Single-link Robot Arm Research Articles

Improved Adaptive Fuzzy Output-Feedback Dynamic Surface Control of Nonlinear Systems With Unknown Dead-Zone Output

This article presents an adaptive fuzzy output-feedback dynamic surface control (DSC) for the nonlinear systems with dead-zone output nonlinearity. First, a novel smooth approximation of the output dead zone is given to conveniently fuse with the backstepping technique. After that a nonlinear fuzzy state observer is constructed to estimate the unmeasurable states, by employing the fuzzy logic systems for identifying the unknown compounded nonlinear functions, which releases the limitation in the existing references that the state observer needs to be linear in the presence of dead-zone output nonlinearity. Then, to reduce the effect of unknown dead-zone coefficients, an adaptive compensation mechanism is introduced by using the characteristic of hyperbolic tangent function, which can replace the widely used Nussbaum-type function-based control strategy. Furthermore, a novel DSC method based on the nonlinear filters is proposed, which not only avoids the issue of explosion of complexity inherent in the backstepping procedure, but also improves the system control performance. Under the certain assumptions, the stability of the closed-loop system is proved by use of Lyapunov function stability theory. Finally, the applicability of the proposed control method is rigorously verified by a single-link robot arm simulation example.

Event-triggered receding horizon control via actor-critic design

In this paper, we propose a novel event-triggered near-optimal control for nonlinear continuous-time systems. The receding horizon principle is utilized to improve the system robustness and obtain better dynamic control performance. In the proposed structure, we first decompose the infinite horizon optimal control into a series of finite horizon optimal problems. Then a learning strategy is adopted, in which an actor network is employed to approximate the cost function and an critic network is used to learn the optimal control law in each finite horizon. Furthermore, in order to reduce the computational cost and transmission cost, an event-triggered strategy is applied. We design an adaptive trigger condition, so that the signal transmissions and controller updates are conducted in an aperiodic way. Detailed stability analysis shows that the nonlinear system with the developed event-triggered optimal control policy is asymptotically stable. Simulation results on a single-link robot arm with different noise types have demonstrated the effectiveness of the proposed method.

SMC for semi-Markov jump T-S fuzzy systems with time delay

This paper investigates the issue of robust stabilization for delayed semi-Markov jump T-S fuzzy systems via sliding mode control (SMC). In order to reduce some conservativeness, an integral sliding mode surface (ISMS) is designed without assumption that the input matrices are plat-rule independent with full column rank, which is one of the critical factors for system performance. Based on Lyapunov functional theory, sufficient condition is provided for stochastic stability of the closed-loop system, and then extended to the case where the input matrices are independent of plant-rule. In addition, a fuzzy SMC controller is established to guarantee the finite time reachability of the predetermined fuzzy manifold. Finally, the superiorities of the proposed method are validated by a single-link robot arm model.

Observer-Based Adaptive Sliding Mode Control for Nonlinear Stochastic Markov Jump Systems via T–S Fuzzy Modeling: Applications to Robot Arm Model

In this article, the issue of sliding mode control for nonlinear stochastic Markovian jump systems with uncertain time-varying delay is investigated. Considering the system state measurements and the state-dependent disturbances are not available for feedback purposes, an observer-based adaptive control strategy is proposed. Based on the decomposition of the input matrices, the state-space representation of the system is turned into a regular form with the aid of T-S fuzzy models first. Then, a fuzzy observer system is constructed, which could be transformed into two lower order subsystems. By choosing a common linear switching surface, on which it also obtains linear sliding mode dynamics in a simple form. Further, an adaptive controller is synthesized relying on the bounded system delay information to ensure the estimated states driven on the predefined sliding surface and remain the sliding motion. Also, the stochastic stability analysis of the sliding mode dynamics is undertaken with two types of transition rates, and an interesting result reveals that the stability for the dynamics with type of uncertain transition rates may cover the completely known type. Finally, a single-link robot arm model is provided to verify the validity of the proposed method.

Fuzzy-Model-Based Output Feedback Reliable Control for Network-Based Semi-Markov Jump Nonlinear Systems Subject to Redundant Channels.

This article investigates the reliable output feedback control problem for networked nonlinear semi-Markov jump systems, in which a control strategy with redundant channels is established to reduce the adverse effect caused by packet dropouts. The actuator faults are fully considered in the setup. On the basis of stochastic analysis theory and fuzzy-model-based method, some criteria are established to guarantee the σ -error mean-square stability for the considered systems. As a consequence, the reliable output feedback controller design method is proposed, which can be utilized to deal with the actuator failures problem effectively. Finally, two illustrative examples are employed to explain the availability of the presented design approach, where the single-link robot arm system model is contained.

