The position-based impedance control combined with compliance-eliminated and feedforward compensation for HDU of legged robot

In this paper, the hydraulic drive unit (HDU) driving the joint motion of the legged robot is the research object. Through the experiment on HDU, it is observed that the control accuracy of the traditional position-based impedance control is not high enough. The further analysis researches the serial-parallel composition on dynamic compliances from both position control inner and impedance outer loop. Then, the two reasons affecting control accuracy are found out. Therefore, aimed at the first reason, a compliance-eliminated controller with multiple serial branches is designed. Aimed at the second reason, a feedforward compensation controller is designed. Finally, the dynamic compliance composition is rearranged. The results of experiments conducted indicate that the proposed method significantly improves the control accuracy compared to that of traditional position-based impedance control.     

Networked predictive control for linear systems with quantizers by an event-driven strategy

In this paper, networked predictive control is investigated for a networked control system with quantizers by an event-driven strategy. An event generator is designed according to a deviation of state estimation between the current time and last trigger time. A predictive strategy is proposed to compensate effect of network-induced delays and packet dropouts. The quantizers are used to deal with signals by converting real-valued signals into effective ones in both feedback and forward channels. Based on a “zoom” strategy, sufficient conditions are given to ensure stabilization of the networked control system by solving linear matrix inequalities. A simulation example is proposed to exhibit advantages and availability of the developed techniques.     

Data filtering based maximum likelihood extended gradient method for multivariable systems with autoregressive moving average noise

For multivariable systems with autoregressive moving average noises, we decompose the multivariable system into m subsystems (m denotes the number of outputs) and present a maximum likelihood generalized extended gradient algorithm and a data filtering based maximum likelihood extended gradient algorithm to estimate the parameter vectors of these subsystems. By combining the maximum likelihood principle and the data filtering technique, the proposed algorithms are effective and have computational advantages over existing estimation algorithms. Finally, a numerical simulation example is given to support the developed methods and to show their effectiveness.     

Finite-time control for periodic systems with Markov jump sensor nonlinearities and random input gains

Finite-time control for periodic systems with sensor nonlinearities and random input gains is addressed in this work. The variation of sensor nonlinearities is modeled by a Markov chain, and a stochastic variable is used to describe the influence of the actuator. A mode- and sensor nonlinearity-dependent non-fragile controller is designed to improve the performance and the non-fragility of the controller. The finite-time boundedness of the closed-loop system is ensured by a sufficient condition, the corresponding controller is then designed. Finally, the effectiveness of the developed results is illustrated by a numerical example.     

Event-triggered dissipative state estimation for Markov jump neural networks with random uncertainties

This paper is concerned with the problem of event-triggered dissipative state estimation for Markov jump neural networks with random uncertainties. The event-triggered mechanism is introduced to save the limited communication bandwidth resource and preserve the desired system performance. The phenomenon of randomly occurring parameter uncertainties is considered to increase utilizability of the proposed method. To describe such a randomly occurring phenomenon, some mutually independent Bernoulli distributed white sequences are adopted. A mode-dependent state estimator is designed in this paper, which ensures that the estimation error system is extended stochastically dissipative. By using the Lyapunov–Krasovskii functional approach and an optimized decoupling approach, an expected state estimator can be built by solving some sufficient conditions. Two numerical examples are presented to demonstrate the correctness and effectiveness of the proposed method.     

Composite anti-disturbance control for uncertain Markovian jump systems with actuator saturation based disturbance observer and adaptive neural network

This paper studies the problem of composite control for a class of uncertain Markovian jump systems (MJSs) with partial known transition rates, multiple disturbances and actuator saturation. Compared with the existing results, a novel robust composite control scheme is put forward by virtue of adaptive neural network technique. For MJSs, the partial unknown information on transition rates and the actuator saturation influence the design of disturbance observer and the robust H_∞ controller. Firstly, without taking account of external disturbances, the network reconstruction error and saturation, a novel robust adaptive control strategy is established to ensure that all the signals of the closed-loop system are asymptotically bounded in mean square. Secondly, the solvability condition for ensuring the robust H_∞ performance is given by using a modified adaptive law, where the saturation is treated as a disturbance-like signal. Finally, the simulations for a numerical example and an application example are performed to validate the effectiveness of the proposed results.     

