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Near-Optimal Rapid MPC Using Neural Networks: A Primal-Dual Policy Learning Framework

IEEE TRANSACTIONS ON control SYSTEMS TECHNOLOGY 2021年第5期29卷 2102-2114页

作者： Zhang, Xiaojing Bujarbaruah, Monimoy Borrelli, Francesco Univ Calif Berkeley Model Predict Control Lab Berkeley CA 94720 USA

In this article, we propose a novel framework for approximating the MPC policy for linear parameter-varying systems using supervised learning. Our learning scheme guarantees feasibility and near-optimality of the approximated MPC policy with high probability. Furthermore, in contrast to most existing approaches that only learn the MPC policy, we also learn the "dual policy," which enables us to keep a check on the approximated MPC's optimality online during the control process. If the check deems the control input from the approximated MPC policy safe and near-optimal, then it is applied to the plant;otherwise, a backup controller is invoked, thus filtering out (severely) suboptimal control inputs. The backup controller is only invoked with a bounded (low) probability, where the exact probability level can be chosen by the user. Since our framework does not require solving any optimization problem during the control process, it enables the deployment of MPC on resource-constrained systems. Specifically, we illustrate the utility of the proposed framework on a vehicle dynamics control problem. Compared with online optimization methods, we demonstrate a speedup of up to 62x on a desktop computer and 10x on an automotive-grade electronic control unit, while maintaining high control performance.

关键词： Deep neural networks (DNNs) explicit model predictive control model predictive control (MPC) policy learning randomized algorithms safe learning sample complexity

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

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IEEE TRANSACTIONS ON POWER SYSTEMS 2020年第1期35卷 462-473页

作者： Qiu, Yiwei Lin, Jin Liu, Feng Song, Yonghua Tsinghua Univ Dept Elect Engn State Key Lab Control & Simulat Power Syst & Gene Beijing 100087 Peoples R China Univ Macau Dept Elect & Comp Engn Macau 999078 Peoples R China Tsinghua Univ Dept Elect Engn Beijing 100087 Peoples R China

The imbalance of generation and load caused by the increasing integration of volatile generations poses challenges on frequency regulation. AGC is required to respond to the generation fluctuations without violating operational and security constraints. explicit model predictive control (EMPC) provides an approach to reaching such requirements, which calculates the control laws of MPC in an explicit form, allowing for offline validation of the controller and enabling fast online computation. However, the partition number of EMPC & x0027;s 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 alternative explicit control approach for AGC by approximating the control laws of EMPC using Legendre polynomial series expansions, thus entirely eliminating the partition issue. The Galerkin method is applied to the KKT conditions of EMPC & x0027;s multiparametric quadratic programming (mp-QP) problem to compute the approximation. Case studies in an illustrative system and IEEE 118-Bus System verify the performance and efficiency of the proposed controller.

关键词： Automatic generation control Frequency control Power system dynamics predictive control Optimization Method of moments Optimal control Automatic generation control explicit model predictive control galerkin projection legendre polynomials multi-parametric programming optimal control spectral method

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A Pontryagin Principle-Based Frequency Governor for Constrained Computing Systems

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IEEE TRANSACTIONS ON control SYSTEMS TECHNOLOGY 2024年第4期32卷 1442-1450页

作者： Rao, Sachit Malpani, Nishant Rao, Shrisha Int Inst Informat Technol Bangalore IIIT B Bangalore 560100 India Aeva Percept Bangalore 560093 India

