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Some Necessary and Sufficient Conditions for Correctness of Linear Machine in Presence of Numerical Errors

IFAC-PapersOnLine 2020年第2期53卷 11368-11373页

作者： Aditi Sharma Mani Bhushan Department of Chemical Engineering Indian Institute of Technology Bombay India

Linear machine (LM) has been recently proposed (Airan et al., 2017) for solving the point location problem which arises in explicit model predictive control (e-MPC). LM associates a linear discriminant function with each critical region identified in the offline phase in e-MPC. The solution to the online point location problem in the LM approach then simply corresponds to the region whose discriminant function attains the largest value amongst all the discriminant functions. LM involves two steps: (i) identification of neighbouring critical regions, and (ii) finding the discriminant functions by writing constraints involving discriminant functions of neighbouring pairs of regions. Both these steps involve solving linear programming (LP) problems. Similar to any other optimization problem, the constraints of the LP are satisfied with some tolerances. Even though theoretically sound, the resulting LM may not accurately identify the critical region due to the numerical errors arising from these tolerances. In the current work, we identify some conditions which can be used as an aid by the user to judge the accuracy of LM results. In particular, we give a necessary condition for step (i) whose violation will yield incorrect misclassification for some point location problems. We also propose a sufficient condition whose satisfaction guarantees the accuracy of linear machine solution despite numerical errors which may have crept in during step (ii) of the LM design. This condition needs to be evaluated for each specified point during the point location phase. We illustrate these ideas on the well known quadruple tank system.

关键词： point location explicit model predictive control multi-parametric programming

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explicit spline-based continuous-time MPC: a study on design and performance

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IFAC-PapersOnLine 2020年第2期53卷 7013-7019页

作者： Boris Rohaľ-Ilkiv Martin Gulan Peter Minarčík Institute of Automation Measurement and Applied Informatics Faculty of Mechanical engineering Slovak University of Technology in Bratislava Námestie slobody 17 812 31 Bratislava Slovakia

This paper presents a continuous-time model predictive control scheme based on B-spline functions used for signals and model approximation. The proposed controller offers two interesting advantages. First, it formulates the control signal as a continuous polynomial spline function, the nature of which is determined by its control polygon that is subject of optimization. Second, all continuous constraints assumed over prediction horizon are consistently transformed into constraints imposed on a finite number of elements of this control polygon. Using parametric quadratic programming we further show how to obtain an explicit representation of the proposed controller, which is known for its efficient online implementation. The featured simulation study demonstrates that by a suitable choice of number and position of knots of the spline function over the prediction horizon it is possible to substantially reduce the number of critical regions of the explicit controller while preserving control performance, and to mitigate the direct correlation between number of regions and chosen length of prediction horizon.

关键词： explicit model predictive control parametric programming linear systems B-spline functions continuous-time control efficient implementation

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Low-complexity stabilizing PWA controllers for linear systems with parametric uncertainties

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IFAC-PapersOnLine 2020年第2期53卷 7286-7291页

作者： Liang Lu Michal Kvasnica Ningbo Research Institute Zhejiang University Ningbo China Department of Information Engineering and Process Control Slovak University of Technology in Bratislava Slovakia

explicit MPC often results in a large number of irregular partitions in the feasible region as the dimension of the system increases and the storage requirement for the control and region parameters often limit its applications. In this paper, we consider a class of discrete-time linear systems with polytopic parametric uncertainties and provide a robust control Lyapunov based synthesis method to obtain robust low-complexity PWA controllers on regular partitionings. By implementing a refinement procedure, we can fit the PWA feedback control law in each regular partitioning based on feasibility of linear programming problems, which preserves stability, constraint satisfaction, and certain performance requirement. Numerical examples will demonstrate the effectiveness of the approach.

关键词： explicit model predictive control control Lyapunov function Piecewise affine control Parametric uncertainties Linear programming

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An explicit MPC Based on Galerkin Method for AGC Considering Volatile Generations

An Explicit MPC Based on Galerkin Method for AGC Considering...

