Particle swarm optimization-based algorithm of a symplectic method for robotic dynamics and control

Multibody system dynamics provides a strong tool for the estimation of dynamic performances and the optimization of multisystem robot design. It can be described with differential algebraic equations(DAEs). In this paper, a particle swarm optimization(PSO) method is introduced to solve and control a symplectic multibody system for the first time. It is first combined with the symplectic method to solve problems in uncontrolled and controlled robotic arm systems. It is shown that the results conserve the energy and keep the constraints of the chaotic motion, which demonstrates the efficiency, accuracy, and time-saving ability of the method. To make the system move along the pre-planned path, which is a functional extremum problem, a double-PSO-based instantaneous optimal control is introduced. Examples are performed to test the effectiveness of the double-PSO-based instantaneous optimal control. The results show that the method has high accuracy, a fast convergence speed, and a wide range of applications.All the above verify the immense potential applications of the PSO method in multibody system dynamics.

THEORY AND METHOD OF OPTIMAL CONTROL SOLUTION TODYNAMIC SYSTEM PARAMETERS IDENTIFICATION (Ⅰ)──FUNDAMENTAL CONCEPT AND DETERMINISTIC SYSTEM PARAMETERS IDENTIFICATION

Based on the concept of optimal control solution to dynamic system parameters identification and the optimal control theory of deterministic system,dyna-mics system parameters identfication problem is brought into correspondence with optimal control problem. Then the theory and algorithm of optimal control are introduced into the study of dynamic system parameters identification. According to the theory of Hamilton-Jacobi-Bellman (HJB) equations solution, the existence and uniqueness of optimal control solution to dynamic system parameters identification are resolved in this paper. At last, the parameters identification algorithm of determi-nistic dynamic system is presented also based on above mentioned theory and concept.

THEORY AND ALGORITHM OF OPTIMAL CONTROL SOLUTION TO DYNAMIC SYSTEM PARAMETERS IDENTIFICATION(Ⅱ)──STOCHASTIC SYSTEM PARAMETERS IDENTIFICATION AND APPLICATION EXAMPLE

Based on the contents Of part (Ⅰ) and stochastic optimal control theory, the concept of optimal control solution to parameters identification of stochastic dynamic system is discussed at first. For the completeness of the theory developed in this paper and part (Ⅰ), then the procedure of establishing HamiltonJacobi-Bellman (HJB) equations of parameters identification problem is presented.And then, parameters identification algorithm of stochastic dynamic system is introduced. At last, an application example-local nonlinear parameters identification of dynamic system is presented.

Temporal Prediction of Aircraft Loss-of-Control: A Dynamic Optimization Approach

Loss of Control (LOC) is the primary factor responsible for the majority of fatal air accidents during past decade. LOC is characterized by the pilot’s inability to control the aircraft and is typically associated with unpredictable behavior, potentially leading to loss of the aircraft and life. In this work, the minimum time dynamic optimization problem to LOC is treated using Pontryagin’s Maximum Principle (PMP). The resulting two point boundary value problem is solved using stochastic shooting point methods via a differential evolution scheme (DE). The minimum time until LOC metric is computed for corresponding spatial control limits. Simulations are performed using a linearized longitudinal aircraft model to illustrate the concept.

Design of Retarded Fractional Delay Differential Systems Using the Method of Inequalities

Methods based on numerical optimization are useful and effective in the design of control systems. This paper describes the design of retarded fractional delay differential systems （RFDDSs） by the method of inequalities, in which the design problem is formulated so that it is suitable for solution by numerical methods. Zakian＇s original formulation, which was first proposed in connection with rational systems, is extended to the case of RFDDSs. In making the use of this formulation possible for RFDDSs, the associated stability problems are resolved by using the stability test and the numerical algorithm for computing the abscissa of stability recently developed by the authors. During the design process, the time responses are obtained by a known method for the numerical inversion of Laplace transforms. Two numerical examples are given, where fractional controllers are designed for a time-delay and a heat-conduction plants.