Management of power is a crucial problem in computing systems where power is finite, processor performance and energy needs are high, and thermal constraints have to be respected. The trade-off between performance and energy expenditure is well recognized. To satisfy these conflicting requirements, in this article, a dynamic system framework is adopted, and results from optimal control theory, notably Pontryagin's Minimum Principle (PMP), are applied to derive an energy-optimal (EO) time-varying processor speed law, or frequency governor, to execute assigned tasks. PMP is chosen as it allows for system input constraints as well as thermal and power budget constraints to be considered;the PMP-based governor is also compared with a model predictive controller (MPC) implemented by following the explicit-MPC framework using a linear model. The main contributions of this article are 1) determining an empirical time-invariant nonlinear dynamic model of an Intel CPU with task execution rate, power consumption, and temperature as the outputs, and clock frequency as the input;2) the Linux implementation of a PMP-based clock frequency governor on the CPU based on a linear model as well as the nonlinear model;and 3) hardware implementation of an explicit-MPC on the same platform using the frequency schedule derived from linear model simulations. Limits on task completion times and energy savings achieved in the execution of three benchmark tasks: MiBench, LINPACK, and Sorting positive integers, are presented. Experimental results show that it is possible to reduce energy consumption with an increase in task execution time while executing these benchmark tasks;it is also shown that it is possible to tune the PMP and MPC parameters to obtain similar performances. The approach presented in this article can be applied to design optimal controllers for other types of stand-alone or heterogeneous computing systems.

关键词： Task analysis Frequency control Time-frequency analysis Computational modeling Servers Process control Clocks Energy-aware computing explicit model predictive control optimal control theory Pontryagin's minimum principle (PMP) power estimation and optimization

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A VSC-HVDC Decentralized model predictive control Scheme for Fast Power Tracking

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IEEE TRANSACTIONS ON POWER DELIVERY 2014年第1期29卷 462-471页

作者： Mariethoz, Sebastien Fuchs, Alexander Morari, Manfred Swiss Fed Inst Technol Automat Control Lab CH-8092 Zurich Switzerland

A hierarchical and decentralized model predictive control scheme is proposed for the fast tracking of active and reactive power references of HVDC systems. The objective is to exploit optimally the system actuation and dynamics to improve power quality, provide voltage support and stabilize the grid. The system constraints are incorporated into the formulation to keep the system within its admissible operating range during all transients. At the high level, two HVDC line model predictive controllers deal with the dc system objectives by manipulating the power references that are given to two low-level ac current model predictive controllers that manipulate the voltage-source-inverter duty cycles. The proposed formulation is suitable for fast implementation and its performance is verified in simulation.

关键词： Decentralized control explicit model predictive control HVDC transmission model predictive control online model predictive control pulsewidth modulation inverters

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On the facet-to-facet property of solutions to convex parametric quadratic programs

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AUTOMATICA 2006年第12期42卷 2209-2214页

作者： Spjotvold, Jorgen Kerrigan, Eric C. Jones, Colin N. Tondel, Petter Johansen, Tor A. Norwegian Univ Sci & Technol Dept Engn Cybernet N-7491 Trondheim Norway Univ London Imperial Coll Sci Technol & Med Dept Aeronaut London SW7 2AZ England Univ London Imperial Coll Sci Technol & Med Dept Elect & Elect Engn London SW7 2AZ England ETH Swiss Fed Inst Technol Automat Control Lab CH-8092 Zurich Switzerland

In some of the recently developed algorithms for convex parametric quadratic programs it is implicitly assumed that the intersection of the closures of two adjacent critical regions is a facet of both closures;this will be referred to as the facet-to-facet property. It is shown by an example, whose solution is unique, that the facet-to-facet property does not hold in general. Consequently, some existing algorithms cannot guarantee that the entire parameter space will be explored. A simple modification, applicable to several existing algorithms, is presented for the purpose of overcoming this problem. Numerical results indicate that, compared to the original algorithms for parametric quadratic programs, the proposed method has lower computational complexity for problems whose solutions consist of a large number of critical regions. (c) 2006 Elsevier Ltd. All rights reserved.