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IEEE-Power-and-Energy-Society General Meeting (PESGM)

作者： Qiu, Yiwei Lin, Jin Liu, Feng Song, Yonghua Tsinghua Univ Dept Elect Engn State Key Lab Control & Simulat Power Syst & Gene Beijing 100084 Peoples R China Univ Macau Dept Elect & Comp Engn Macau 999078 Peoples R China

ISBN: (纸本)9781728119816

Imbalance of generation and load caused by volatile generations poses challenges on frequency regulation. AGC is required to respond to the generation fluctuations without violating operational and security constraints. While explicit model predictive control (EMPC) provides an approach, the partition number of the piecewise affine control laws grows exponentially with the number of constraints and prediction/control horizons, which hinders its application in large systems. In this paper, we propose an EMPC approach for AGC by approximating the control laws using Legendre polynomial series expansions, thus entirely eliminating the partition issue. Galerkin method is applied to the KKT conditions of EMPC's multiparametric quadratic programming (mp-QP) problem to compute the approximations. Case study in New England 39-bus system verifies the performance and efficiency of the proposed controller.

关键词： Automatic generation control explicit model predictive control Galerkin method Legendre polynomials optimal control spectral method

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Verification of advanced controllers for safety-critical systems

Verification of advanced controllers for safety-critical sys...

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作者： Siaulys, Kestutis University of Cambridge

学位级别：博士

In order to design and deploy a feedback controller in a real application, one must de- termine suitable specifications that the design must meet ("validate"), and then ensure that the chosen specifications have been met ("verify"). In this thesis, we investigate a verification paradigm based on formal methods, such as the Satisfiability Modulo Theories (SMT) and quantifier elimination (Weispfenning's virtual term substitution and quantifier elimination by cylindrical algebraic decomposition) algo- rithms. Any control design requirement (such as satisfactory performance, robustness to uncertainties, stability, etc.) that can be expressed in a first order logic formula can be (in principle) verified by using one of these methods. Consequently, in principle, this allows us to consider problems like general non-convex optimisation, exact computation of structured singular value, and synthesis of non-convex feasible parameter sets. In practice, the generality of algorithms like quantifier elimination by cylindrical algebraic decomposition come with a downside of high running time when applied to more complex systems with more parameters. This, in some cases, limits the complexity of the system that we could consider. Therefore, we focused our attention on control problems such as obtaining an explicit MPC law for a linear time invariant system with a quadratic objective and polytopic constraints, or computation of the structured singular value for a system under parametric (and not norm- bounded) uncertainty. Such problems can be expressed as quantifier elimination problems with a particular quantification structure that allows us to take advantage of a specialised quantifier elimination algorithm - the quantifier elimination by Weispfenning's virtual term substitution procedure that has much lower worst-case running time on these types of prob- lems than quantifier elimination by cylindrical algebraic decomposition algorithm. Despite these constraints, we were able to

关键词： model predictive control (MPC) Formal Methods Quantifier Elimination Cylindrical Algebraic Decomposition Weispfenning's virtual term substitution Satisfiability Modulo Theories (SMT) Robust Flight control Why3 MetiTarski Exclusion Regions Structured Singular Value explicit model predictive control Linear Temporal Logic RECONFIGURE Simulink

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explicit model predictive control of Networked control Systems with Time-Delay

Explicit Model Predictive Control of Networked Control Syste...

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23rd Chinese control and Decision Conference

作者： Zhang Ju Zhang Haihua Zhejiang Univ Technol Coll Informat Engn Hangzhou 310032 Zhejiang Peoples R China

ISBN: (纸本)9781424487363

In order to deal with random communication time delay in Networked control Systems(NCS), an explicit model predictive control (eMPC) method is presented in this paper. The algorithm is based on multi-parametric quadratic programming to get a state feedback control law which is explicit to the states. And based on this control law, the piecewise affine model of the closed-loop model predictive control system is established. We show that the control law is piecewise linear and continuous for the finite horizon problem. Thus, the on-line control computation reduces to the simple evaluation of a piecewise affine model. Since the algorithm does not require repeated online optimization, it improves the on-line calculation speed of the controller, making the system better in real-time. The algorithm deals with the random communication time delay well. Simulation results show the effectiveness of the proposed method.

