Nussbaum Gain Method Research Articles

Iterative Learning Consensus for Nonstrict Feedback Multiagent Systems With Unknown Control Direction and Saturation Input

This article addresses the adaptive iterative learning control consensus problem for a class of unknown nonlinear high-order nonstrict feedback multiagent systems with partially unknown virtual and actual control directions and saturation inputs. Due to the unknown nonlinear dynamics of all follower agents, fuzzy logic systems combined with adaptive way are employed to design control protocol. And the Nussbaum-gain method is utilized to deal with partially unknown virtual and actual control directions in each step of the backstepping design procedure. With backstepping design process constructing adaptive fuzzy iterative learning control scheme for each agent, our proposed new control algorithm ensures that the outputs of all follower agents can accurately track the leader on finite time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$[ {0,T} ]$</tex-math></inline-formula> . Finally, the performance of our new algorithm is demonstrated by two simulation examples.

RESO-based distributed bipartite tracking control for stochastic MASs with actuator nonlinearity

This paper focuses on addressing the bipartite tracking control issue for stochastic nonlinear multiagent systems (MASs) with unmeasured states, unknown external disturbances and actuator nonlinearity. During the design procedure, a category of distributed reduced-order extended state observers (RESOs) are constructed to compensate for the total disturbances and estimate unknown states. Moreover, in order to solve the adverse impacts caused by actuator nonlinearity (saturation and dead-zone), an auxiliary variable and the Nussbaum gain method are adopted. Compared with the existing results, the proposed scheme has a better approximation effect. Based on distributed RESOs, the command-filtered backstepping method, and stochastic Lyapunov stability theory, a bipartite tracking control protocol is designed such that all signals of the closed-loop system are semi-global uniformly ultimately bounded (SGUUB) in probability. Finally, the effectiveness and superiority of the proposed method are verified via simulation examples and comparison results.

Observer-based adaptive fuzzy finite-time prescribed performance tracking control for strict-feedback systems with input dead-zone and saturation

This paper considers the problems of finite-time prescribed performance tracking control for a class of strict-feedback nonlinear systems with input dead-zone and saturation simultaneously. The unknown nonlinear functions are approximated by fuzzy logic systems and the unmeasurable states are estimated by designing a fuzzy state observer. In addition, a non-affine smooth function is used to approximate the non-smooth input dead-zone and saturated nonlinearity, and it is varied to the affine form via the mean value theorem. An adaptive fuzzy output feedback controller is developed by backstepping control method and Nussbaum gain method. It guarantees that the tracking error falls within a pre-set boundary at finite time and all the signals of the closed-loop system are bounded. The simulation results illustrate the feasibility of the design scheme.

Universal output feedback and Nussbaum gain adaptive control of supersonic missiles with unknown control direction

Based on the previous works in Lei and Lin (Syst Control Lett 56:529–537, 2007) and Kim et al. (Control Eng Pract 12:149–154, 2004) two kinds of novel universal output feedback controllers are proposed to solve the unmeasurable states problem for a uncertain missile system. Furthermore, in order to solve the unknown control direction problem which is not considered in the above reference, the unilateral Nussbaum gain method is adopted. Finally, to integrate the universal output feedback method with the Nussbaum gain method better, a special regulation law for the controller is designed to update the Nussbaum gain. Also, the numerical simulation result testified the rightness of this method.

Observer based adaptive double-layer fuzzy control for nonlinear systems with prescribed performance and unknown control direction

This paper investigates an observer based adaptive double-layer fuzzy control design problem for strict feedback nonlinear systems with prescribed performance and unknown control direction. To this end, a class of T-S fuzzy systems with unknown fuzzy rules are considered, and an adaptive interval type-2 (IT2) fuzzy controller is proposed for these systems. By using the presented control scheme, the unknown functions of the system can be ultimately approximated by the double-layer fuzzy logic systems (FLSs) which contain the first-layer type-1 FLSs and the second-layer IT2 FLSs. A state observer is applied to handle the unmeasurable states, and the Nussbaum gain method is employed to cope with the unknown control direction. In order to guarantee the prescribed performance of the output tracking error, a tracking error transformation method is utilized, and an improved robust adaptive control scheme is proposed based on the backstepping technique. Then, the stability of the closed-loop system and the achievability of the prescribed tracking performance are proved. Finally, simulation results illustrate the efficacy of the proposed control method.

