller. Simulation results illustrate the robustness of the proposed controller over an existing one in terms of rejecting external disturbances.

Robust auto-landing of fixed-wing UAVs using neuro-adaptive design

An innovative neuro-adaptive design philosophy is presented in this paper embedding a Sobolev norm based Lyapunov function for directional learning of the unknown function, which is capable of learning both the unknown function in the system model and its Jacobian. This facilitates fast learning (model adaptation) without much of transient effects. The updated model is then used in the framework of dynamic inversion to design the guidance (outer) loop as well as the control (inner) loop. Using this philosophy a robust adaptive nonlinear guidance and control design is presented for robust automatic landing. The performance of the proposed approach is successfully verified through numerous simulation studies using the six degrees-of-freedom (six-DOF) nonlinear model of a prototype UAV. All possible disturbance effects that arise in practice, namely modeling inaccuracies, wind disturbances and ground effect, have been considered in the simulation studies.

The control of the electro-hydraulic shaking table based on dynamic surface adaptive robust control

The electro-hydraulic shaking table is investigated, in the present paper, to simulate the vibrational working environment of industrial components and equipment. Adaptive robust control can be applied to the shaking table system because electro-hydraulic systems suffer from internal parameter uncertainties and external disturbances. However, the adaptive robust controller design is complicated and has a large computational cost owing to the ‘explosion of terms’ problem. Thus dynamic surface control is applied in the design procedure of adaptive robust controllers to overcome the ‘explosion of terms’ problem. In this work, dynamic surface adaptive robust control is proposed. It simplifies the designed procedure of the controller and decreases its computational cost. Firstly, the structure of a shaking table is formulated and the operation principles of the shaking table, including the hydraulic and control principles, are analysed. A change is made in the mechanical-hydraulic system of the fluid circuit to address the problem of changing the vibration direction. Secondly, a dynamic model of a shaking table is proposed. Based on analysis of this model, the design of a dynamic surface adaptive robust controller for a shaking table is presented so as to improve its performance. Finally, comparative simulations and experiments are carried out. The comparison of performance results with proportional-integral-derivative control verify the correctness of the hydraulic scheme and control principle, as well as the high-performance of the dynamic surface adaptive robust controller. The shaking table achieves a guaranteed dynamical performance and tracking accuracy for the output in the presence of parameter and load uncertainties.

Robust adaptive position and force controller design of robot manipulator using fuzzy neural networks

This paper presents a robust adaptive position and force control scheme for an n-link robot manipulator under unknown environment. The robot manipulator’s model and the stiffness coefficient of contact environment are assumed to be not exactly known. Therefore, the traditional impedance force controller cannot be applied. We herein adopt the fuzzy neural networks (FNNs) to estimate the unknown model matrices of robot manipulator and the adaptive tracking position and force control is developed by the proposed adaptive scheme. Based on the Lyapunov stability theory, the stability of the closed-loop system and convergence of adjustable parameters are guaranteed. The corresponding update laws of FNNs’ parameters and estimated stiffness coefficient of contacting environment can be derived. Finally, simulation results of a two-link robot manipulator with environment constraint are introduced to illustrate the performance and effectiveness of our approach.

Adaptive fuzzy asymptotic tracking control of uncertain nonaffine nonlinear systems with non-symmetric dead-zone nonlinearities

This paper is concerned with the problem of robust adaptive fuzzy tracking controller design for a class of uncertain nonaffine nonlinear systems with external disturbances and non-symmetric dead-zone nonlinearities. With the help of fuzzy logic systems (FLSs) to approximate the desired nonlinear functions, a novel direct adaptive tracking control scheme is established. First, the implicit function theorem and the mean value theorem are used to deal with the nonaffine term with unknown dead-zone input. Then, based on the estimation information for the unknown upper bound of the compounded disturbance, an adaptive fuzzy tracking controller with the corresponding parameter updating laws is designed to eliminate the effect of the compounded disturbance. Furthermore, it is proved that all the resulting closed-loop system signals are uniformly bounded and the tracking error can asymptotically converge to zero via the Lyapunov stability analysis. Finally, a numerical example is provided to verify the effectiveness of the proposed adaptive fuzzy asymptotic tracking design method.

Robust adaptive fuzzy control design for nearspace vehicle

In this paper, a T-S fuzzy model of the NSV (Nearspace Vehicle) kinematic model is established based on fuzzy approximation theory, and a new fuzzy robust tracking control law is designed in reference to the feedforward control of the linear system. In order to account for a case in which no augmented matrix is introduced, the control law is designed as a compound form of feedback and feedforward, and the gains of feedback and feedforward are solved by LMI (Linear Matrix Inequalities). The strategy is applied to the anti-interference control of NSV attitudes, and the convergence of tracking errors is analyzed according to the Lyapunov method. Simulation results based on the NSV demonstrate the validity of the proposed method.

