Reinforcement learning based adaptive control for uncertain mechanical systems with asymptotic tracking

This paper mainly focuses on the development of a learning-based controller for a class of uncertain mechanical systems modeled by the Euler-Lagrange formulation.The considered system can depict the behavior of a large class of engineering systems,such as vehicular systems,robot manipulators and satellites.All these systems are often characterized by highly nonlinear characteristics,heavy modeling uncertainties and unknown perturbations,therefore,accurate-model-based nonlinear control approaches become unavailable.Motivated by the challenge,a reinforcement learning(RL)adaptive control methodology based on the actor-critic framework is investigated to compensate the uncertain mechanical dynamics.The approximation inaccuracies caused by RL and the exogenous unknown disturbances are circumvented via a continuous robust integral of the sign of the error(RISE)control approach.Different from a classical RISE control law,a tanh(·)function is utilized instead of a sign(·)function to acquire a more smooth control signal.The developed controller requires very little prior knowledge of the dynamic model,is robust to unknown dynamics and exogenous disturbances,and can achieve asymptotic output tracking.Eventually,co-simulations through ADAMS and MATLAB/Simulink on a three degrees-of-freedom(3-DOF)manipulator and experiments on a real-time electromechanical servo system are performed to verify the performance of the proposed approach.

Prediction and Output Estimation of Pattern Moving in Non-Newtonian Mechanical Systems Based on Probability Density Evolution

A prediction framework based on the evolution of pattern motion probability density is proposed for the output prediction and estimation problem of non-Newtonian mechanical systems,assuming that the system satisfies the generalized Lipschitz condition.As a complex nonlinear system primarily governed by statistical laws rather than Newtonian mechanics,the output of non-Newtonian mechanics systems is difficult to describe through deterministic variables such as state variables,which poses difficulties in predicting and estimating the system’s output.In this article,the temporal variation of the system is described by constructing pattern category variables,which are non-deterministic variables.Since pattern category variables have statistical attributes but not operational attributes,operational attributes are assigned to them by posterior probability density,and a method for analyzing their motion laws using probability density evolution is proposed.Furthermore,a data-driven form of pattern motion probabilistic density evolution prediction method is designed by combining pseudo partial derivative(PPD),achieving prediction of the probability density satisfying the system’s output uncertainty.Based on this,the final prediction estimation of the system’s output value is realized by minimum variance unbiased estimation.Finally,a corresponding PPD estimation algorithm is designed using an extended state observer(ESO)to estimate the parameters to be estimated in the proposed prediction method.The effectiveness of the parameter estimation algorithm and prediction method is demonstrated through theoretical analysis,and the accuracy of the algorithm is verified by two numerical simulation examples.

Lie-form invariance of nonholonomic mechanical systems

The Lie-form invariance of a nonholonomic mechanaical system is studied. The definition and criterion of the Lie-form invariance of the nonholonomic mechaaical system are given. The Hojman conserved quantity and a new type of conserved quantity are obtained from the Lie-form invariance. An example is givea to illustrate the application of the results.

On the Motion of Controllable Mechanical Systems Having Variable Mass

The differential equations of motion of a comtlaint system with parameters and variable mass, of a system with variable mass and servo constraints and those for the control problem on the forced motion of constraint systems with variable mass are given respectively. Finally, an example is presented.

A Novel Method for Vibration Mitigation of Complex Mechanical Systems

Taking the complex mechanical systems as the research project,a theoretical multi-degree-of-freedom(MDOF)model was established.Based on the vibration characteristics analysis of this system,a novel method of vibration mitigation was proposed,which can be applied to most of the complex mechanical systems.Through this method,limited grounding stiffness was made use of and added to certain degree of freedom(DOF)discretely.Thus,the root-meansquare(RMS)of the systems amplitude can be reduced to ideal level.The MATLAB code based on this method was attached,which was tested on the theoretical model.Consider that complex mechanical systems are nonlinear and uncertain,theoretically the optimal solution of vibration mitigation is inaccessible.However,this method can always provide a relatively effective solution.

Robust stabilization and disturbance attenuation for a class of underactuated mechanical systems

The robust control problem for a class of underactuated mechanical systems called acrobots is addressed. The goal is to drive the acrobots away from the straight-down position and balance them at the straight-up unstable equilibrium position in the presence of parametric uncertainties and external disturbance. First, in the swing-up area, it is shown that the time derivative of energy is independent of the parameter uncertainties, but exogenous disturbance may destroy the characteristic of increase in mechanical energy. So, a swing-up controller with compensator is designed to suppress the influence of the disturbance. Then, in the attractive area, the control problem is formulated into a H~ control framework by introducing a proper error signal, and a sufficient condition of the existence of Hoo state feedback control law based on linear matrix inequality （LMI） is proposed to guarantee the quadratic stability of the control system. Finally, the simulation results show that the proposed control approach can simultaneously handle a maximum ±10% parameter perturbation and a big disturbance simultaneously.

