Comparison of a Filter- and a Model Predictive Control Based Motion Cueing Algorithm

Motion Cueing Algorithms (MCA) include control strategies to take into account the motion-based driving simulator's restrictions concerning workspace limits and dynamic boundaries. A typical 6-DoF simulator consists of a motion system which exhibits three translational and rotational degrees of freedom. Its actuators are capable of realizing accelerations, velocities and positions in a limited range. Based on these facts MCAs aim to generating realistic simulations of the driving motion (such as a driving manoeuvre) in order to immerse persons in virtual environments provided by the simulator. Filter-based, classical MCAs belong to the most applied algorithms and mainly consist of linear transfer functions. Whereas, Model Predictive Control (MPC) algorithms rest upon a reduced model of the technical system's dynamics and, optionally, a model of the human motion perception system. An optimization problem subject to the restrictions of the motion system predicts the control variables over a time horizon. This paper addresses the strengths and weaknesses of the two stated approaches with focus on Motion Cueing errors. These errors describe discrepancies between the motion that is to be simulated (e.g. a driving manoeuvre) and the motion that is eventually provided by the combination of the MCA and the motion simulator. On basis of the results, it gives an outlook why optimization based algorithms have a higher potential to improve driving simulation. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Non-Linear Procurement Model with Quantity Discounts

This paper presents a procurement model for a multinational oil company with affiliate plants located worldwide. The proposed model uses a quantity discount relationship to reduce the total procurement cost. We use a non-linear programming method to solve the model and make comparisons with the current approach used by the oil company. The proposed approach has several distinct advantages: assured minimum cost, ease of data management, flexibility in design, and accuracy in results.     

A Prediction Model for State Observation and Model Predictive Control of Biped Robots

Biped walking robots present a class of mechanical systems with many different challenges such as nonlinear multi-body dynamics, a large number of degrees of freedom and unilateral contacts. The latter impose constraints for physically feasible motions and in stabilization methods as the robot can only interact due to pressure forces with the environment. This limitation can cause the system to fall under unknown disturbances such as pushing or uneven terrain. In order to face such problems, an accurate and fast model of the robot to observe the current state and predict the state evolution into the future has to be used. This work presents a nonlinear prediction model with two passive degrees of freedom (dof), point masses and compliant unilateral contacts. We show that the model is applicable for real-time model predictive optimization of the robot's motion. Experiments on the biped robot LOLA [1] underline the effectiveness of the proposed model to increase the system's long term stability under large unknown disturbances. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

LMI Approach to Robust Model Predictive Control

This paper introduces a new approach to robust model predictive control (MPC) based on conservative approximations to semi-infinite optimization using linear matrix inequalities (LMIs). The method applies to problems with convex quadratic costs, linear and convex quadratic constraints, and linear predictive models with bounded uncertainty. If the MPC optimization problem is feasible at the initial control step (the first application of the MPC optimization), it is shown that the MPC optimization problems will be feasible at all future time steps and that the controlled system will be closed-loop stable. The method is illustrated with a solenoid control example. The authors thank the anonymous reviewers for suggestions that improved the presentation of this work. The work was supported in part by the EPRI/DoD Complex Interactive Networks/Systems Initiative under Contract EPRI-W08333-05 and by the US Army Research Office Contract DAAD19-01-1-0485.     

Real-time Model Predictive Control of a Pendulum

In this work, a model predictive approach is applied on a mechanical system with a view on a real-time capable implementation. The mechanical system is represented by a pendulum, which consists of a sphere at the end of a long, thin rod. The rod is mounted on gimbals on a cross table, which can be moved by two DC motors. The control objective is trajectory tracking of the sphere, which can be realized by the control of these motors. In this work, linear model predictive control techniques are designed for the pendulum and are simulatively compared with regard to an accurate trajectory tracking and a real-time capable algorithm. A linear time-invariant approach is implemented on the experiment. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Note on an Input Control Model of a Predictive Regression Interval

A well-known problem of prediction in linear regression models is to find a confidence interval for the random value of the dependent variable when the values of the independent variables are given. Such a situation may arise in economic quality control models when the independent variables are costly inputs and the dependent variable is some measure of quality or production. In such a circumstance, an important control objective may be to find values for the inputs that will maximize the lower limit of the prediction confidence interval for a fixed budget, or alternatively, to minimize the cost of the inputs for a fixed lower limit of the confidence interval. In this paper, we shall show that global optima can be found using known algorithms. The special case of simple linear regression is discussed and an illustrative example is provided.     

Supply Chain Optimization via Distributed Model Predictive Control

Supply chains networks describe the flow of material, energy and information from their sources to end costumers. Typically, such a network consists of several stages such as suppliers, manufacturers and retailers, which contribute to the completion of a product. Here, we restrict ourselves to one arc from supplier to costumer. Instead of known strategies such as postponement, we apply a model predictive control scheme to deal with the optimal steering problem of the considered arc in a distributed way. To this end, we assign one controller to each stage along the considered arc. Since the stages may represent different companies, local cost criteria are imposed, which are optimized subject to local and global constraints while communicating with neighbors. Additionally, we discuss the applicability of such an approach regarding information requirements and respective policies of companies. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Application of Interior-Point Methods to Model Predictive Control

We present a structured interior-point method for the efficient solution of the optimal control problem in model predictive control. The cost of this approach is linear in the horizon length, compared with cubic growth for a naive approach. We use a discrete-time Riccati recursion to solve the linear equations efficiently at each iteration of the interior-point method, and show that this recursion is numerically stable. We demonstrate the effectiveness of the approach by applying it to three process control problems.     