CONTROLLING ROBOT MANIPULATORS BY DYNAMIC PROGRAMMING

A certain number of considerations should be taken into account in the dynamic control of robot manipulators as highly complex non-linear systems.In this article,we provide a detailed presentation of the mechanical and electrical impli- cations of robots equipped with DC motor actuators.This model takes into account all non-linear aspects of the system.Then,we develop computational algorithms for optimal control based on dynamic programming.The robot's trajectory must be predefined,but performance criteria and constraints applying to the system are not limited and we may adapt them freely to the robot and the task being studied.As an example,a manipulator arm with 3 degrees of freedom is analyzed.

Harmony search algorithm with differential evolution based control parameter co-evolution and its application in chemical process dynamic optimization

A modified harmony search algorithm with co-evolutional control parameters(DEHS), applied through differential evolution optimization, is proposed. In DEHS, two control parameters, i.e., harmony memory considering rate and pitch adjusting rate, are encoded as a symbiotic individual of an original individual(i.e., harmony vector). Harmony search operators are applied to evolving the original population. DE is applied to co-evolving the symbiotic population based on feedback information from the original population. Thus, with the evolution of the original population in DEHS, the symbiotic population is dynamically and self-adaptively adjusted, and real-time optimum control parameters are obtained. The proposed DEHS algorithm has been applied to various benchmark functions and two typical dynamic optimization problems. The experimental results show that the performance of the proposed algorithm is better than that of other HS variants. Satisfactory results are obtained in the application.

Substructure design optimization and nonlinear responses control analysis of the mega-sub controlled structural system (MSCSS) under earthquake action

The newly proposed mega sub-controlled structure system(MSCSS)and related studies have drawn the attention of civil engineers for practice in improving the performance and enhancing the structural effectiveness of mega frame structures.However,there is still a need for improvement to its basic structural arrangement.In this project,an advanced,reasonable arrangement of mega sub-controlled structure models,composed of three mega stories with different numbers and arrangements of substructures,are designed to investigate the control performance of the models and obtain the optimal model configuration(model with minimum acceleration and displacement responses)under strong earthquake excitation.In addition,the dynamic parameters that affect the performance effectiveness of the optimal model of MSCSS are studied and discussed.The area of the relative stiffness ratio RD,with different mass ratio MR,within which the acceleration and displacement of the optimal model of MSCSS reaches its optimum(minimum)value is considered as an optimum region.It serves as a useful tool in practical engineering design.The study demonstrates that the proposed MSCSS configuration can efficiently control the displacement and acceleration of high rise buildings.In addition,some analytical guidelines are provided for selecting the control parameters of the structure.

An Improved Control Vector Iteration Approach for Nonlinear Dynamic Optimization. II. Problems with Path Constraints

This paper considers dealing with path constraints in the framework of the improved control vector iteration （CVI） approach. Two available ways for enforcing equality path constraints are presented, which can be directly incorporated into the improved CVI approach. Inequality path constraints are much more difficult to deal with, even for small scale problems, because the time intervals where the inequality path constraints are active are unknown in advance. To overcome the challenge, the ll penalty function and a novel smoothing technique are in-troduced, leading to a new effective approach. Moreover, on the basis of the relevant theorems, a numerical algo-rithm is proposed for nonlinear dynamic optimization problems with inequality path constraints. Results obtained from the classic batch reaCtor operation problem are in agreement with the literature reoorts, and the comoutational efficiency is also high.

PARAMETER IDENTIFICATION METHOD OF NONLINEAR JOINTS

Joints are widely used in many kinds of engineering structures, which often leads to the structures to exhibit local nonlinearities, and moreover, they are difficult to model because the complexity of configuration and operating mode. Therefore, parameter identification technique is usually used to model the joints and estimate the model parameters. A novel parameter identification method of nonlinear joints inside a structure is introduced in this paper, by expressing the force transmitted by the joint as a function of its mechanical state and assuming that the other part of the structure is known. In general, the force transmitted by the joints inside a structure and their mechanical state are difficult to measure. To overcome this difficulty, the algorithm of stochastic optimal control is used to identify the force transmitted by the joints and their mechanical state. After that, parameters of the joints can be identified by least squares parameter estimation method. Numerical simulation examples are also given to validate the effectiveness of the proposed method.