Observer-Based H Tracking Control Scheme and Its Application to Robot Arms

Abstract In this paper, an adaptive dynamic programming (ADP)-based H∞ tracking control method is proposed for unknown continuous-time nonlinear systems. By constructing a neural network (NN) observer with system input and output data, the dynamics of completely unknown systems can be identified online. Then, an augmented system composed of tracking error and reference trajectory dynamics is formulated, and the H∞ tracking control problem is regarded as a zero-sum game problem which is solved by using ADP technique. A critic NN is employed to approximate the cost function to solve the Hamilton-Jacobi-Isaacs equation. Furthermore, the ultimate uniform boundedness of observation errors, critic NN weights, and tracking errors are all proved through Lyapunov’s direct method. Finally, the proposed method is applied to a single link robot arm with unknown dynamics to demonstrate its effectiveness.

Co-Design of Event-Triggered Scheme and H∞ Output Control for Markov Jump Systems Against Deception Attacks

This paper is concerned with the co-design problem of event-triggered scheme and $H_{\infty }$ static output control of linear Markov jump systems with deception attacks. To save the previous communication resources, a mode-dependent event-triggered scheme is utilized based on system output. To describe the deception attacks, a random variable satisfying Bernoulli distribution is employed. By using a separation approach, sufficient linear matrix inequality conditions for the existence of event-triggered output controllers that ensure the stochastic stability with prescribed $H_{\infty }$ are obtained. Then, a co-design algorithm is proposed to obtain the trade-off between the communication cost and $H_{\infty }$ performance. Lastly, the validity of the developed method is verified by a numerical example and a practical single-link robot arm system.

Stabilizing transmission intervals and delays in nonlinear networked control systems through hybrid-system-with-memory modeling and Lyapunov–Krasovskii arguments

This article employs the hybrid-system-with-memory formalism to attain transmission intervals and delays that provably stabilize Networked Control Systems (NCSs). Nonlinear time-varying plants and controllers with variable discrete and distributed input, output and state delays along with nonconstant discrete and distributed network delays are considered. We bring together nominal system L2-stability, Uniformly Globally Exponentially Stable (UGES) scheduling protocols and linear upper bounds of network-induced output error dynamics to infer Uniform Global pre-Asymptotic Stability (UGpAS) of the closed-loop system via Lyapunov–Krasovskii arguments. Namely, we replace the Lyapunov–Razumikhin conditions and trajectory-based small-gain theorem with linear L2-gains arguments, featured in our previous works, with Lyapunov–Krasovskii functionals to prove UGpAS of interconnected hybrid systems with memory. The present methodology allows for more general delays (e.g., multiple input/output/state discrete and distributed delays) and output error dynamics (e.g., multiple discrete and distributed delays) as well as less conservative estimates of Maximally Allowable Transfer Intervals (MATIs). Our results are applicable to control problems with output feedback and the so-called large delays, that is, delays larger than the transmission intervals. In addition, model-based estimators between two consecutive updates, rather than merely the Zero-Order Hold (ZOH) strategy, are allowed for in order to prolong MATIs. Lastly, a nonlinear numerical example involving a single-link robot arm and observer–predictor-based control law is provided to illustrate our theoretical findings.

Adaptive unknown input observer for nonlinear systems with application to fault diagnosis

An adaptive unknown input observer for nonlinear systems whose nonlinear functions satisfy Lipschitz condition is presented. The main advantage of the proposed observer is that it is sufficient to satisfy the standard existence conditions of normal unknown input observer design. Another advantage is that it estimates both states and parameters simultaneously. So it can be very much useful for robust control and fault diagnosis. As a possible application, an actuator fault diagnosis scheme is developed for single link robot arm. Finally, numerical simulation is performed to validate the effectiveness of the proposed observer in estimating the parameter along with states.

Reliable non-fragile memory state feedback controller design for fuzzy Markov jump systems

This paper concentrates on solving the finite-time bounded control problem for a family of discrete-time Takagi–Sugeno fuzzy Markov jump systems with a memory state feedback controller. In the proposed controller design, the non-fragile control protocol is considered to overcome the effect of gain perturbations and a more practical actuator fault model is employed to tolerate the time-varying faults. With the aid of a mode-dependent Lyapunov–Krasovskii functional and the Abel lemma-based finite sum inequality, sufficient conditions ensuring the stochastic finite-time boundedness for the closed-loop system are derived in the framework of matrix inequalities. Under which, a desired extended passivity performance index is guaranteed for the system under consideration. The proposed memory state feedback controller gains are computed by solving the derived matrix inequalities. Further, the feasibility and virtue of obtained theoretical findings are illustrated through two practical models, namely, single link robot arm system and Hénon system.

