STOCHASTIC OPTIMAL CONTROL OF STRONGLY NONLINEAR SYSTEMS UNDER WIDE-BAND RANDOM EXCITATION WITH ACTUATOR SATURATION

A bounded optimal control strategy for strongly non-linear systems under non-white wide-band random excitation with actuator saturation is proposed. First, the stochastic averaging method is introduced for controlled strongly non-linear systems under wide-band random excitation using generalized harmonic functions. Then, the dynamical programming equation for the saturated control problem is formulated from the partially averaged Itō equation based on the dynamical programming principle. The optimal control consisting of the unbounded optimal control and the bounded bang-bang control is determined by solving the dynamical programming equation. Finally, the response of the optimally controlled system is predicted by solving the reduced Fokker-Planck-Kolmogorov （FPK） equation associated with the completed averaged Itō equation. An example is given to illustrate the proposed control strategy. Numerical results show that the proposed control strategy has high control effectiveness and efficiency and the chattering is reduced significantly comparing with the bang-bang control strategy.

Optimal control strategies for stochastically excited quasi partially integrable Hamiltonian systems

In this paper two different control strategies designed to alleviate the response of quasi partially integrable Hamiltonian systems subjected to stochastic excitation are proposed. First, by using the stochastic averaging method for quasi partially integrable Hamiltonian systems, an n-DOF controlled quasi partially integrable Hamiltonian system with stochastic excitation is converted into a set of partially averaged It^↑o stochastic differential equations. Then, the dynamical programming equation associated with the partially averaged It^↑o equations is formulated by applying the stochastic dynamical programming principle. In the first control strategy, the optimal control law is derived from the dynamical programming equation and the control constraints without solving the dynamical programming equation. In the second control strategy, the optimal control law is obtained by solving the dynamical programming equation. Finally, both the responses of controlled and uncontrolled systems are predicted through solving the Fokker-Plank-Kolmogorov equation associated with fully averaged It^↑o equations. An example is worked out to illustrate the application and effectiveness of the two proposed control strategies.

Topology Optimization for Harmonic Excitation Structures with Minimum Length Scale Control Using the Discrete Variable Method

Continuumtopology optimization considering the vibration response is of great value in the engineering structure design.The aimof this studyis toaddress the topological designoptimizationof harmonic excitationstructureswith minimumlength scale control to facilitate structuralmanufacturing.Astructural topology design based on discrete variables is proposed to avoid localized vibration modes,gray regions and fuzzy boundaries in harmonic excitation topology optimization.The topological design model and sensitivity formulation are derived.The requirement of minimum size control is transformed into a geometric constraint using the discrete variables.Consequently,thin bars,small holes,and sharp corners,which are not conducive to the manufacturing process,can be eliminated from the design results.The present optimization design can efficiently achieve a 0–1 topology configuration with a significantly improved resonance frequency in a wide range of excitation frequencies.Additionally,the optimal solution for harmonic excitation topology optimization is not necessarily symmetric when the load and support are symmetric,which is a distinct difference fromthe static optimization design.Hence,one-half of the design domain cannot be selected according to the load and support symmetry.Numerical examples are presented to demonstrate the effectiveness of the discrete variable design for excitation frequency topology optimization,and to improve the design manufacturability.

ASUBOPTIMAL DESIGN OF H∞DECENTRALIZED STATE FEEDBACK CONTROL FOR INTERCONNEC TED SYSTEMS

In the paper, the problem of H∞ decentralized state feedback control for largescale systems is described. An algorithm is proposed which uses the method of a feasible direction matrix. The algorithm only requires the solution of an algebraic Riccati equation (ARE) and makes the H∞norm of the closedloop transfer function matrix from disturbance inputs to controlled outputs less than a given constant which ensure the stability of the overall controlled system at each iteration. The given example shows that the convergence of the algorithm is satisfactory.