An Algorithm for Constrained Non-Linear Least-Squares

An algorithm is presented for finding a constrained stationarypoint of a non-linear least squares problem when the constraintsare upper bounds, lower bounds, and a set x₁ x₂ ... x_k. Themethod is based on the unconstrained Levenberg-Marquardt algorithm,reducing at each iteration to an unconstrained least squaresproblem. Also incorporated is a model-prediction of the desirabilityof leaving an active constraint at each interation, so thatit is not necessary to locate an approximate local minimum ina manifold before investigating whether to alter the manifold.A new method of control for the damping parameter is presented,and three numerical examples given covering the inversion ofa Fredholm integral equation and spline and exponential datafitting.     

用奇异值分解求解的PI型有约束广义预测控制算法

本文推得了一种比例积分型广义预测控制算法，在算法中加入了对系统的输入和输出信号的约束以加强算法应用能力，在控制值的优化示解中使用了矩阵奇异值分解以增加算法的精度和数值稳定性。     

Nonlinear Model Predictive Control via Feasibility-Perturbed Sequential Quadratic Programming

Model predictive control requires the solution of a sequence of continuous optimization problems that are nonlinear if a nonlinear model is used for the plant. We describe briefly a trust-region feasibility-perturbed sequential quadratic programming algorithm (developed in a companion report), then discuss its adaptation to the problems arising in nonlinear model predictive control. Computational experience with several representative sample problems is described, demonstrating the effectiveness of the proposed approach.     

Output Feedback Model Predictive Tracking Control Using a Slope Bounded Nonlinear Model

In this paper, an output feedback model predictive tracking control method is proposed for constrained nonlinear systems, which are described by a slope bounded model. In order to solve the problem, we consider the finite horizon cost function for an off-set free tracking control of the system. For reference tracking, the steady state is calculated by solving by quadratic programming and a nonlinear estimator is designed to predict the state from output measurements. The optimized control input sequences are obtained by minimizing the upper bound of the cost function with a terminal weighting matrix. The cost monotonicity guarantees that tracking and estimation errors go to zero. The proposed control law can easily be obtained by solving a convex optimization problem satisfying several linear matrix inequalities. In order to show the effectiveness of the proposed method, a novel slope bounded nonlinear model-based predictive control method is applied to the set-point tracking problem of solid oxide fuel cell systems. Simulations are also given to demonstrate the tracking performance of the proposed method.     

一类稳定的连续时间广义预测控制

引入无穷时域的1-范数性能指标,通过施加新的终端等式约束确定出无穷时域性能指标的一个上界,将不可解的优化问题转化为可解的优化问题,从而提出保证连续时间广义预测控制闭环稳定性的准无穷时域方法.仿真例子证明了算法的有效性.     

Elements of Applied Stochastic Processes

Journal of the Operational Research Society -     

A Non-Linear Filter

Abstract

Using a measure change related to Bayes' rule recursive estimates are obtained for an approximate conditional density where a state process has deterministic dynamics and it is observed in additive Gaussian noise.     

经验正交函数与遗传算法结合的副热带高压位势场非线性模型反演

针对副热带高压的动力预报模型难以准确构建的困难,基于T106数值预报产品500 hPa位势高度场序列,用经验正交函数（EOF）分解方法对位势场序列进行了时、空分解,引入了动力系统重构思想,以EOF分解的空间模态的时间系数序列作为动力模型变量,用遗传算法全局搜索和并行计算优势,进行了动力模型参数的优化反演,建立了客观合理的非线性动力模型．通过对动力模型积分和EOF的时、空重构,实现了副热带高压的中、长期预报．试验结果表明,本文反演的动力模型的副热带高压预报效果优于常规的数值预报产品,该研究工作为副热带高压等复杂天气系统和要素场预报提供了新的方法思路和技术途径．     

Model Predictive Control for Heating Ventilating and Air Conditioning Systems

In heating ventilating and air conditioning (hvac) systems, model predictive control (mpc) is rarely used up to now. However, the following properties of hvac systems make mpc a well suited control methodology: the plant is a multiple input, multiple output system and its inputs are constrained – both in their value and in their rate of change. Moreover, several disturbances acting on the plant like varying outdoor air temperature or outdoor humidity can be measured. Furthermore, time constants are relatively large which makes it easy to perform the required optimization of the mpc strategy in time. This contribution presents the application of mpc to a real world hvac system. The considered hvac system consists of standard industrial components. The core components of the system are water-to-air heat exchangers, both for heating and for cooling purposes as well as a steam humidifier. Hence, air temperature and air humidity can be varied with the help of the investigated hvac system. The derivation of the plant model based on thermodynamic relations is presented as well as the application of the mpc strategy to the real world system. The plant contains some nonlinear elements which have to be dealt with when applying the mpc strategy. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

一元非线性系统的BP算法研究

详细研究了一种一元非线性系统的BP算法,提出并证明了该算法的收敛性定理,给出了该算法的应用实例.计算机仿真结果表明:对于随机给定的初始点,该算法都能稳定收敛到它的一个实根,而且计算精度可控,因此,该算法是有效的.与传统的计算方法相比,本文算法不仅具有收敛速度快,而且计算精度可控以及初始点随机给定的集中优点.