Presence Of Unmodeled Dynamics Research Articles

Decentralized adaptive proportional‐integral tracking control for strong interconnected nonlinear systems subject to unmodeled dynamics and uncertain input delays

AbstractIn this paper, the problem of decentralized adaptive proportional‐integral (PI) tracking control is investigated for a class of strong interconnected nonlinear systems in presence of unmodeled dynamics and uncertain input delays. A novel compensation mechanism is proposed to deal with the considered strong interconnection functions by applying a smooth switching function to the design algorithm, and the difficulty generated by unmodeled dynamics is dominated by using a dynamic auxiliary signal. By utilizing the suitable error transformations and selecting the appropriate Lyapunov‐Krasovskii function, the effects of uncertain input delays could be surmounted. The novelty of this study is that, for the first time, a new decentralized adaptive PI tracking control scheme including a switching compensation mechanism is developed for the considered strong interconnected nonlinear systems. It is proved that all the signals in the closed‐loop systems are uniformly ultimately bounded (UUB) and the tracking errors converge to a bounded compact set. Finally, a simulation example is carried out to illustrate the effectiveness of the proposed approach.

Disturbance Compensation in Discrete-Time Sliding Mode Control – A Comparative Study

This work is intended to compare three methods for disturbances estimation and compensation in discrete-time variable structure systems with sliding modes. All methods detect disturbance, which appear in control channel, with time delay of one sampling period. The first method is based on nominal discrete-time plant model and can be used in any type of discrete-time control systems. The second and the third methods detect disturbance by measurement of sliding function, and it is applicable in discrete-time sliding mode control systems only. The main task of this work is to check efficiency of the given methods in the presence of unmodeled inertial dynamics in actuators and position and velocity sensors of a positional servo system. It is shown that all three methods give near identical results in the nominal case, while the second and the third methods are superior in the presence of unmodelled dynamics. The third method introduces zig-zag motion in the nominal case. Results of research are illustrated by computer simulation of an example of positional servo system.

Adaptive backstepping dynamic sliding mode control for maglev turning motor spindle based on limited time preset performance

In the process of turning a maglev motorized spindle, there are problems such as system model time-varying, cross-coupling of control parameters, difficult measurement of system state variables, and nonlinear characteristics of active magnetic bearings, which lead to the inevitable cutting chatter phenomenon, difficult control algorithm design, and then the reduction of workpiece surface quality and accuracy, affecting machining efficiency and tool life. In this paper, the “multimodal-distributed parameter” model is extended to the “magnetic bearing-rotor-workpiece” variable mass turning process. An adaptive backstepping fast dynamic terminal sliding mode control is designed to address the model’s time-varying parameters and cross-coupling issues. In view of the difficulty in measuring the vibration displacement at the cutting point, the displacement field reconstruction method was introduced to reconstruct the vibration displacement field online and provide effective feedback for the previously designed control strategy. Finally, the proposed controller is applied to adjust and control the turning process of a maglev motorized spindle and compared with other advanced controllers. The simulation results show that the proposed control method has a better control effect than other control methods in the presence of unmodeled dynamics, uncertainties, and external disturbances.

Disturbance observer based actor-critic learning control for uncertain nonlinear systems

This paper investigates the disturbance observer based actor-critic learning control for a class of uncertain nonlinear systems in the presence of unmodeled dynamics and time-varying disturbances. The proposed control algorithm integrates a filter-based design method with actor-critic learning architecture and disturbance observer to circumvent the unmodeled dynamic and the time-varying disturbance. To be specific, the actor network is employed to estimate the unknown system dynamic, the critic network is developed to evaluate the control performance, and the disturbance observer is leveraged to provide efficient estimation of the compounded disturbance which includes the time-varying disturbance and the actor-critic network approximation error. Consequently, high-gain feedback is avoided and the improved tracking performance can be expected. Moreover, a composite weight adaptation law for actor network is constructed by utilizing two types of signals, the cost function and the modeling error. Eventually, theoretical analysis demonstrates that the developed controller can guarantee bounded stability. Extensive simulations and experiments on a robot manipulator are implemented to validate the performance of the resulted control strategy.