Multi-rate sensor fusion-based adaptive discrete finite-time synergetic control for flexible-joint mechanical systems

This paper proposes an adaptive discrete finite-time synergetic control （ADFTSC） scheme based on a multi-rate sensor fusion estimator for flexible-joint mechanical systems in the presence of unmeasured states and dynamic uncertainties. Multi-rate sensors are employed to observe the system states which cannot be directly obtained by encoders due to the existence of joint flexibilities. By using an extended Kalman filter （EKF）, the finite-time synergetic controller is designed based on a sensor fusion estimator which estimates states and parameters of the mechanical system with multi-rate measurements. The proposed controller can guarantee the finite-time convergence of tracking errors by the theoretical derivation. Simulation and experimental studies are included to validate the effectiveness of the proposed approach.

Intelligent Integrated Control of Underactuated Mechanical Systems with Second-order Nonholonomic Constraints

This paper describes an intelligent integrated control of an acrobot, which is an underactuated mechanical system with second-order nonholonomic constraints. The control combines a model-free fuzzy control, a fuzzy sliding-mode control and a model-based fuzzy control. The model-free fuzzy controller designed for the upswing ensures that the energy of the acrobot increases with each swing. Then the fuzzy sliding-mode controller is employed to control the movement that the acrobot enters the balance area from the swing-up area. The model-based fuzzy controller, which is based on a Takagi-Sugeno fuzzy model, is used to balance the acrobot. The stability of the fuzzy control system for balance control is guaranteed by a common symmetric positive matrix, which satisfies linear matrix inequalities.

Finslerian Mechanical Systems on Manifolds

The goal of this paper is to present Finslerian mechanical systems on manifolds.In conclusion,some differential geometrical and physical results on the related mechanic systems have been given.

Periodic event-triggered secure consensus for networked mechanical systems under Denial-of-Service attacks

This paper concentrates on the secure consensus problem of networked mechanical/Euler–Lagrange systems.First,a new periodic event-triggered(PET)secure distributed observer is proposed to estimate the leader information.The proposed distributed observer only relies on the PET data from its neighbors,which can significantly reduce the communication and computational burden.More importantly,it is secure in the sense that it can work normally regardless of the Denial-of-Service(DoS)attacks.Second,based on the proposed distributed observer,an adaptive fuzzy control law is proposed for each Euler–Lagrange system.A PET mechanism is integrated into the controller,which can reduce the control update.This is helpful for both energy saving and fault tolerance of actuators.Moreover,the PET mechanism naturally makes the controller easy to be implemented in digital platform.The property of fuzzy logic systems and Gronwall inequality are skillfully utilized to show the stability of the closed-loop system.Finally,the proposed control scheme is verified on real Euler–Lagrange systems,which contain a robot manipulator and several servo motors.

Controller design for 2-DOF underactuated mechanical systems based on controlled Lagrangians and application to Acrobot control

On the basis of controlled Lagrangians,a controller design is proposed for underactuated mechanical systems with two degrees of freedom.A new kinetic energy equation(K-equation)independent of the gyroscopic forces is found due to the use of their property.As a result,the necessary and sufficient matching condition comprises the new K-equation and the potential energy equation(P-equation)cascaded,the regular condition,and the explicit gyroscopic forces.Further,for two classes of input decoupled systems that cover the main benchmark examples,the new K-equation,respectively,degenerates from a quasilinear partial differential equation(PDE)into an ordinary differential equation(ODE)under some choice and into a homogeneous linear PDE with two kinds of explicit general solutions.Benefiting from one of the general solutions,the obtained smooth state feedback controller for the Acrobots is of a more general form.Specifically,a constant fixed in a related paper by the system parameters is converted into a controller parameter ranging over an open interval along with some new nonlinear terms involved.Unlike what is mentioned in the related paper,some categories of the Acrobots cannot be stabilized with the existing interconnection and damping assignment passivity based control(IDA-PBC)method.As a contribution,the system can be locally asymptotically stabilized by the selection of the new controller parameter except for only one special case.

Nonconservative mechanical systems with nonholonomic constraints

A geometric setting for generally nonconservative mechanical systems on fibred manifolds is proposed. Emphasis is put on an explicit formulation of nonholonomic mechanics when an unconstrained Lagrangian system moves in a generally non-potential force field depending on time, positions and velocities, and the constraints are nonholonomic, not necessarily linear in velocities. Equations of motion, and the corresponding Harniltonian equations in intrinsic form are given. Regularity conditions are found and a nonholonomic Legendre transformation is proposed, leading to a canonical form of the nonholonomic Hamiltonian equations for nonconservative systems.