Finite-Time Observer-Based Sliding Mode Control for Quantized Semi-Markov Switching Systems With Application

This article investigates the problem of sliding mode control (SMC) for semi-Markov switching systems (S-MSSs) with quantized measurement in finite-time level. The transition between different subsystems obeys a stochastic semi-Markov process related to nonexponential distribution. Additionally, due to the sensor information constraints, the state vectors are not always measurable in practice. Moreover, compared with existing results in literature, the output quantization is first considered for finite-time SMC problem via a logarithmic quantizer. Our attention is to design an appropriate finite-time SMC law to attenuate the influences of parametrical uncertainty and external disturbance onto the overall performance of the system under consideration. First, by the key points of stochastic semi-Markov Lyapunov function and observer design theory, a desired SMC law is constructed to guarantee that the system trajectories can arrive at the specified sliding surface (SSS) within an assigned finite-time level. Then, ST-dependent sufficient conditions are established to ensure the required finite-time boundedness performance including both reaching phase and sliding motion phase. Finally, the applicability of the proposed results is demonstrated by a single-link robot arm model.

Adaptive Fuzzy Fault-Tolerant Tracking Control for Partially Unknown Systems With Actuator Faults via Integral Reinforcement Learning Method

In this paper, a fuzzy reinforcement learning (RL)-based tracking control algorithm is first proposed for partially unknown systems with actuator faults. Based on Takagi–Sugeno fuzzy model, a novel fuzzy-augmented tracking dynamic is developed and the overall fuzzy control policy with corresponding performance index is designed, where four kinds of actuator faults, including actuator loss of effectiveness and bias fault, are considered. Combining the RL technique and fuzzy-augmented model, the new fuzzy integral RL-based fault-tolerant control algorithm is designed, and it runs in real time for the system with actuator faults. The dynamic matrices can be partially unknown and the online algorithm requires less information transmissions or computational load along with the learning process. Under the overall fuzzy fault-tolerant policy, the tracking objective is achieved and the stability is proven by Lyapunov theory. Finally, the applications in the single-link robot arm system and the complex pitch-rate control problem of F-16 fighter aircraft demonstrate the effectiveness of the proposed method.

Event-Triggered Optimal Neuro-Controller Design With Reinforcement Learning for Unknown Nonlinear Systems

This paper develops an optimal control scheme for continuous-time unknown nonlinear systems using the event-triggering mechanism. Different from designing controllers using the time-triggering mechanism, the event-triggered controller is updated only when the system state deviates more than a certain threshold from a prescribed value. To obtain the event-triggered optimal controller, we develop an identifier-critic architecture under the framework of reinforcement learning. The identifier network, composed of a feedforward neural network (FNN), aims to derive the knowledge of unknown system dynamics, and the critic network, constituted of an FNN, intends to derive the event-triggered optimal controller. The identifier network is tuned via the combination of a standard back-propagation algorithm and an e-modification method, and the critic network is updated using a modification of the gradient descent method. By introducing an additional stability term to update the critic network, the initial admissible control is no longer required. Meanwhile, by using historical and instantaneous state data together, the persistence of excitation condition is relaxed. A stability analysis of the closed-loop system is provided based on the Lyapunov method. The effectiveness of the proposed designs is illustrated through simulations of a nonlinear example and a single link robot arm system.

Takagi–Sugeno Model Based Event-Triggered Fuzzy Sliding-Mode Control of Networked Control Systems With Semi-Markovian Switchings

This paper is focused on the event-triggered fuzzy sliding-mode control of networked control systems regulated by semi-Markov process. First, through movement-decomposition method, the networked control system is transformed into two lower-order subsystems. Then, an event-triggered scheme based on a delay system model approach is proposed in designing the switching surface and obtaining the sliding mode dynamics. Furthermore, a fuzzy sliding-mode controller is developed to realize reachability of a predefined switching surface and desirable sliding motion. Moreover, in terms of linear matrix inequality method, sufficient conditions for stochastic stability of the obtained sliding mode dynamics is developed in the sense of generally uncertain transition rates. Finally, the applicability of the proposed results are verified numerically on the single-link robot arm system.

<html>H<sub>∞</sub> sliding mode control for Markov jump systems with interval time-varying delays and general transition probabilities</html>

This paper is devoted to design $H_\infty$ sliding mode controller for continuous-time Markov jump systems with interval time-varying delays and general transition probabilities. An integral sliding surface is constructed and its reachability is guaranteed via a sliding mode control law. Meanwhile, a linearisation strategy is applied to treat the nonlinearity induced by general transition probabilities. Using a separation method based on Finsler lemma to eliminate the coupling among Lyapunov variables and controller parameters, sufficient conditions for asymptotically stochastic stability of sliding mode dynamics are formulated in terms of linear matrix inequalities. Finally, a single-link robot arm system is simulated to demonstrate the effectiveness of the proposed method.