Adaptive fuzzy finite-time tracking control of nonlinear systems with unmodeled dynamics

This paper considers an adaptive fuzzy finite-time tracking control issue for uncertain nonlinear systems in the presence of unmodeled dynamics via the backstepping technique. In the design procedure, the traditional dynamic signal structure is improved firstly such that it is suitable for the controller design within finite-time interval universally for the controlled systems and it can be utilized to dominate the unmodeled dynamics. The dynamic disturbances are compensated by nonlinear damping terms. The fuzzy logic systems (FLSs) are used to package the unknown nonlinearities. By constructing the appropriate Lyapunov functions in recursive step and employing the finite-time stability theorem, the developed FLS-based adaptive tracking control strategy within finite-time interval, which ensures the boundedness of all the closed-loop signals and the convergence of tracking error. In the end, simulation results are provided to test the availability of the developed strategy.

Data-Driven Nonlinear Iterative Inversion Suspension Control

The commercial operation of the maglev train has strict requirements for the reliability and safety of the suspension control system. However, due to a large number of unmodeled dynamics of the suspension system, it is difficult to obtain the precise mathematical model of the suspension system. After the suspension system has been operated for a long time with high load, the system model will change due to the wear, aging and failure of components, as well as the settlement of the line and track. The control performance is degraded. Therefore, this paper proposes a data-driven nonlinear iterative inversion suspension control algorithm, which can achieve high-precision tracking performance recovery control after control performance degradation without depending on the suspension system model. The control performance of the suspension system is improved by learning the measured data of the historical suspension system, and the fast convergence of the tracking error and high-precision stable suspension control are realized in the presence of unmodeled dynamics and external noise interference. Based on the historical suspension data of the maglev train suspension control system, the inverse dynamics model of the suspension system is identified by iterative inversion learning based on data drive, and the suspension control framework based on iterative inversion is designed. Then, the nonlinear input update strategy is used to realize the rapid convergence of the learning process. Finally, the simulation experiment of the maglev train suspension system and the physical experiment of the maglev system experimental platform are combined. It is verified that the proposed levitation control algorithm can achieve high-precision fast tracking performance recovery control after the system control performance degrades under noise environment.

Recursive identification of a nonlinear state space model

SummaryThe convergence of a recursive prediction error method is analyzed. The algorithm identifies a nonlinear continuous time state space model, parameterized by one right‐hand side component of the differential equation and an output equation with a fixed differential gain, to avoid over‐parametrization. The method minimizes the criterion by simulation using an Euler discretization. A stability analysis of the associated differential equations results in conditions for (local) convergence to a minimum of the criterion function. Simulations verify the theoretical analysis and illustrate the performance in the presence of unmodeled dynamics, by identification of the nonlinear drum boiler dynamics of a power plant model.

A novel asymmetrical integral barrier Lyapunov function-based trajectory tracking control for hovercraft with multiple constraints

This paper addresses the trajectory tracking control problem of a hovercraft with asymmetrical time-varying multiple state constraints in the presence of unmodeled dynamics and external disturbances. By using the four-degree-of-freedom vector mathematical model of hovercraft, an extended state observer is adopted to provide the lumped disturbance estimation. Then, the virtual surge velocity and yaw angular velocity control laws are obtained by using a regular log-type barrier Lyapunov function to stabilize the position and yaw errors. In addition, compared with the traditional symmetric integral barrier Lyapunov function, a new asymmetric integral barrier Lyapunov function is introduced to the design process in this paper to address asymmetric state constraint problems. The surge velocity and yaw angular velocity to the inside of the boundary are analyzed to guarantee the safe turning motion or performance required at high speed, and the tracking errors of the closed-loop system are ultimately uniformly bounded by using the cascade system’s stability lemma. The effectiveness of the proposed control scheme is shown via numerical simulations.