STOCHASTIC OPTIMAL VIBRATION CONTROL OF PARTIALLY OBSERVABLE NONLINEAR QUASI HAMILTONIAN SYSTEMS WITH ACTUATOR SATURATION

An optimal vibration control strategy for partially observable nonlinear quasi Hamiltonian systems with actuator saturation is proposed. First,a controlled partially observable non-linear system is converted into a completely observable linear control system of finite dimension based on the theorem due to Charalambous and Elliott. Then the partially averaged It stochastic differential equations and dynamical programming equation associated with the completely observable linear system are derived by using the stochastic averaging method and stochastic dynamical programming principle,respectively. The optimal control law is obtained from solving the final dynamical programming equation. The results show that the proposed control strategy has high control effectiveness and control effciency.

A New Design of Robust H∞Load-Frequency Controller for Optimal Coordination of Energy Generation in Power System Stability Using LMI Approach

This paper presents the problem of robust H∞?load frequency controller design and robust H￥ based approach called advanced frequency control (AFC). The objective is to split the task of balancing frequency deviations introduced by renewable energy source (RES) and load variations according to the capabilities of storage and generators. The problem we address is to design an output feedback controller such that, all admissible parameter uncertainties, the closed-loop system satisfies not only the prespecified H∞? norm constraint on the transfer function from the disturbance input to the system output. The conventional generators mainly balance the low-frequency components and load variations while the energy storage devices compensate the high- frequency components. In order to enable the controller design for storage devices located at buses with no generators, a model for the frequency at such a bus is developed. Then, AEC controllers are synthesized through decentralized static output feedback to reduce the complexity. The conditions for the existence of desired controllers are derived in terms of a linear matrix inequality (LMI) algorithm is improved. From the simulation results, the system responses with the proposed controller are the best transient responses.

Mathematical Analysis of Nipah Virus Infections Using Optimal Control Theory

The optimal use of intervention strategies to mitigate the spread of Nipah Virus (NiV) using optimal control technique is studied in this paper. First of all we formulate a dynamic model of NiV infections with variable size population and two control strategies where creating awareness and treatment are considered as controls. We intend to find the optimal combination of these two control strategies that will minimize the cost of the two control measures and as a result the number of infectious individuals will decrease. We establish the existence for the optimal controls and Pontryagin’s maximum principle is used to characterize the optimal controls. The numerical simulation suggests that optimal control technique is much more effective to minimize the infected individuals and the corresponding cost of the two controls. It is also monitored that in the case of high contact rate, controls have to work for longer period of time to get the desired result. Numerical simulation reveals that the spread of Nipah virus can be controlled effectively if we apply control strategy at early stage.

Science Letters:A minimax optimal control strategy for uncertain quasi-Hamiltonian systems

A minimax optimal control strategy for quasi-Hamiltonian systems with bounded parametric and/or external disturbances is proposed based on the stochastic averaging method and stochastic differential game. To conduct the system energy control, the partially averaged Ito stochastic differential equations for the energy processes are first derived by using the stochastic averaging method for quasi-Hamiltonian systems. Combining the above equations with an appropriate performance index, the proposed strategy is searching for an optimal worst-case controller by solving a stochastic differential game problem. The worst-case disturbances and the optimal controls are obtained by solving a Hamilton-Jacobi-Isaacs （HJI） equation. Numerical results for a controlled and stochastically excited DulTlng oscillator with uncertain disturbances exhibit the efficacy of the proposed control strategy.

OPTIMAL CONTROL OF HYPERBOLIC H-HEMIVARIATIONAL INEQUALITIES WITH STATE CONSTRAINTS

The optimal control problems of hyperbolic H-hemivariational inequalities with the state constraints and nonnomotone multivalued mapping term are considered.The optimal solutions are obtained.In addition,their approximating problems are also studied.

Robust H_∞ control for aseismic structures with uncertainties in model parameters

This paper presents a robust H∞ output feedback control approach for structural systems with uncertainties in model parameters by using available acceleration measurements and proposes conditions for the existence of such a robust output feedback controller. The uncertainties of structural stiffness, damping and mass parameters are assumed to be norm-bounded. The proposed control approach is formulated within the framework of linear matrix inequalities, for which existing convex optimization techniques, such as the LM1 toolbox in MATLAB, can be used effectively and conveniently. To illustrate the effectiveness of the proposed robust H∞ strategy, a six-story building was subjected both to the 1940 E1 Centro earthquake record and to a suddenly applied Kanai-Tajimi filtered white noise random excitation. The results show that the proposed robust H∞ controller provides satisfactory results with or without variation of the structural stiffness, damping and mass parameters.