Necessary conditions of exponential stability for a class of linear uncertain systems with a single constant delay

In this paper, we will investigate the necessary conditions, described by the Lyapunov matrix, for the robust exponential stability for a class of linear uncertain systems with a single constant delay and time-invariant parametric uncertainties, which are some generalizations of the existing results on uncertain linear time-delay systems. As a medium step, several pivotal properties of parameter-dependent Lyapunov matrix are proposed, which set up the relationships between fundamental matrix and Lyapunov matrix for the considered system. In addition, to calculate the parameter-dependent Lyapunov matrix, we introduce the differential equation method and the Lagrange interpolation method, respectively. Furthermore, it is noted that the proposed necessary conditions can be used to estimate the range of time delay, when the linear uncertain time-delay system is robust exponential stability. Finally, the validity of the obtained theoretical results is illustrated via numerical examples.     

Quantitative mean square exponential stability and stabilization of stochastic systems with Markovian switching

This paper is concerned with the quantitative mean square exponential stability and stabilization for stochastic systems with Markovian switching. First, the concept of quantitative mean square exponential stability(QMSES) is introduced, and two stability criteria are derived. Then, based on an auxiliary definition of general finite-time mean square stability(GFTMSS), the relations among QMSES, GFTMSS and finite time stochastic stability (FTSS) are obtained. Subsequently, QMSE-stabilization is investigated and several new sufficient conditions for the existence of the state and observer-based controllers are provided by means of linear matrix inequalities. An algorithm is given to achieve the relation between the minimum states’ upper bound and the states’ decay velocity. Finally, a numerical example is utilized to show the merit of the proposed results.     

Consensus analysis for multi-agent systems via periodic event-triggered algorithms with quantized information

In this article, a novel distributed event-triggered control protocol for the consensus of second-order multi-agent systems with undirected topology is studied. Based on the proposed control protocol, the event-triggered condition is evaluated only at every sampling instant. The control input for each agent will be updated with local information if and only if its condition is violated. Both ideal and quantized relative state measurements are considered under this framework. Some sufficient conditions for achieving consensus are derived using spectral properties of edge Laplacian matrix and the discrete-time Lyapunov function method. Finally, numerical examples are given to demonstrate the effectiveness of our theoretical results.     

A new Lyapunov functional approach to sampled-data synchronization control for delayed neural networks

This paper discusses the problem of synchronization for delayed neural networks using sampled-data control. We introduce a new Lyapunov functional, called complete sampling-interval-dependent discontinuous Lyapunov functional, which can adequately capture sampling information on both intervals from $r(t?\overline{\tau })$ to $r(t_k?\overline{\tau })$ and from $r(t?\overline{\tau })$ to $r(t_{k+1}?\overline{\tau })$. Based on this Lyapunov functional and an improved integral inequality, less conservative conditions are derived to ensure the stability of the synchronization error system, leading to the fact that the drive neural network is synchronized with the response neural network. The desired sampled-data controller is designed in terms of solutions to linear matrix inequalities. A numerical example is provided to demonstrate that the proposed approaches are effective and superior to some existing ones in the literature.     

Non-fragile control of positive Markovian jump systems

This paper investigates the non-fragile control for positive Markovian jump systems both in continuous-time and discrete-time cases with actuator uncertainty. It is assumed that the coefficient matrices of the non-fragile controller is unknown and bounded. The state-feedback controller gain consists of nominal controller gain and gain perturbation. First, a set of state-feedback controllers for the considered system are designed by using a stochastic co-positive Lyapunov function integrated with linear programming approach. Under the designed controllers, the resulting closed-loop systems are positive and stochastically stable. Then, the proposed controller design approach is extended to discrete-time systems. Through comparisons, it is shown that existing results are special cases of the presented ones in the paper. Finally, two examples are given to illustrate the effectiveness of the proposed design.     

Reliable control for event-triggered singular Markov jump systems with partly unknown transition probabilities and actuator faults

In this paper, the problem of reliable controller design for event-triggered singular Markov jump systems with partly known transition probabilities, nonlinear perturbations and actuator faults is studied. To mitigate the burden of data transmissions over network, two event-triggered schemes with different triggering conditions are introduced. The switch law between the two event-triggered schemes is governed by a random variable with Bernoulli distribution. Taking nonlinear perturbations and actuator faults into account, the resulting closed-loop system is converted into a time-delay singular Markov jump system with partly known transition probabilities. Sufficient conditions of stochastically admissible for the resulting closed-loop system are obtained in terms of a group of linear matrix inequalities. The co-design of desirable reliable controller and weighting matrices of event-triggered schemes is presented. Finally, two numerical examples are given to show the effectiveness of the developed results.     