The Regional Dynamical Model of the Atmospheric Ozonosphere

The TOMS zonal average total ozone data in the Northern Hemisphere are decomposed with the empirical orthogonal function (EOF) method. According to the features of the spatial characteristic vectors, the characteristic vectors that have been obtained with EOF method can be used as the ordered orthogonal radixes to unfold the phase space. After the corresponding time functions are embedded in phase space, the traces of the state vectors of the regional ozonosphere dynamical system are constructed, and can be used to describe the attractor integral information of the asymptotic state of the regional ozonosphere system and the dynamical features of the regional ozonosphere system, and then the embedded saturation dimension of the regional ozonosphere system attractor is successfully obtained. Based on these works mentioned above, by using the time function series we solve a problem contrary to the numerical solution and retrieve the control parameters of the state equations in which quadratic nonlinear terms are included, and then the dynamical models that can objectively reflect the temporal variation of the regional ozonosphere system are finally established.

Identification and Control of Typical Industrial Process

Many industrial processes such as heating furnaces have over damping dynamic characteristics. Based on an innovative impulse response model, a method of identification and control for the over damping plant is introduced in the paper. The number of parameters of the model is much less than conventional impulse response model. The model based on tuning procedure of numerical optimum PID controller parameters is presented. For an actual instance, a large scale airflow circulatory resistance furnace control system with cascades of time delays is developed. In the system, the optimum PID control is used in the inner loop. A nonlinear PI compensation control is applied in the outer loop. The coordinating control among each output is realized by a fuzzy control strategy. A process surveillance organization monitors running situation of system and tunes controller parameters.

STOCHASTIC OPTIMAL CONTROL FOR THE RESPONSE OF QUASI NON-INTEGRABLE HAMILTONIAN SYSTEMS

A strategy is proposed based on the stochastic averaging method for quasi non- integrable Hamiltonian systems and the stochastic dynamical programming principle.The pro- posed strategy can be used to design nonlinear stochastic optimal control to minimize the response of quasi non-integrable Hamiltonian systems subject to Gaussian white noise excitation.By using the stochastic averaging method for quasi non-integrable Hamiltonian systems the equations of motion of a controlled quasi non-integrable Hamiltonian system is reduced to a one-dimensional av- eraged It stochastic differential equation.By using the stochastic dynamical programming princi- ple the dynamical programming equation for minimizing the response of the system is formulated. The optimal control law is derived from the dynamical programming equation and the bounded control constraints.The response of optimally controlled systems is predicted through solving the FPK equation associated with It stochastic differential equation.An example is worked out in detail to illustrate the application of the control strategy proposed.

DISOPE distributed model predictive control of cascade systems with network communication

A novel distributed model predictive control scheme based on dynamic integrated system optimization and parameter estimation （DISOPE） was proposed for nonlinear cascade systems under network environment. Under the distributed control structure, online optimization of the cascade system was composed of several cascaded agents that can cooperate and exchange information via network communication. By iterating on modified distributed linear optimal control problems on the basis of estimating parameters at every iteration the correct optimal control action of the nonlinear model predictive control problem of the cascade system could be obtained, assuming that the algorithm was convergent. This approach avoids solving the complex nonlinear optimization problem and significantly reduces the computational burden. The simulation results of the fossil fuel power unit are illustrated to verify the effectiveness and practicability of the proposed algorithm.

SOME ISSUES OF TURBULENCE STATISTICS

The issue of dropping the random force f(i) and the arbitrariness of choosing the basic variable in the variational approach to turbulence closure problem, pointed out recently by the Russian scientists Bazdenkov and Kukharkin, are discussed. According to the mean-square estimation method, the random force f(i) should be dropped in the error expression of the LFP (Langevin-Fokker-Planck) model. However, f(i) is not neglected, its effect has been taken into account by the variational approach. In order to optimize the perturbation solution of the Liouville equation, the LFP model requires that the basic variable is as near to Gaussian as possible. Hence, the velocity, instead of the vorticity, should be chosen as the basic variable in the three-dimensional turbulence. Although the LFP model and the zero-order Gaussian term of PDF (probability density function) imply whiteness assumption (zero correlation time of f(i)), the higher-order non-Gaussian terms of PDF correspond to the nonwhiteness of turbulence dynamics, the variational approach does calculate the nonwhiteness effect properly.