Parameters Optimization and Performance Evaluation of the Tuned Inerter Damper for the Seismic Protection of Adjacent Building Structures

In order to improve the seismic performance of adjacent buildings,two types of tuned inerter damper(TID)damping systems for adjacent buildings are proposed,which are composed of springs,inerter devices and dampers in serial or in parallel.The dynamic equations of TID adjacent building damping systems were derived,and the H2 norm criterion was used to optimize and adjust them,so that the system had the optimum damping performance under white noise random excitation.Taking TID frequency ratio and damping ratio as optimization parameters,the optimum analytical solutions of the displacement frequency response of the undamped structure under white noise excitation were obtained.The results showed that compared with the classic TMD,TID could obtain a better damping effect in the adjacent buildings.Comparing the TIDs composed of serial or parallel,it was found that the parallel TIDs had more significant advantages in controlling the peak displacement frequency response,while the H2 norm of the displacement frequency response of the damping system under the coupling of serial TID was smaller.Taking the adjacent building composed of two ten-story frame structures as an example,the displacement and energy collection time history analysis of the adjacent building coupled with the optimum design parameter TIDs were carried out.It was found that TID had a better damping effect in the full-time range compared with the classic TMD.This paper also studied the potential power of TID in adjacent buildings,which can be converted into available power resources during earthquakes.

Designing mixed <i>H</i>₂/<i>H</i>_&infin;structure specified controllers using Particle Swarm Optimization (PSO) algorithm

This paper proposes an efficient method for designing accurate structure-specified mixed H2/H∞ optimal controllers for systems with uncertainties and disturbance using particle swarm (PSO) algorithm. It is designed to find a suitable controller that minimizes the performance index of error signal subject to an unequal constraint on the norm of the closed-loop system. Although the mixed H2/H∞ for the output feedback approach control is considered as a robust and optimal control technique, the design process normally comes up with a complex and non-convex optimization problem, which is difficult to solve by the conventional optimization methods. The PSO can efficiently solve design problems of multi-input-multi-output (MIMO) optimal control systems, which is very suitable for practical engineering designs. It is used to search for parameters of a structure-specified controller, which satisfies mixed performance index. The simulation and experimental results show high feasibility, robustness and practical value compared with the conventional proportional-integral-derivative (PID) and proportional-Integral (PI) controller, and the proposed algorithm is also more efficient compared with the genetic algorithm (GA).

基于反馈线性化方法的励磁系统非线性H_∞控制研究

本文提出了一种基于微分几何反馈线性化理论的非线性Ｈ∞控制设计方法，并对这种方法的干扰抑制性能给予了讨论。同时，依据这种方法设计了励磁系统的非线性Ｈ∞控制器。

汽车四轮转向系统的H_2/H_∞混合控制

为使汽车四轮转向系统具有良好的鲁棒性和干扰抑制性能 ,针对外界干扰 ,对汽车四轮转向系统模型进行了分析 ,并将其转化为H2 /H∞ 控制问题 ,运用Matlab的LMI控制工具箱设计了H2 /H∞ 混合最优控制器。仿真结果表明 ,设计的最优控制器具有良好控制效果。

基于H_∞控制与最优跟踪控制相结合的三相PWM整流器控制策略

针对三相PWM整流器的特点,提出了一种基于H∞控制与最优跟踪控制相结合的混合控制策略。电流内环,采用了最优控制策略,无需解耦;电压外环,采用H∞控制策略。基于PWM整流器的数学模型,建立了满足H∞控制标准型的状态方程,并选择合适的权函数。通过求解Riccati不等式,得到H∞控制器。由于混合控制器待定参数较多,计算所得控制器参数难以保证系统运行在最优状态中。本文基于PSO算法,结合模拟退火以及混沌搜索的优点,设计了一种改进的PSO算法,对所设计控制器进行参数整定和优化,进一步提高了PWM整流器的控制性能,具有更好的动态性能和抗干扰性。仿真和实验证明了本文所提出方法的可行性和有效性。