Command filter and dynamic surface control technology based adaptive optimal control of uncertain nonlinear systems in strict‐feedback form

AbstractIn this article, the problem of command filter and event‐triggered mechanism based adaptive neural optimal control is discussed for a class of nonlinear systems in the presence of unmodeled dynamics in strict‐feedback form. The overall controller design is composed of feedforward controller and feedback controller as well as event‐triggered controller design. In the first part, the feedforward controller is constructed by exploiting command filter and introducing the compensation error, and the first‐order filter in the classical dynamic surface control technology is replaced by utilizing the second‐order filter. In the second part, adaptive dynamic programming algorithm is used to estimate the unknown optimal index function and optimal control signal by the aid of the capability of neural networks. In the third part, based on the feedforward and feedback controllers, an adaptive event‐triggered control is developed to avoid the occurrence of Zeno behavior. All the signals in the controlled system are proved to be semi‐globally uniformly ultimately bounded through theoretical analysis. Two numerical examples are employed to verify the availability of the proposed method.

Robust Actor–Critic Learning for Continuous-Time Nonlinear Systems With Unmodeled Dynamics

This article considers the robust optimal control problem for a class of nonlinear systems in the presence of unmodeled dynamics. An adaptive optimal controller is designed using the online actor–critic learning and is robustified against unmodeled dynamics. To deal with unmodeled dynamics, an auxiliary signal with the system state as its input signal is designed to capture the input-to-state stability. In addition to the critic network for value function approximation, a novel robustifying term is developed and introduced into the actor network to ensure robustness during the learning process. It is shown that both the actor and the critic weights learning converge to their optimal values while guaranteeing the boundedness of all the signals in the closed loop. Simulation examples are conducted to verify the efficacy of the presented scheme.

Reinforcement learning-based saturated adaptive robust neural-network control of underactuated autonomous underwater vehicles

This paper studies a high-performance intelligent online adaptive robust saturated dynamic surface control framework for underactuated autonomous underwater vehicles by engaging Actor–Critic neural networks in the presence of unmodeled dynamics, uncertainties, ocean disturbances and actuator saturation. The proposed controller is designed based on reinforcement learning method to compensate the effects of unmodeled dynamics and uncertainties more accurately that can lead to a better performance for the controller. The Actor–Critic neural networks are trained real-time by designing online training laws creatively and a new critic function is proposed to supervise the closed-loop performance with the aid of the Critic neural network. The proposed structure for the reinforcement learning method benefits from a model-free algorithm and only relies on the measurable variables of the closed-loop control system. This independency from system dynamics results in considerable low computational burden for the controller and, hence, the proposed control algorithm is efficient computationally. The hyperbolic tangent function is ingeniously used as a saturated stabilizer term to bound the control signals that results in low-amplitude control action and the probability of actuator saturation phenomenon is minimized by learning and compensating the actuator saturation nonlinearity as well. Finally, the stability of the proposed closed-loop system is investigated by the Lyapunov’s direct methodology and simulations along a comparative study with some quantitative assessments certify the contributions of this paper.

Adaptive PID computed-torque control of robot manipulators based on DDPG reinforcement learning

This paper presents a design of an adaptive PID gain tuning based on deep deterministic policy gradient reinforcement learning agent for PID computed-torque control of robot manipulators, taking the presence of unmodelled dynamics and external disturbances into consideration. The proposed approach adaptively computes the outer-loop PID controller gains, that minimise trajectory tracking errors and reject disturbances, while the closed-loop dynamics remain stable. Since the control scheme requires the knowledge of the robot's dynamics, both kinematic and dynamic equations of n-link serial manipulator are developed. The agent is implemented on UR5e robot manipulator model, using the most valid dynamic and kinematic parameters provided by the manufacturer and related works. Simulation results show that the proposed approach is robust against bounded internal and external disturbances, and achieves a good trajectory tracking performance, due to the adaptability of gain tuning over the conventional PID controller.

