Control design plays a major part in electrostatic linear comb actuator (ELCA) systems. Most existing control methods of ECLA mainly focus on traditional PID method. However, proportional–integral–derivative (PID) controller is only appropriate for the reference to be known as constant. In this article, the problem of establishing the dynamic model and designing the controller is investigated for ECLA working in the time-varying reference. The tracking effectiveness is constructed for ECLA systems based on the consideration of roots of the equivalent differential equation in tracking error model. Moreover, the convergence velocity is also tuned by changing the parameters in the presented control scheme. Simulation results guarantee the performance of the nonlinear control scheme as well as dynamic model to be established.

http://ijpeds.iaescore.com/index.php/IJPEDS/article/download/21579/13828

Modelling and control design of the electrostatic linear comb actuator

Task-space cooperative tracking control of the networked multiple Euler–Lagrange systems is studied in this paper. On the basis of establishing kinematic and dynamic modeling of a Euler–Lagrange system, an innovative task-space coordination controller is designed to deal with the time-varying communicating delays and uncertainties. First, in order to weaken the influence of the uncertainty of kinematic and dynamic parameters on the control error of the system, the product of the Jacobian matrix and the generalized spatial velocity are linearly parameterized; thus, the unknown parameters are separated from known parameters. The online estimation of uncertain parameters is realized by designing parameters and by proposing new adaptive laws for the dynamic and kinematic parameters. Furthermore, to describe the transmission of time-varying delay errors among networked agents, a new error term is introduced, obtained by adding the observation error and tracking error, and the coefficient of the network mutual coupling term related to the time-varying delay rate is added with reference to the generalized space velocity and task-space velocity of the Lagrange systems. In the end, the influence of the time-varying delay on the cooperative tracking control error of the networked multiple Euler–Lagrange systems is eliminated. With the help of Lyapunov stability theory, the tracking errors and synchronization errors of this system are calculated by introducing the Lyapunov–Krasovskii functional; the asymptotic convergence results rigorously prove the stability of the adaptive cooperative control systems. The simulation results verify the excellent performance of the controller.

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Task-Space Cooperative Tracking Control for Networked Uncalibrated Multiple Euler–Lagrange Systems

This paper focuses on the fixed-time leader-following consensus problem for multiple Euler–Lagrange (EL) systems via non-singular terminal sliding mode control under a directed graph. Firstly, for each EL system, a local fixed-time disturbance observer is introduced to estimate the compound disturbance (including uncertain parameters and external disturbances) within a fixed time under the assumption that the disturbance is bounded. Next, a distributed fixed-time observer is designed to estimate the leader’s position and velocity, and the consensus problem is transformed into a local tracking problem by introducing such an observer. On the basis of the two types of observers designed, a novel non-singular terminal sliding surface is proposed to guarantee that the tracking errors on the sliding surface converge to zero within a fixed time. Furthermore, the presented control algorithm also ensures the fixed-time reachability of the sliding surface, while avoiding the singularity problem. Finally, the effectiveness of the proposed observers and control protocol is further verified by a numerical simulation. 

Disturbance observer-based fixed-time leader-following consensus control for multiple Euler-Lagrange systems: A non-singular terminal sliding mode scheme

This paper is concerned with the dynamic quantized control for switched fuzzy systems with singular perturbation and an improved event-triggered protocol. Essentially apart from the transition probabilities, the nonhomogeneous sojourn probabilities are employed to characterize the dynamic behavior of switched fuzzy singularly perturbed systems based on a deterministic switching signal. Benefiting from the dynamic quantization parameter, the quantization-based event-triggered protocol is presented, thereby decreasing the communication load. Based on the hidden Markov model, a novel event-triggered asynchronous control law is built. Finally, two examples are shown to clarify the practicality of the obtained results. 

Dynamic quantized control for switched fuzzy singularly perturbation systems with event-triggered protocol

In this paper, we consider the consensus of uncertain multiple Euler–Lagrange​ systems. Based on switching topologies, the time-varying delay compensation, event-triggered mechanism, and finite-time convergence are considered, which can satisfy the needs of an actual system. First, the nonlinear uncertainties of the system are well approximated by applying the neural-networked scheme. Second, the new event-triggered mechanism can avoid the influence of the limited signal bandwidth and effectively decrease the data transmission times. Third, an adaptive law is used to compensate for the model and external disturbances. Fourth, the proposed switching topology scheme can respond to different scenarios, including when some agents fail to suddenly connect with their neighbors, and meet a wider range of collaborative needs. The effectiveness and feasibility of the proposed technique are demonstrated in theorem analysis and simulations. 

Robust event-triggered cooperative control of uncertain multiple Euler-Lagrange systems based on three kinds of random transformation topologies.

This paper addresses the consensus problem for a class of multiple Euler-Lagrange systems, where agents communicate with neighbors under an event-triggered mechanism. Due to the more complex dynamical characteristics, the consensus problem of multiple Euler-Lagrange systems is more challenging than that of ordinary second-order multi-agent systems. In this study, we assume that the inertia matrix, the Coriolis and centrifugal term, and the gravitational torque are totally unknown, then a protocol is derived by integrating the Lyapunov functional method, neural network approximation and adaptive control techniques. In addition, the event-triggered mechanism effectively reduces the communication traffic, and the Zeno behavior is well excluded. By a demonstrative example, the effectiveness of the protocol is illustrated.

Neural-network-based consensus of multiple Euler-Lagrange systems with an event-triggered mechanism

Adaptive Fully Distributed Consensus for a Class of Second-order Nonlinear Multi-agent Systems With Switching Networks

—Zero-sum Markov Games (MGs) has been an ef- ﬁcient framework for multi-agent systems and robust control, wherein a minimax problem is constructed to solve the equilib- rium policies. At present, this formulation is well studied under tabular settings wherein the maximum operator is primarily and exactly solved to calculate the worst-case value function. However, it is non-trivial to extend such methods to handle complex tasks, as ﬁnding the maximum over large-scale action spaces is usually cumbersome. In this paper, we propose the smoothing policy iteration (SPI) algorithm to solve the zero-sum MGs approximately, where the maximum operator is replaced by the weighted LogSumExp (WLSE) function to obtain the nearly optimal equilibrium policies. Specially, the adversarial policy is served as the weight function to enable an efﬁcient sampling over action spaces. We also prove the convergence of SPI and analyze its approximation error in ∞− norm based on the contraction mapping theorem. Besides, we propose a model-based algorithm called Smooth adversarial Actor-critic (SaAC) by extending SPI with the function approximations. The target value related to WLSE function is evaluated by the sampled trajectories and then mean square error is constructed to optimize the value function, and the gradient-ascent-descent methods are adopted to optimize the protagonist and adversarial policies jointly. In addition, we incorporate the reparameterization technique in model-based gradient back-propagation to prevent the gradient vanishing due to sampling from the stochastic policies. We verify our algorithm in both tabular and function approximation settings. Results show that SPI can approximate the worst-case value function with a high accuracy and SaAC can stabilize the training process and improve the adversarial robustness in a large margin.

Sheng Li

Papers

Neural-network-based consensus of multiple Euler-Lagrange systems with an event-triggered mechanism

Adaptive Fully Distributed Consensus for a Class of Second-order Nonlinear Multi-agent Systems With Switching Networks

Smoothing Policy Iteration for Zero-sum Markov Games