Robust adaptive constrained backstepping flight controller design for re-entry reusable launch vehicle under input constraint

A nonlinear constrained controller is designed for a reusable launch vehicle during re-entry phase in the presence of model uncertainty, external disturbance, and input constraint, via combining sliding mode control and adaptive backstepping control. Since the complex coupling between the translational and rotational dynamics of reusable launch vehicle, a control-oriented model derived from rotational dynamic is used for controller design. During the virtual control input design procedure, a dynamic robust term is utilized to compensate for the uncertainty. In addition, a filter is applied to handle “explosion of terms” problem during the actual control input design. To reduce the computational burden, adaptive law is used to evaluate the unknown norm bound of the lumped uncertainty. An auxiliary system is constructed to compensate for the input constraint effect. The stability of the closed-loop system is analyzed based on Lyapunov theory. Simulation results demonstrate the validity of the developed controller in providing stable tracking of the guidance command by numerical simulation on the 6-degree-of-freedom model of reusable launch vehicle.

Robust Nonlinear Adaptive Controller Design for Horizontal Position Control of a Rotary Wing Autonomous Vehicle Using Backstepping Method

In this paper, a new approach of designing robust adaptive backstepping controller for horizontal position control of a rotary wing autonomous unmanned vehicle (RAUV) with consideration of parametric uncertainties and external disturbances is proposed. Based on this new approach, the proposed RAUV controller is adaptive to the parametric uncertainties and robust to the external disturbances. To prove the convergence of different tracking error to zero, a control Lyapunov function (CLF) is formulated in every step of the design process of controller and which is guaranted through the negative definiteness of the derivative of CLF. At last, a numerical evaluation is performed on a highly fedility nonlinear simulation model to justify the usefulness of the proposed controller. The performance of the designed controller is also compared with a classical PID controller. Simulation results demonstrate that the proposed controller provides an improved performance for the closed-loop system in the presence of parametric and external uncertainties within the UAH model over the existing controller.

Robust Adaptive Fuzzy Control for a Class of Uncertain MIMO Nonlinear Systems with Input Saturation

This paper studies the robust adaptive fuzzy control design problem for a class of uncertain multiple-input and multiple-output (MIMO) nonlinear systems in the presence of actuator amplitude and rate saturation. In the control scheme, fuzzy logic systems are used to approximate unknown nonlinear systems. To compensate the effect of input saturations, an auxiliary system is constructed and the actuator saturations then can be augmented into the controller. The modified tracking error is introduced and used in fuzzy parameter update laws. Furthermore, in order to deal with fuzzy approximation errors for unknown nonlinear systems and external disturbances, a robust compensation control is designed. It is proved that the closed-loop system obtainsH∞tracking performance through Lyapunov analysis. Steady and transient modified tracking errors are analyzed and the bound of modified tracking errors can be adjusted by tuning certain design parameters. The proposed control scheme is applicable to uncertain nonlinear systems not only with actuator amplitude saturation, but also with actuator amplitude and rate saturation. Detailed simulation results of a rigid body satellite attitude control system in the presence of parametric uncertainties, external disturbances, and control input constraints have been presented to illustrate the effectiveness of the proposed control scheme.

A class of adaptive robust controllers for uncertain dynamical systems with unknown virtual control coefficients

The problem of backstepping approach-based adaptive robust controller design is considered for a class of nonlinear systems in the presence of uncertain system parameters, external disturbances, and unknown time-varying virtual control coefficients. It is supposed that the upper bounds of external disturbances and unknown time-varying virtual control coefficients are unknown. In particular, it is also supposed that the lower bounds of time-varying virtual control coefficients are unknown. Then, the improved adaptation laws with σ-modification are employed to estimate the unknown values containing all the unknown bounds of such uncertainties. With the help of the adaptation laws, a class of backstepping approach-based continuous adaptive robust state feedback controllers is developed. Furthermore, by employing the improved Lyapunov-Krasovskii functional method, it is also shown that the proposed adaptive robust backstepping controller can guarantee the uniform asymptotic stability of such uncertain dynamical systems. Finally, a numerical example is given to demonstrate the validity of the results.

Robust adaptive control design for rotorcraft unmanned aerial vehicles based on sliding mode approach

This paper presents a nonlinear robust control design method for a generic rotorcraft unmanned aerial vehicle (RUAV). The control objective is to let the RUAV track some pre-defined time-varying position and heading trajectories. The proposed controller employs feedback linearization process to realize the dynamic decoupling control and applies adaptive sliding mode control to compensate for the parametric uncertainties and external disturbances. The global asymptotical stability is proved via stability analysis. Compared with the cascaded controller, the proposed controller demonstrates a superior tracking performance and robustness through numerical simulation in the presence of parametric uncertainties and unknown disturbances.