Smooth sliding control to overcome chattering arising in classical SMC and super-twisting algorithm in the presence of unmodeled dynamics

The earlier smooth sliding control (SSC) is revisited. New global stability and chattering alleviation analysis is presented under the more general situation of simultaneous presence of plant uncertainty, unmodeled dynamics and external disturbance. Based on an appropriate prediction error loop, it delivers a smooth filtered control signal to the plant. New explicit conditions are presented for SSC to eliminate chattering. Considering numerical examples recently used in a lively debate between continuous and discontinuous sliding mode control options, the SSC is shown to overcome chattering arising in both classical first-order sliding mode (FOSM) control and the super-twisting algorithm (STA) in the presence of unmodeled dynamics. Besides the original theoretical contribution, one main purpose here is to stir new research about chattering avoidance in both classical and higher-order sliding mode algorithms for uncertain systems.

Outlier robust identification of dual‐rate Hammerstein models in the presence of unmodeled dynamics

AbstractThe article considers the outlier‐robust recursive least squares algorithm for identification of SISO (single‐input single‐output) dual‐rate Hammerstein model. The output sampling period is an integer multiple of the input sampling period. By using polynomial transformation technique we get a model which is suitable for parameter estimation for dual‐rate measurement data. After that deterministic dual‐rate Hammerstein model is extended with stochastic disturbance (which includes outliers) and unmodeled dynamics. Synthesis of identification algorithm is based on Newton–Raphson method which requires that loss function should be twice differentiable. Huber loss function, relevant for outliers treatment, has just first derivative. In order to overcome problem pseudo‐Huber loss function is introduced. This function behaves similarly to Huber loss function and has derivatives of arbitrary orders. Given recursive algorithm is based on synergy of Huber and pseudo‐Huber loss functions. Then we consider the robustness of algorithm. The main contributions of the article are: (i) determination of dual‐rate Hammerstein model which includes stochastic disturbance with outliers and unmodeled dynamics; (ii) derivation of robust recursive algorithm; (iii) determination of robustness for parameter estimate.

A fast and robust closed-loop photovoltaic MPPT approach based on sliding mode techniques

This article presents a closed-loop Maximum Power Point Tracking (MPPT) method for a photovoltaic (PV) system that includes a PV array, a DC-DC converter and a DC bus. The proposal consists of a controller and two observers developed into the sliding mode (SM) theoretical framework. The converter switching signal is driven by an Integral First-Order Sliding Mode (IFOSM) controller whose input corresponds to the PV power gradient estimation. This estimation is obtained through a pair of Second Order Sliding Mode Observers (SOSM). The first one corresponds to a Levant’s differentiator which estimates the first-time derivative of the PV voltage and feds a specific SOSM which delivers the PV power gradient estimation. These kinds of observers converge in finite time even in the presence of unmodeled dynamics and external perturbations. The proposed structure permits to synthesise a whole MPPT closed-loop system with a fast-tracking dynamics, a moderate computational burden and a reduced hardware cost, requiring only two variable measurements. This approach, simplifies the controller design and the system start-up, which does not need any specific initial conditions to be started from. The system performance is evaluated using representative computer simulations with standardised radiation and temperature profiles and corroborated through experimental tests. Finally, the proposal capabilities to work under partial shading conditions are also evaluated.

Passivity-based adaptive tracking control of spacecraft line-of-sight relative motion with thrust saturation

This paper considers the control problem of spacecraft line-of-sight (LOS) relative motion with thrust saturation in the presence of unmodeled dynamics, external disturbance and unknown mass property. By using skew-symmetric property, reference trajectory generator and anti-windup technique, a novel passivity-based adaptive sliding mode control (SMC) scheme is proposed without prior knowledge of uncertainty/disturbance bound. Within the Lyapunov framework, the establishment of a real sliding mode (which induces the practical stability of closed-loop error system) is validated. The main contributions are that a new control gain adaptive algorithm is adopted to attenuate the overestimation of switching gain and a differentiable projection-based parameter adaptive algorithm is proposed to force the mass approximator to remain in a desired domain, then the adaptive control law is modified by the reference trajectory generator and anti-windup technique to compensate for the effect of thrust saturation. Finally, simulations are conducted to show the fine performance of proposed control scheme.