Adaptive disturbance attenuation for a class of uncertain nonlinear systems: A double-gain nonlinear observer method

This paper is concerned with the problem of adaptive disturbance attenuation for a class of nonlinear systems. The traditional adaptive methods are almost impossible to compensate the time-varying unknown disturbance by designing parameter adaptive laws without a priori knowledge about the bounds of external disturbances. To solve the problem, a new strategy is proposed by constructing an augmented system where the external disturbance is considered as another component of the augmented state vector. Based on this, a double-gain nonlinear observer is employed to estimate the state of the augmented nonlinear system. Further, an output feedback control strategy is designed, and it is proved that the proposed strategy ensures that all the signals are bounded and the tracking error exponentially converges to an adjustable compact set. Finally, an example is performed to demonstrate the validity of the proposed scheme.     

Static group synchronization of second-order multi-agent systems via pinning control

This paper investigates the expected static group synchronization problem of the second-order multi-agent systems via pinning control. For directed communication topology with spanning tree, based on Gershgorin disk theorem and the matrix property, a static pinning control protocol with fixed gains is first introduced and some sufficient and necessary static group synchronization criteria are also established. It is worth mentioning that a rigorous proof is also given that only one pinning node is needed to guarantee static group synchronization, which could be inferred that our protocol might be more economical and effective in large scale of multi-agent systems. Then, for weakly connected directed communication topology with nodes of zero in-degree, an adaptive pinning control applied to the node with zero in-degree is also proposed to achieve static group synchronization. Finally, the efficiency of the proposed protocols is verified by two simulation examples.     

Observer-based control for singular nonhomogeneous Markov jump systems with packet losses

This paper is concerned with the observer-based H_∞ control for a class of singular Markov jump systems over a finite-time interval, where the transition probability (TP) is time-varying and is limited to a convex hull. Due to the limited capacity of network medium, packet losses are presented in the underlying systems. Firstly, using a stochastic Lyapunov functional, a sufficient condition on singular stochastic H_∞ finite-time boundedness for the corresponding closed-loop error systems is provided. Subsequently, a linear matrix inequality (LMI) condition on the existence of the H_∞ observer-based controller is developed from a new perspective. Finally, three numerical examples are provided to illustrate the effectiveness of the proposed controller design method, wherein it is shown that the proposed method yields less conservative results than those in the literature.     

A new distributed Kalman filtering based on means-quare estimation upper bounds

In this paper, a novel distributed Kalman filter consisting of a bank of interlaced filters is proposed for a signal model whose dynamic equation and measurement equation are coupled. Each of the interlaced filters estimates a part of state rather than the global state using its and its neighbor information, which is different from other distributed filters already existed (e.g., distributed Kalman filter based on diffusion strategy or consensus strategy, distributed fuzzy filter and distributed particle filter with Gaussian mixer approximation, etc). This relieves the calculation and communication burden in networks. In addition, the proposed distributed Kalman filtering contains no consensus strategies, which is useful in some cases since consensus usually requires an infinite number of iterations.     

A hierarchical least squares identification algorithm for Hammerstein nonlinear systems using the key term separation

Mathematical models are basic for designing controller and system identification is the theory and methods for establishing the mathematical models of practical systems. This paper considers the parameter identification for Hammerstein controlled autoregressive systems. Using the key term separation technique to express the system output as a linear combination of the system parameters, the system is decomposed into several subsystems with fewer variables, and then a hierarchical least squares (HLS) algorithm is developed for estimating all parameters involving in the subsystems. The HLS algorithm requires less computation than the recursive least squares algorithm. The computational efficiency comparison and simulation results both confirm the effectiveness of the proposed algorithms.     

Model free adaptive iterative learning control for a class of nonlinear systems with randomly varying iteration lengths

This paper proposes a novel model free adaptive iterative learning control scheme for a class of unknown nonlinear systems with randomly varying iteration lengths. By applying the dynamic linearization technique along the iteration axis, such systems can be transformed into iteration-depended time varying linear systems. Then, an improved model free adaptive iterative learning control scheme can be constructed only using input and output data of the system. From the rigorous theoretical analysis, it is shown that the mathematical expectation of tracking errors converge to zero as iteration increases. This design does not require any dynamic information of the ILC systems and prior information of randomly varying iteration lengths. An illustrative example verifies the effectiveness of the proposed design.