F81A MENDELIAN RANDOMIZATION APPROACH TOWARDS MODEL SELECTION: STUDYING THE NATURE OF THE RELATIONS BETWEEN NEUROTICISM SYMPTOMS

A Nussbaum adaptive fault-tolerant controller is designed for the longitudinal motion of a twin-engine hypersonic vehicle containing uncertain parameters and unexpected actuator faults. We first apply feedback linearization to design the controller under nominal condition. Through a combination of parametrization and adaptive law, the model uncertainty can be well coped with. And Nussbaum gain method is used to solve the uncertain control direction function. Based on the previous work, considering the existence of throttle faults, a fault-tolerant controller is developed by choosing the appropriate range of the controller parameters, which is defined to compensate the actuator faults. Simulation results confirm the effectiveness of the proposed design.

Nussbaum Gain Adaptive Fault Tolerant Control for Hypersonic Vehicles with Uncertain Parameters and Actuator Faults

A Nussbaum adaptive fault-tolerant controller is designed for the longitudinal motion of a twin-engine hypersonic vehicle containing uncertain parameters and unexpected actuator faults. We first apply feedback linearization to design the controller under nominal condition. Through a combination of parametrization and adaptive law, the model uncertainty can be well coped with. And Nussbaum gain method is used to solve the uncertain control direction function. Based on the previous work, considering the existence of throttle faults, a fault-tolerant controller is developed by choosing the appropriate range of the controller parameters, which is defined to compensate the actuator faults. Simulation results confirm the effectiveness of the proposed design.

Spatial target path following control based on Nussbaum gain method for underactuated underwater vehicle

This paper investigates path following problem of underactuated underwater vehicle (UUV) which follows desired spatial path with constraint control inputs. Three dimensional path following error dynamics in Serret–Frenet coordinate frame is set up. The virtual target point on the desired spatial path is not the nearest point to UUV, which relaxes the restrictions on the initial conditions of controller. Considering speed of UUV and introducing the line-of-sight navigation, path following errors can converge rapidly. Hyperbolic tangent functions are employed to design path following controller which generates amplitude-limited control signals to prevent the actuators from the saturation. This improves the transient performance for large initial tracking errors in path following problem. Moreover, Nussbaum gains are incorporated into the control laws in order to estimate unknown parameters. This makes the controller realizable. The control method was proposed based on Lyapunov theory and backstepping technique. Theoretical proof and simulation experiment showed that the proposed method is effective to deal with path following problem of UUV.

Restricted Nussbaum Gain Control Method and Its Application in One Order System

The unknown control direction is one of the most open difficult question in nonlinear control theory. A new kind of restricted Nussbaum method is proposed to solve the unknown control direction problem without using high gain feedback. Although High gain has some advantages for improving the dynamic performance of a control system such as it can improve the quickness of the system and it can make the steady state error as small as possible. But now experienced engineers also realized that it causes many problems such as make the system unstable for big signal or high frequency noise. A kind of restricted Nussbaum gain method is firstly proposed to solve the problem. And simulation results show that it has better control effect compared with the traditional Nussbaum gain method. What is worthy pointing out is that the robustness of the Nussbaum gain strategy is improved obviously.

Robust adaptive repetitive learning control for a class of time-varying nonlinear systems with unknown control direction

A robust adaptive repetitive learning control method is proposed for a class of time-varying nonlinear systems. Nussbaum-gain method is incorporated into the control design to counteract the lack of a priori knowledge of the control direction which determines the motion direction of the system under any input. It is shown that the system state could converge to the desired trajectory asymptotically along the iteration axis through repetitive learning. Simulation is carried out to show the validity of the proposed control method.

Feedback nonlinear discrete-time systems

In this paper, we design an adaptive iterative learning control method for a class of high-order nonlinear output feedback discrete-time systems with random initial conditions and iteration-varying desired trajectories. An n-step ahead predictor approach is employed to estimate future outputs. The discrete Nussbaum gain method is incorporated into the control design to deal with unknown control directions. The proposed control algorithm ensures that the tracking error converges to zero asymptotically along the iterative learning axis except for the beginning outputs affected by random initial conditions. A numerical simulation is carried out to demonstrate the efficacy of the presented control laws.