Robust Fractional Order Attitude Controller for Launch Vehicle with Flexible Dynamics

The importance of Fractional Order Proportional Integral Differential (FOPID) controller is increased due to the presence of two design parameters more than the conventional PID controller. This paper uses of these additional degrees of freedom in designing the attitude controller for launch vehicle system with unstable rigid body dynamics and flexible dynamics. The parameters of the controller are designed to meet time domain specifications by optimizing the performance indices using genetic algorithms. The proposed tracking controller exhibits the robustness property to the parameter variations during highly unstable atmospheric phase of the attitude controller. The tracking performance of the controller is analysed with flexible vehicle dynamics in presence of two bending modes. The proposed controller can reduce the steady state error by 30% and the settling time is reduced by 50%. The time domain analysis confirms the effectiveness of the proposed controller even in the presence of unmodelled dynamics and wind disturbance without losing stability of launch vehicle. In order to assure the robustness property of the proposed controller, the plant parameters such as control moment coefficient and aerodynamic coefficients are varied by 25%. The tracking performance with these off nominal parameters shows only 1% deviation from the response of plant with nominal parameters.

Direct Policy Optimization Using Deterministic Sampling and Collocation

We present an approach for approximately solving discrete-time stochastic optimal-control problems by combining direct trajectory optimization, deterministic sampling, and policy optimization. Our feedback motion-planning algorithm uses a quasi-Newton method to simultaneously optimize a reference trajectory, a set of deterministically chosen sample trajectories, and a parameterized policy. We demonstrate that this approach exactly recovers LQR policies in the case of linear dynamics, quadratic objective, and Gaussian disturbances. We also demonstrate the algorithm on several nonlinear, underactuated robotic systems to highlight its performance and ability to handle control limits, safely avoid obstacles, and generate robust plans in the presence of unmodeled dynamics.

Learning Adaptive Sliding Mode Control for Repetitive Motion Tasks in Maglev Rotary Table

Considering the increasingly strict motion precision requirements and repetitive task characteristics of magnetic levitation systems (MLSs) in the sophisticated industry, this article proposes a novel learning adaptive sliding mode control (LASMC) strategy for the MLS to achieve an excellent tracking performance. The LASMC scheme is obtained by combining adaptive sliding mode control (ASMC) and iterative learning control (ILC) terms in a parallel structure. ASMC can guarantee system stability and strong robustness, which employs an adaptive switching gain and parameter adaption algorithm. Even if the accurate disturbance bounds of MLS are not known, the ASMC item can also adjust the switching control gain online to ensure the stability and robustness of the system. Additionally, the ILC term can further improve the MLS performance for repetitive motion tasks without the accurate dynamics model. The asymptotic stability of the LASMC strategy is verified based on the Lyapunov theorem in the presence of unmodeled dynamics, disturbances, and saturation. Comparative experiments carried out on a maglev rotary table demonstrate that the proposed control strategy achieves excellent tracking accuracy and disturbance robustness in the practical MLS. The LASMC scheme provides a decent idea for the application of intelligent control technology in the controller design of MLSs.

Unified adaptive event‐triggered control of uncertain multi‐input multi‐output nonlinear systems with dynamic and static constraints

AbstractIn this article, a unified adaptive neural event‐triggered control strategy is presented for uncertain multi‐input multi‐output (MIMO) nonlinear systems with dynamic and static constraints in the presence of unmodeled dynamics. By introducing an invertible nonlinear mapping based on hyperbolic tangent function, the constrained original system is transformed into an equivalent unconstrained MIMO pure‐feedback system. A dynamic signal is employed to dispose of the dynamical uncertainties in the novel system. Based on the transformed system, unified adaptive event‐triggered controller is formed by using modified dynamic surface control technique and the bounded characteristic of Gaussian function. Using the introduced compact set in stability analysis and Lyapunov function method, all signals in the closed‐loop system are proved to be the semiglobal uniform ultimate boundedness. Furthermore, all states and output signals can strictly comply with the defined constraint conditions. Simulations of two numerical examples including 2‐link rigid manipulator are provided to verify and clarify the theoretical results.