Fault evolution-test dependency modeling for mechanical systems

Tracking the process of fault growth in mechanical systems using a range of tests is important to avoid catastrophic failures, So, it is necessary to study the design for testability （DFT）. In this paper, to improve the testability performance of me- chanical systems for tracking fault growth, a fault evolution-test dependency model （FETDM） is proposed to implement DFT. A testability analysis method that considers fault trackability and predictability is developed to quantify the testability performance of mechanical systems. Results from experiments on a centrifugal pump show that the proposed FETDM and testability analysis method can provide guidance to engineers to improve the testability level of mechanical systems.

滚-跳多运动模式球形机器人的动力学仿真研究

复杂的探索环境对探测机器人的通行能力提出了更高要求,具有多种运动模式的球形机器人是探测机器人领域的研究热点之一。通过对球形机器人内部构件质量分布的调节,设计了一种基于单摆驱动式的滚-跳多运动模式球形机器人,其具有滚动、转向、爬坡与跳跃4种基本运动能力;随后,又根据球形机器人的设计方案建立了球形机器人4种基本运动动力学方程。利用Automatic Dynamics Analysis of Mechanical Systems(ADAMS)软件构建该球形机器人虚拟样机并对其进行了滚动、转向、爬坡与跳跃的动力学仿真,最后以此为依据计算滚动、转向、爬坡与跳跃运动性能的仿真值,并制作实验室样机验证了动力学仿真的正确性。

Production of ZnO Nanobelts and Meso-Scale Study of Mechanical Properties

We investigate a peculiar phenomenon by processing ZnO nanobelts with an atomic force microscope （AFM）. In the contact mode of AFM, peculiar bending occurs in meso-scale when the nanobelt is applied with force in lateral direction. We study the mechanical properties of ZnO nanobelts under the influence of small size effect, with finite element analysis and mathematical analysis by means of Matlab. Based on this abnormal effect, a novel measuring method is proposed, which allows the surface morphology and surface properties to be characterized at the same time.

Security Analysis of a Block Encryption Algorithm Based on Dynamic Sequences of Multiple Chaotic Systems

Recently, the cryptosystem based on chaos has attracted much attention. Wang and Yu （Commun. Nonlin. Sci. Numer. Simulat. 14（2009）574） proposed a block encryption algorithm based on dynamic sequences of multiple chaotic systems. We analyze the potential flaws in the algorithm. Then, a chosen-plaintext attack is presented. Some remedial measures are suggested to avoid the flaws effectively. Furthermore, an improved encryption algorithm is proposed to resist the attacks＂ and to keep all the merits of the original cryptosystem.

Electromechanical Behavior of Interdigitated SiO2 Cantilever Arrays

Bending and first flexural mode vibration behavior of electrostatic actuated nanometer-sized interdigitated cantilever arrays are characterized under vacuum conditions. The pull-in＇＇ effect in dc driving and the hard spring effect＇＇ in ac driving are observed. A mass sensitivity of 20 fg is expected for our devices due to the ultra-small mass of the arm and relative high Q factor. The mass-spring lump model combined with Green＇s function method is used to fit the dc driving behaviors including the pull-in voltage. For the ac driving case, the polynomial expansion of the capacitive force is used in the model. The successfully fittings of the pull-in voltage and the hard spring effect prove that our simulation method could be used for guiding the geometrical design of cantilever-based sensors.

Hamiltonian Mechanics Systems on Three-Dimensional Almost Kenmotsu Manifolds

In this study,we concluded the Hamiltonian equations on(M3,φ,ξ,η,g𝑔),being a model.Finally introduce,some geometrical and physical results on the related mechanic systems have been discussed.

From MEMS to NEMS： Smart Chips with Senses and Muscles

The last half-century was transformed by the electronic revolution that essentially reproduced the human brain and its computing capacity on a chip. But over time, scientists have realized that something was missing to give life, so to speak, to the small chip with a brain： One needed to awaken its senses and develop its muscles! This challenge was solved through MEMS （micro electro mechanical systems）. Indeed, MEMS today are equipped with the sense of sight, smell, hearing, taste and touch through microsensors. They are also capable of physical exertion through small muscles called microactuators. These new capabilities open wide fields of imagination and important specific applications.

Actively-controlled Beds for Ambulances

During transportation by ambulance, a patient is exposed to inertial acceleration when an ambulance decelerates or turns a corner. Such acceleration often gives a patient physical stress such as blood pressure variation or body sway, which causes strong pain, feeling of discomfort or sometimes critical damage for seriously injured persons. To reduce this undesirable effect of the acceleration, the authors developed the actively-controlled bed （ACB） which controls the posture of a stretcher in real time to reduce foot-to-head and lateral acceleration acting on a supine person. This paper describes development of the ACB, including control system design and performance evaluation. The control system is designed by Zakian＇s framework, which comprises the principle of matching and the method of inequalities, so that the design specifications on the tracking error and the motor torque are satisfied. From the results of driving experiments and simulation, it is estimated that the ACB can reduce the acceleration acting on a patient by 65% in the foot-to-head direction and by 75% in the lateral direction.