Single-link Robot Arm System Research Articles

Event-Triggered Resilient Filtering With the Interval Type Uncertainty for Markov Jump Systems.

The problem of event-triggered resilient filtering for Markov jump systems is investigated in this article. The hidden Markov model is used to characterize asynchronous constraints between the filters and the systems. Gain uncertainties of the resilient filter are the interval type in this article, which is more accurate than the norm-bounded type to model the uncertain phenomenon. The number of linear matrix inequalities constraints can be decreased significantly by separating the vertices of the uncertain interval, so that the difficulty of calculation and calculation time can be reduced. Moreover, the event-triggered scheme is applied to depress the consumption of network resources. In order to find a balance between reducing bandwidth consumed and improving system performance, the threshold parameter is designed as a diagonal matrix in the event-triggered scheme. Utilizing the convex optimization method, the sufficient conditions are derived to guarantee that the filtering error systems are stochastically stable and satisfy the extended dissipation performance. Finally, a single-link robot arm system is delivered to certify the effectiveness and advantages of the proposed method.

Asynchronous Dissipative Control of Discrete-Time Fuzzy Markov Jump Systems With Dynamic State and Input Quantization

A numerically tractable two-step approach based on backtrack and optimization searches is proposed for asynchronous quantized dissipative control of discrete-time fuzzy Markov jump systems (DFMJSs) under the networked control framework. The asynchrony of modes between the plant and controller is described by a hidden Markov model. Both dynamic state and input quantization are considered. The dynamic zooming factors of the quantizers are designed as piecewise functions with respect to their arguments to avoid division by zero. A fuzzy asynchronous quantized controller is devised to make sure that the closed-loop system is stochastically stable and strictly <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(\mathcal {Q},\mathcal {S},\mathcal {R})$</tex-math></inline-formula> - dissipative via using a quadratic Lyapunov function and equivalent matrix transformations. Then, the iterative two-step approach is used to determine the optimal dissipativity level and the corresponding control gain and quantization parameters. Analysis and control synthesis for DFMJSs without quantization are also presented, covering some previous results as special cases. Finally, a single-link robot arm system and another numerical example are utilized to validate the present asynchronous dissipative control approaches for the quantization and non-quantization cases, respectively.

Exponential bipartite synchronisation of stochastic signed networks via intermittent pinning discrete-time state observations control

This paper studies the exponential bipartite synchronisation in mean square (EBS-MS) of stochastic signed networks (SSNs) via periodically intermittent pinning control. It is important to note that intermittent control is an extension of existing literature, which depends on discrete observations instead of continuous observations during the work period. Additionally, only a small percentage of the network nodes are controlled by intermittent control. Several sufficient conditions are established by the Lyapunov method and graph theory. Especially, when the duration τ between two consecutive observations tends to zero, our control will degenerate into common periodically intermittent pinning control. Meanwhile, a corollary about the EBS-MS of SSNs is presented. Besides, theoretical results are applied to a single-link robot arm system and an oscillator system. Finally, numerical simulations are presented to show the feasibility of the theoretical results.

Adaptive event-triggered filtering for semi-Markov jump systems under communication constraints

This paper investigates the problem of adaptive event-triggered filtering for a class of semi-Markov jump systems. A more general scenario of semi-Markov jump systems under communication constraints is explored, where the output signal occurs with saturation nonlinearity, packet loss, and quantization. The saturation nonlinearity and packet dropout are described by two random variables subject to Bernoulli distribution. The mode-dependent adaptive event-triggered mechanism is designed by combining the system mode information. Based on the output error, the trigger threshold adaptive law is designed to make the threshold change dynamically. The mode-dependent time-varying filter is constructed and sufficient conditions for the desired filter with H∞ performance are obtained. Finally, a single-link robot arm system verifies the effectiveness of the proposed filter design method, and the adaptive event-triggered protocol can effectively reduce the number of data transmissions.

Observer-based dynamic event-triggered secure control for nonlinear networked control systems with false data injection attacks

This paper considers the problem of observer-based dynamic event-triggered secure control for nonlinear networked control systems (NCSs) under false data injection attacks (FDIA). A novel output feedback controller is developed by utilizing a sampled-data observer to relieve the impacts of unmeasured states and FDIA. To make full use of the limited network resources, a dynamic periodic event-triggered mechanism (PETM) with an auxiliary variable is designed, which can reduce the transmission of information. Then, an approximation of injected false data is implemented based on an adaptive neural network (NN) in the presence of FDIA. Based on the proposed control strategy, the boundness of the nonlinear NCSs can be ensured by selecting some proper parameters. Finally, the effectiveness and validity of the proposed control strategy are illustrated via simulation of a single link robot arm system.