Design of flying vehicle control system by signal to noise ratio

Presents the new concept of ″Desired to be small″ based on the basic function of vehicle flight control system for an optimal design of flying vehicle control system, and the definition of S/N ratio and calculation formula for ″Desired to be small″ dynamic characteristics, and the S/N ratio method established for design of velicle flight control systems, by which, an orthogrnal table is used to arrange test schemes, and error facters are used to simulate various interferences, and the use of S/N ratio as a design criterion to synthesise the design of dynamic and static characteristics for definition of an optimal scheme, the application of S/N ratio method to the design of a type of vehicle control system and the single run success abtained in design of control system, technical evaluation test and design finalization flight test.

THE OPTIMAL CONTROL VARIATIONAL PRINCIPLE AND FINITEELEMENTS ANALYSIS FOR VISCOPLASTIC DYNAMICS

This paper presents the optimal control variational principle for Perzyna modelwhich is one of the main constitutive relation of viscoplasticity in dynamics. And itcould also be transformed to solve the parametric quadratic programming problem.The FEM form of this problem and its implementation have also been discussed in thepaper.

Decoupling control and zero dynamics stabilization for shunt hybrid active power filter

An inverse system method based optimal control strategy was proposed for the shunt hybrid active power filter （SHAPF） to enhance its harmonic elimination performance. Based on the inverse system method, the d-axis and q-axis current dynamics of the SHAPF system were decoupled and linearized into two pseudolinear subsystems. Then, an optimal feedback controUer was designed for the pseudolinear system, and the stability condition of the resulting zero dynamics was presented. Under the control strategy, the current dynamics can asymptotically converge to their reference states and the zero dynamics can be bounded. Simulation results show that the proposed control strategy is robust against load variations and system parameter mismatches, its steady-state performance is better than that of the traditional linear control strategy.

An Iterative Method for Optimal Feedback Control and Generalized HJB Equation

Abstract--In this paper, a new iterative method is proposed to solve the generalized Hamilton-Jacobi-Bellman （GHJB） equation through successively approximate it. Firstly, the GHJB equation is converted to an algebraic equation with the vector norm, which is essentially a set of simultaneous nonlinear equations in the case of dynamic systems. Then, the proposed algorithm solves GHJB equation numerically for points near the origin by considering the linearization of the non-linear equations under a good initial control guess. Finally, the procedure is proved to converge to the optimal stabilizing solution with respect to the iteration variable. In addition, it is shown that the result is a closed-loop control based on this iterative approach. Illustrative examples show that the update control laws will converge to optimal control for nonlinear systems. Index Terms--Generalized Hamilton-Jacobi-Bellman （HJB） equation, iterative method, nonlinear dynamic system, optimal control.

基于多目标狼群算法的机场行李导入系统仿真优化研究

针对民航机场行李导入系统运行过程中旅客行李注入等待时间长、系统能耗高等问题,综合考虑虚拟视窗控制方式、收集带式输送机运行速度、虚拟视窗长度及同时开放值机柜台数量等关键控制参数对机场行李导入系统运行效率的影响,提出一种求解该问题的仿真优化框架。通过分析机场行李导入系统实际运行工况,建立参数化仿真优化模型。以最小化旅客行李注入平均等待时间和系统能耗为优化目标,结合系统设计和运行过程中的实际约束条件,建立该问题的数学模型,并设计了一种多目标自适应并行狼群算法进行求解。该算法针对所提问题特性及经典狼群算法易陷入局部最优和收敛速度慢等不足,提出一种混合整实数单链编码方式,融合反向学习策略生成初始种群,引入自适应游走概率机制和智能行为并行机制,采用局部和全局自适应邻域搜索及启发式保优策略实现狼群算法智能行为搜索,使用Pareto非支配排序进行寻优迭代并获得最优解集。以国内某大型国际航空枢纽机场行李导入系统为例设计不同规模多种算法对比实验,验证了所提方法的有效性和优越性。