Discrete-time adaptive iterative learning control for high-order nonlinear systems with unknown control directions

An adaptive iterative learning control method is proposed for a class of nonlinear strict-feedback discrete-time systems with random initial conditions and iteration-varying desired trajectories. An n-step ahead predictor approach is employed to estimate the future states in the control design. Discrete Nussbaum gain method is utilised to deal with the lack of a priori knowledge of control directions. The proposed control algorithm guarantees the boundedness of all the signals in the controlled system. The tracking error converges to zero asymptotically along the iterative learning axis except for beginning states affected by random initial conditions. The effectiveness of the proposed control scheme is verified through numerical simulation.

Controller Design for a Second-Order Plant with Uncertain Parameters and Disturbance: Application to a DC Motor

This paper shows the controller design for a second-order plant with unknown varying behavior in the parameters and in the disturbance. The state adaptive backstepping technique is used as control framework, but important modifications are introduced. The controller design achieves mainly the following two benefits: upper or lower bounds of the time-varying parameters of the model are not required, and the formulation of the control and update laws and stability analysis are simpler than closely related works that use the Nussbaum gain method. The controller has been developed and tested for a DC motor speed control and it has been implemented in a Rapid Control Prototyping system based on Digital Signal Processing for dSPACE platform. The motor speed converges to a predefined desired output signal.

Discrete-time adaptive iterative learning control with unknown control directions

An adaptive iterative learning control scheme is proposed for a class of discrete-time nonlinear systems with random initial conditions and iteration-varying desired trajectories. The discrete Nussbaum gain method is incorporated into the control design to tackle the problem associated with the lack of a priori knowledge of the control directions. The proposed control algorithm guarantees the boundedness of all the signals in the controlled system. The tracking error converges to zero asymptotically along the iterative learning axis. The effectiveness of the proposed control law is verified through numerical simulation.

Repetitive learning control for triangular systems with unknown control directions

A backstepping repetitive learning control method is proposed for a class of high-order non-linear systems with triangular structure with unknown control coefficients. The Nussbaum-gain method is incorporated into the control design to counteract the lack of a priori knowledge of the control directions. A differential-difference repetitive control law is presented to avoid the difficulties encountered in the derivation of the fictitious control. It is proved that the output of controlled system converges to the desired trajectory asymptotically along the iterative learning axis through repetitive learning. Simulation is carried out to show the validity of the proposed control method.

Repetitive Learning Control for Nonlinear Systems with Unknown Control Directions

AbstractA repetitive learning control method combined with backstepping technology is proposed for a class of high-order nonlinear systems with triangular structure with unknown control coefficients. The Nussbaum-gain method is incorporated into the control design to counteract the lack of a priori knowledge of the control directions. A differential-difference repetitive control law is presented to avoid the difficulties encountered in the derivation of the fictitious control. It is shown that the output of the controlled system could converge to the desired trajectory asymptotically through repetitive learning.

A Nussbaum gain adaptive synchronization of a new hyperchaotic system with input uncertainties and unknown parameters

The sign of unknown input coefficients is assumed to be known in most papers about the input uncertainties. In this paper, a Nussbaum gain method is adopted to cope with the situation that both the sign and the value of input are unknown. And the unknown parameters can be estimated under the situation of unknown sign of control. The synchronization is achieved for a class of hyperchaotic systems with unknown parameters and input uncertainties by adopting of the Nussbaum gain method and the global terminal adaptive method. And the conclusions are made as follows: First, the proposed method is effective in the situation that the sign of input is unknown. Second, the estimation of unknown parameters can be achieved only when the number of unknown parameters satisfied some condition and no uncertainty exist in the input of systems. Third, the unknown parameters cannot be estimated correctly with common adaptive method when there are input uncertainties in the system. But the Nussbaum gain method can get good result in the estimation of unknown parameters. At last, numerical simulations are done to show the effectiveness of the proposed method.

Output feedback adaptive control of multivariable nonlinear systems using Nussbaum gain method

A new output feedback adaptive control scheme for multi-input and multi-output nonlinear systems with parametric uncertainty is presented based on the Nussbaum gain method and the backstepping approach. The high frequency gain matrix of the linear part of the system is not necessarily positive definite, but can be transformed into a lower or upper triangular matrix whose signs of diagonal elements are unknown. The new required condition for the high frequency gain matrix can be easily checked for certain plants so that the proposed method is widely applicable. The global stability of the closed loop systems is guaranteed through this control scheme, at the same time the tracking error converges to zero.