Adaptive event-triggered finite-time [formula omitted] control for fuzzy semi-Markovian jump systems with immeasurable premise variables

This paper addresses the adaptive event-triggered finite-time H∞ control problem of Takagi-Sugeno fuzzy semi-Markovian jump systems with immeasurable premise variables. Firstly, different from some existed works, the restrictions of measurable system states and measurable premise variables of nonlinear plant are removed and the fuzzy observer is designed to estimate unmeasurable system states. Then, a novel adaptive event-triggered scheme is firstly proposed to reduce the number of data transmission while ensuring the reliable system performance. Subsequently, the asynchronous problem about premise variables, namely, the premise variables of fuzzy system are not consistent with premise variables of fuzzy event-triggered controller is dealt with by utilizing an asynchronous method. By applying the delay system method, free-weighting matrix approach and slack matrix variables, novel sufficient conditions are derived to guarantee the finite-time H∞ performance of the closed-loop system, where the nonlinear terms caused by network-induced delay and partly unknown transition rates can be tackled by using suitable method. Finally, the single-link robot arm system is presented to affirm the efficiency of the obtained theoretical results.

Improved high gain observer design for a class of disturbed nonlinear systems

This paper provides a redesigned version of the Standard High Gain Observer (SHGO) to cope with the peaking phenomenon occurring during the transient periods as well as the sensitivity to high frequency measurement noise. The observer design is performed for a class of uniformly observable systems with noise free as well as noisy output measurements and the resulting observer is referred to as Non Peaking Filtered High Gain Observer (NPFHGO). The NPFHGO shares the same structure as its underlying SHGO and differs only by its corrective term which is still parameterized by a unique positive scalar up to an appropriate expression involving nested saturations. Of a fundamental interest, the power of the scalar parameter does not exceed one unlike in the case of the SHGO where this power grows from 1 to the system dimension. Moreover, it is shown that the equations of the NPFHGO become identical to those of the SHGO after a transient time horizon that can made arbitrarily small for sufficiently high values of the design parameter. A particular emphasis is put on the case of systems with noisy output measurements. It is shown how a multiple integrator of the corrupted outputs can be cascaded with the original system leading to an augmented system included in the class of systems for which the NPFHGO has been designed. The performance and main properties of the NPFHGO are highlighted and compared to those of its underlying SHGO through simulation results involving a single link robot arm system.

Design of [formula omitted]-based sampled-data control for fuzzy Markov jump systems with stochastic sampling

This paper concentrates on analyzing the stability problem for fuzzy Markov jump systems (FMJSs) via stochastic sampling and H∞-based sampled-data control scheme. With the help of input-delay technique, the probabilistic sampling intervals are reconstructed into a continuous time-varying system under stochastic parameters in the system matrices. Subsequently, a set of sufficient conditions ensuring the stochastic stability of the addressed FMJS with an allowable H∞ disturbance attenuation value is formulated in the form of linear matrix inequalities (LMIs) by choosing a proper Lyapunov–Krasovskii functional involving triple integral terms and utilizing Wirtinger-based integral inequality. The desired sampled-data control gain can be determined in terms of the solution to the obtained LMIs. Lastly, the developed theoretical results and the benefits of the desired controllers are verified through numerical examples including a single link robot arm system.

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.

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.

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.

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.

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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.

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.

Tracking Control of a Class of Cyber-Physical Systems via a FlexRay Communication Network.

Due to properties of flexibility, adaptiveness, error tolerance, and time-determinism performance, the FlexRay communication protocol has been widely used to investigate robot systems and new generation of automobiles. In this paper, with the FlexRay communication protocol, the tracking problem of a class of cyber-physical systems are investigated by developing a general hybrid model, in which an emulation controller is utilized. Based on the proposed hybrid model, some sufficient conditions are established to guarantee the convergence of tracking errors. Then, the maximum allowable transmission interval (MATI) of the static/dynamic segment is obtained with a more general formula than the ones in some the previous works. The obtained MATI over the FlexRay communication network can be adjusted via the appropriate length of the static/dynamic segment, which reflects the flexibility of FlexRay. Finally, the results are verified by considering the tracking problem of a single-link robot arm system as well as the stabilization of a batch reactor system.

Observer-based quantized sliding mode $${\varvec{\mathcal {H}}}_{\varvec{\infty }}$$ H ∞ control of Markov jump systems

An adjustable quantized approach is adopted to treat the \(\mathcal {H}_{\infty }\) sliding mode control of Markov jump systems with general transition probabilities. To solve this problem, an integral sliding mode surface is constructed by an observer with the quantized output measurement and a new bound is developed to bridge the relationship between system output and its quantization. Nonlinearities incurred by controller synthesis and general transition probabilities are handled by separation strategies. With the help of these measurements, linear matrix inequalities-based conditions are established to ensure the stochastic stability of the sliding motion and meet the required \(\mathcal {H}_{\infty }\) performance level. An example of single-link robot arm system is simulated at last to demonstrate the validity.

A sojourn probability approach to fuzzy-model-based reliable control for switched systems with mode-dependent time-varying delays

This paper addresses reliable control design for a switched system (SS) described by T-S fuzzy model subject to actuator failures and mode-dependent time-varying delay. A different type of switching law is introduced with the aid of sojourn probabilities (SPs) technique. The sojourn probability depicts the probability of a switched system staying in subsystem. It should be pointed out that, the SPs describe the probabilities of SSs stay in each subsystems which is easily measured. Both completely known and partly unknown SPs are proposed for the T-S fuzzy SSs. By using a matrix inequality approach and by constructing a proper Lyapunov–Krasovskii functional, less conservatism sufficient conditions are achieved in the form of linear matrix inequalities. A single link robot arm system is given to illustrate the validity of proposed design procedure.