基于H_∞优化抗扰控制的柔性机械臂振动抑制

针对受未知扰动和建模误差影响的压电柔性机械臂系统,提出并开发了一种H_∞优化的抗扰控制算法并将其应用于压电柔性机械臂的振动抑制。运用有限元法建立了压电柔性机械臂的机电耦合动力学模型及状态空间模型。使用由阶跃函数构成的扰动模型,构造了比例积分(PI:proportional integral)扰动观测器。基于H_∞优化方法,并应用S/T混合灵敏度和区域极点配置分别计算了扰动观测器和抗扰控制器的反馈增益,保证了观测器与控制器的动态性能和鲁棒性。通过压电柔性机械臂振动抑制仿真,验证了H_∞优化抗扰控制算法抑制未知扰动所致振动的有效性和对系统模型误差的鲁棒性,并与使用通用比例积分(GPI:generalized proportional integral)观测器的抗扰控制算法进行了比较。

基于LMI的4WS-4WD车辆H_∞鲁棒控制器设计

基于线性矩阵不等式(LMI)设计了H_∞鲁棒最优控制器以及H_∞鲁棒非脆弱控制器.通过两自由度(2-DOF)车辆模型推导并建立H_∞鲁棒控制系统,此外,定义系统摄动并对摄动矩阵进行分解,进而利用线性矩阵不等式求解控制器.仿真结果表明,H_∞鲁棒最优控制器对侧偏角及横摆角速度的控制效果显著优于LQR控制器.同时,在控制器存在摄动及对侧偏角及横摆角速度进行控制的情况下,H_∞鲁棒非脆弱控制器的鲁棒性能显著优于普通鲁棒H_∞控制器.因此,H_∞鲁棒最优控制器解决了普通鲁棒H_∞控制器控制性能差的问题,H_∞鲁棒非脆弱控制器则解决了普通H_∞鲁棒控制器对参数变化敏感的问题.

基于LMI的结构振动多目标鲁棒H_2/H_∞控制

研究了考虑建筑结构动力特性具有不确定性的多目标鲁棒H2/H∞控制问题。在设计控制器的过程中,将模型参数(包括质量、刚度和阻尼)的不确定性引入到状态方程的摄动矩阵之中,使得闭环系统对所有允许的不确定性同时满足H∞干扰抑制和最优H2性能。基于线性矩阵不等式优化技术,推导得到了线性矩阵不等式组来求解相应的多目标优化问题,应用MATLAB的线性矩阵不等式工具箱设计了输出反馈控制器。最后对一3层结构进行了振动控制仿真分析,结果表明了所提方法的有效性和优越性。

多机电力系统H_∞分散鲁棒励磁控制器的优化设计

基于H∞控制理论,提出了在多机电力系统励磁控制器设计中求取反馈增益的优化方法。该方法设定外部干扰矩阵,基于全状态的分散,将系统干扰项考虑到反馈增益矩阵F中,用迭代方法求F阵以使闭环系统最优。理论分析证明,采用该方法设计的分散鲁棒励磁控制器,能保证闭环系统的稳定性并使其具有良好的动态性能。仿真实验结果表明,该方法可有效地优选出分散励磁控制器的参数,使控制系统具有较强的鲁棒性,很好地实现了多机电力系统的分散协调控制。

非线性H_∞励磁控制器的设计

对单机无穷大系统进行非线性H∞励磁控制器的设计。应用直接反馈线性化方法,直接指定虚拟控制量,简化了计算;采用△d、△w、△Pe和△Vt的积分量为状态变量,以同时改善电力系统的稳定性和调压精度;应用H∞控制理论和MATLAB的m -综合工具箱完成权函数的优化,直接解决鲁棒控制设计;对控制律进行实用化处理,并利用Powersys工具箱进行了仿真分析,收到了较好的效果。