关键词： networked control system explicit model predictive control multi-parametric quadratic programming piecewise affine model

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Constrained linear parameter-varying control using approximate multiparametric programming

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OPTIMAL control APPLICATIONS & METHODS 2018年第5期39卷 1670-1683页

作者： Mohammadkhani, M. A. Bayat, F. Jalali, A. A. Iran Univ Sci & Technol Sch Elect Engn Tehran Iran Univ Zanjan Dept Elect Engn Zanjan *** Iran

We develop an approximate multiparametric convex programming approach with its application to control constrained linear parameter-varying systems. Recently, the application of the real-time model predictive control (MPC) for various engineering systems has been significantly increased by using the multiparametric convex programming tool, known as explicit MPC approach. The main idea of explicit MPC is to move the major parts of the computations to offline phase and to provide an explicit piecewise affine solution of the constrained MPC problem, which is defined over a set of convex polyhedral partitions. In the proposed method, the idea of convex programming and partitioning is applied for linear parameter-varying control systems. The feasible space of the time-varying parameters is divided into simplices in which approximate solutions are calculated such that the approximation error is kept limited by solving sequences of linear programs. The approximate optimal solution within each simplex is obtained by linear interpolation of the optimal solutions in the simplex vertices, and then multiparametric programming tool is utilized to compute an explicit state feedback solution of linear quadratic optimal control problem for simplex vertices subject to state and input constraints. The proposed method is illustrated by a numerical example and the simulation results show the advantages of this approach.

关键词： explicit model predictive control linear parameter-varying systems multiparametric programming

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explicit controller of a single truck stability and rollover mitigation

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JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY 2018年第9期32卷 4373-4381页

作者： Yakub, Fitri Muhammad, Pauziah Toh, Hoong Thiam Abu Talip, M. Sofian Mori, Yasuchika Univ Teknol Malaysia Malaysia Japan Int Inst Technol Kuala Lumpur 54100 Malaysia Univ Malaya Dept Elect Engn Fac Engn Jalan Univ Kuala Lumpur 50603 Malaysia Transportat Syst & Elect Co Ltd Shinjuku Ku 3-13-2 Takadanobaba Tokyo 1690075 Japan

This study's aim was to enhance the maneuverability safety in the coordination of active rear steering and differential braking control for untripped rollover prevention, which performs a panic lane change maneuver to bypass the obstacle encountered in the path. In avoiding rollover accidents, there are several guidance preventions, such as to secure the vehicle from the intention of the driver and to position the vehicle in the actual lane. A crosswind effect is also found to be a crucial factor since this may cause other accidents. Therefore, there is a need to monitor the driver's actual path and maintaining the stability of the vehicle along the desired path in order to avoid rollover accidents. We extended the analysis of Yakub and Mori (2015) [1], by suggesting an explicit model of predictive control, which includes an active rear steering and braking control for each wheel. Our main focus was on the general trade-off between rollover prevention and path tracking. The effectiveness of the explicit control model invented for this study was measured and validated by the simulation results for a heavy vehicle proposed in this research.

关键词： Heavy vehicle Stability Rollover explicit model predictive control Rear steering Braking control

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Comparison of Inverted Pendulum Stabilization with PID, LQ, and MPC control 29

Comparison of Inverted Pendulum Stabilization with PID, LQ, ...

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29th International Conference on Cybernetics & Informatics (K&I)

作者： Bakarac, Peter Klauco, Martin Fikar, Miroslav Slovak Univ Technol Bratislava Bratislava Slovakia

ISBN: (纸本)9781538644218

This paper covers mathematical modeling of the inverted pendulum process and design of three types of controllers: PI, linear-quadratic (LQR), and model predictive controller (MPC). Since the dynamics of the inverted pendulum process is in range of milliseconds, the explicit version of MPC is applied. All three controllers are implemented and experimentally tested on a laboratory scale of the inverted pendulum device.

关键词： inverted pendulum explicit model predictive control complexity reduction

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PID- explicit predictive Dual Mode control for Double -Water Tank 30

PID- Explicit Predictive Dual Mode Control for Double -Water...

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30th Chinese control and Decision Conference (CCDC)

作者： Xiao, Guannan Liu, Fei Hangnail Univ Inst Automat Key Lab Adv Proc Control Light Ind Minist Educ Wuxi 214122 Jiangsu Peoples R China

ISBN: (纸本)9781538612446

A PID-explicit model predictive control (EMPC) based on dual mode strategy is developed in this paper to deal with nonlinear processes. The basic algorithm of EMPC decomposes the controller optimization problem into two steps: offline calculate and online search, which can decrease the online calculation and obtain the explicit function of control law in every state. It is convenient for controller analyzing. The traditional linearization -based nonlinear system control depends on pre-established operating point. By the idea of dual mode control, this paper adopts PID controller for nonlinear area while combining explicit model predictive control for linear area. The proposed algorithm is simulated on a double-water tank, which can decrease calculation time and have a satisfying performance.

关键词： explicit model predictive control PID Dual Mode control

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