Asynchronous Finite-Time Filtering of Markov Jump Nonlinear Systems and Its Applications

In this paper, the problem of asynchronous finite-time filtering issue is addressed for a class of Markov jump nonlinear systems with incomplete transition rate. The so-called asynchronization means that the filter’s modes do not synchronize with the system’s modes. Both the stochastic finite-time boundedness (FTBs) problem and the stochastic input–output finite-time stability (IO-FTSy) problem are involved. By resorting to the mode-dependent Lyapunov function approach and the matrix inequality techniques, some interesting results are derived to verify the properties of the stochastic FTBs and the stochastic IO-FTSy of the asynchronous filtering error system. The asynchronous filter parameters can be reduced to the solvability of some convex optimization problems. Finally, a single-link robot arm and a tunnel diode circuit are applied to elucidate the proposed algorithms.

Stiffness Adjustment for a Single-Link Robot Arm Driven by Series Elastic Actuator in Muscle Training

Series elastic actuators (SEAs) can improve the performance of robots and ensure their safety; therefore, they are widely applied in rehabilitation robots. To effectively exercise muscles in late rehabilitation training, robots utilize different impedance characteristics according to human muscle conditions. In this study, a novel real-time parallel variable-stiffness control method is proposed. The method predicts the muscle stiffness of the human body during the interaction process, and then adjusts the port stiffness of the SEA as needed to improve strength training. The impedance controller is used to meet the port stiffness and stability requirements during interactions. The predictive stiffness control method not only assesses the stiffness of human muscles in real time but also meets the constraint conditions associated with interaction stability, speed, and position. This control structure enables effective and safe strength training. Finally, the experimental results indicate that the stiffness control method based on muscle stiffness prediction can accurately match the port stiffness and provide interaction stability for effective muscle exercise.

Filtered high gain observer for a class of uncertain nonlinear systems with sampled outputs

This paper deals with the design of a Filtered High Gain Observer (FHGO) for a class of uniformly observable systems involving uncertainties. The structure of the proposed observer is very simple as it consists in two cascaded sub-systems of the same dimension as the original system. The first subsystem is nothing else than a copy of the original system with a simple correction term which (linearly) depends on the state of the second subsystem. The latter subsystem is a linear filter driven by the output observation error, namely the error between the output measurement and an output prediction provided by the first subsystem. Of fundamental interest, the FHGO design is first carried out by assuming that the output measurements are continuously available before being extended to the case of sampled outputs, leading thereby to a continuous–discrete time FHGO which inherits the main properties of the original FHGO. The performance and the main properties of the (continuous–discrete time) FHGO are highlighted and compared to those of a standard high gain observer (SHGO) through simulation results involving a single-link robot arm system.

Resilient guaranteed cost control for uncertain T–S fuzzy systems with time-varying delays and Markov jump parameters

This paper aims to investigate the problem of resilient guaranteed cost control for uncertain Takagi–Sugeno fuzzy systems with Markov jump parameters and time-varying delay. A resilient mode-dependent fuzzy controller is designed and a weak sufficient condition is developed to ensure that the resulting closed-loop system is robust almost surely asymptotically stable with guaranteed cost index not exceeding the specified upper bound. Subsequently, the controller gain and upper bound of the guaranteed cost index can be obtained by solving a set of linear matrix inequalities. Finally, numerical and practical examples of the single-link robot arm system are provided to demonstrate the performance of the proposed approach.

Output-Based Dynamic Event-Triggered Mechanisms for Disturbance Rejection Control of Networked Nonlinear Systems.

This paper proposes a new output-based dynamic event-triggered mechanism (ETM) for disturbance rejection control of a class of networked nonlinear uncertain systems subject to additive time-varying disturbance. In the proposed control method, a new robust output feedback controller is first designed based on a generalized proportional-integral observer to attenuate/compensate the undesirable influence of nonlinear uncertainties and disturbances. Different from the static ETM, two new dynamic variables are defined, and thereafter, two kinds of different discrete-time dynamic ETMs are developed only using the sampled-data output signal, such that a better tradeoff between the communication properties and the control properties can be obtained. It is shown that under the proposed control methods, the global bounded stability of the closed-loop hybrid system can be guaranteed by choosing some appropriate parameters. Finally, the numerical simulations of a single link robot arm are conducted to demonstrate the feasibility and efficacy of the proposed control approach.