다기 전력 시스템의 안정화를 위한 탐색화된 정책 반복법 기반 적응형 강인 제어기 설계

다기 전력 시스템의 안정화를 위한 탐색화된 정책 반복법 기반 적응형 강인 제어기 설계

Robust tracking observer-based adaptive fuzzy control design for uncertain nonlinear MIMO systems with time delayed states

This paper addresses the problem of designing robust observer-based adaptive fuzzy tracking control scheme for a class of MIMO nonlinear systems with plant uncertainties, time delayed uncertainties, and external disturbances. A fuzzy logic system (FLS) is utilized to approximate the unknown nonlinear functions and an adaptive fuzzy observer is introduced for state estimations. The proposed control law is based on indirect adaptive fuzzy control and uses two on-line estimations. This allows for the simultaneous inclusion of identifying gains of the delayed state uncertainties and training of the weights of the fuzzy system by introducing estimated error vectors. The advantage of employing an adaptive fuzzy system is the use of linear analytical results instead of estimating nonlinear system functions with online update laws. The adaptive fuzzy tracking control using Variable Structure (VS) control technique is derived based on Lyapunov criterion and the Riccati-inequality to resolve system uncertainties, time delayed uncertainties, and external disturbances. This is done in such a way that all states of the system are bounded and the H∞ tracking performance is achieved. Finally, a two-connected inverted pendulums on carts system (Liu et al., 2011) [29] is used for simulation purposes and some comparisons are given to illustrate the validity and effectiveness of the proposed method.

Robust adaptive neural network control of a class of uncertain strict-feedback nonlinear systems with unknown dead-zone and disturbances

In this paper, a robust adaptive neural control design approach is presented for a class of perturbed strict-feedback nonlinear systems with unknown dead-zone. In the controller design, different from existing methods, all the virtual control laws need not be actually implemented at intermediate steps, and only one actual robust adaptive control law is constructed by approximating the lumped unknown function of the system with a single neural network at the last step. By this approach, the structure of the designed controller is much simpler since the causes for the problem of complexity growing in existing methods are eliminated. Stability analysis shows that the proposed scheme can guarantee the uniform ultimate boundedness of all the closed-loop system signals, and the steady-state tracking error can be made arbitrarily small by appropriately choosing control parameters. Simulation studies demonstrate the effectiveness and merits of the proposed approach.

Nonlinear Adaptive Robust Control Design for Static Synchronous Compensator Based on Improved Dynamic Surface Method

In view of single machine to infinite bus system with static synchronous compensator, which is affected by internal and external disturbances, a nonlinear adaptive robust controller is constructed based on the improved dynamic surface control method (IDSC). Compared with the conventional DSC, the sliding mode control is introduced to the dynamic surface design procedure, and the parameter update laws are designed using the uncertainty equivalence criterions. The IDSC method not only reduces the complexity of the controller but also greatly improves the system robustness, speed and accuracy. The derived controller cannot only attenuate the influences of external disturbances against system output, but also has strong robustness to system parameters variance because the damping coefficient is considered in the internal parameter uncertainty. Simulation result reveals that the designed controller can effectively improve the dynamic performances of the power system.

Robust adaptive dynamic surface control design for a flexible air-breathing hypersonic vehicle with input constraints and uncertainty

The flight control problem of a flexible air-breathing hypersonic vehicle is presented in the presence of input constraint and aerodynamic uncertainty. A control-oriented model, where aerodynamic uncertainty and the strong couplings between the engine and flight dynamics are included, is derived to reduce the complexity of controller design. The flexible dynamics are viewed as perturbations of the model. They are not taken into consideration at the level of control design, the influence of which is evaluated through simulation. The control-oriented model is decomposed into velocity subsystem and altitude subsystem, which are controlled separately. Then robust adaptive controller is developed for the velocity subsystem, while the controller which combines dynamic surface control and radial basis function neural network is designed for the altitude subsystem. The unknown nonlinear function is approximated by the radial basis function neural network. Minimal-learning parameter technique is utilized to estimate the maximum norm of ideal weight vectors instead of their elements to reduce the computational burden. To handle input constraints, additional systems are constructed to analyze their impact, and the states of the additional systems are employed at the level of control design and stability analysis. Besides, “explosion of terms” problem in the traditional backstepping control is circumvented using a first-order filter at each step. By means of Lyapunov stability theory, it is proved theoretically that the designed control law can assure that tracking error converges to an arbitrarily small neighborhood around zero. Simulations are performed to demonstrate the effectiveness of the presented control scheme in coping with input constraint and aerodynamic uncertainty.

One Near Space Hypersonic Aircraft Neural Networks Dynamic Surface Backstepping Control Design

By using multilayer neural networks and dynamic surface backstepping,one new robust adaptive control design method is proposed for one hypersonic aircraft (HSA) uncertain MIMO nonaffine block control system. We adopt dynamic surface control strategy to eliminate the explosion of terms by introducing a series of first order filters to obtain the differentiation of the virtual control inputs. multi-layers nerual network adjust function to compensate the influence from the uncertain, and design the robust terms to solve the problem from approach error. The stability analysis and simulations demonstrate the good performance of the controller. Nonlinear six-degree-of-freedom (6-DOF) numerical simulation results for a HSA model are presented to demonstrate the effectiveness of the proposed method.