关键词： parametric programming quadratic programming explicit model predictive control

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Accelerating nonlinear model predictive control through machine learning

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JOURNAL OF PROCESS control 2020年 92卷 261-270页

作者： Vaupel, Yannic Hamacher, Nils C. Caspari, Adrian Mhamdi, Adel Kevrekidis, Ioannis G. Mitsos, Alexander Rhein Westfal TH Aachen AVT Aachener Verfahrenstechn Proc Syst Engn Forckenbeckstr 51 D-52074 Aachen Germany Johns Hopkins Univ Dept Chem & Biomol Engn Baltimore MD USA JARA Ctr Simulat & Data Sci Aachen Germany Forschungszentrum Julich Inst Energy & Climate Res Energy Syst Engn IEK10 Wilhelm Johnen Str D-52425 Julich Germany

The high computational requirements of nonlinear model predictive control (NMPC) are a long-standing issue and, among other methods, learning the control policy with machine learning (ML) methods has been proposed in order to improve computational tractability. However, these methods typically do not explicitly consider constraint satisfaction. We propose two methods based on learning the optimal control policy by an artificial neural network (ANN) and using this for initialization to accelerate computations while meeting constraints and achieving good objective function value. In the first, the ANN prediction serves as the initial guess for the solution of the optimal control problem (OCP) solved in NMPC. In the second, the ANN prediction is improved by solving a single quadratic program (QP). We compare the performance of the two proposed strategies against two benchmarks representing the extreme cases of (i) solving the NMPC problem to convergence using the shift-initialization strategy and (ii) implementing the controls predicted by the ANN prediction without further correction to reduce the computational delay. We find that the proposed ANN initialization strategy mostly results in the same control policy as the shift-initialization strategy. The computational times are on average similar to 45% longer but the maximum time is similar to 42% smaller and the distribution is tighter, thus more predictable. The proposed QP-based method yields a good compromise between finding the optimal control policy and solution time. Closed-loop infeasibilities are negligible and the objective function is typically greatly improved as compared to benchmark (ii). The computational time required for the necessary second-order sensitivity integration is typically an order of magnitude smaller than for solving the NMPC problem to convergence. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： explicit model predictive control Fast-update methods Machine learning Neural networks

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Flexible Piecewise Function Evaluation Methods Based on Truncated Binary Search Trees and Lattice Representation in explicit MPC

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IEEE TRANSACTIONS ON control SYSTEMS TECHNOLOGY 2012年第3期20卷 632-640页

作者： Bayat, Farhad Johansen, Tor Arne Jalali, Ali Akbar Iran Univ Sci & Technol Dept Elect Engn Tehran *** Iran Zanjan Univ Zanjan *** Iran Norwegian Univ Sci & Technol Dept Cybernet N-7491 Trondheim Norway

Efficient methods for evaluation of piecewise functions defined over convex polyhedral partitions are proposed. As an important application, the explicit model predictive control problem is considered which requires a piecewise affine (PWA) control law to be evaluated online. The widely used binary search tree (BST) method is modified to be able to deal with a wider class of problems for which the BST method becomes prohibitive in terms of preprocessing time or memory requirements. The proposed method combines an orthogonal truncated binary search tree (OTBST) and lattice representation for PWA functions in a unified structure enjoying the advantages of both approaches. Both OTBST and Lattice-based OTBST (LOTBST) methods enable the designer to tradeoff between preprocessing time, storage requirement, and online computation time. The OTBST approach can be applied to more general partitions, e.g., discontinues and overlapping, while the LOTBST is directed towards more efficient evaluation of PWA functions, associated to the explicit MPC solutions. The key feature of the proposed methods is that the exact solution can be computed with predefined worst case online computation time guarantees. The computations are readily implementable using fixed-point arithmetic on a low cost microcontroller since there is no recursive accumulation of round-off errors, and the online algorithm is simple with a small footprint suitable for formal verification of correctness of implementation. Using several examples it is shown that the proposed LOTBST leads to a considerably less preprocessing time and memory requirement comparing to the pure BST and less online computation time comparing to the pure lattice representation.

关键词： Binary search tree (BST) explicit model predictive control lattice representation piecewise affine (PWA) functions piecewise function evaluation

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Linear Machine Solution to Point Location Problem

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IEEE TRANSACTIONS ON AUTOMATIC control 2017年第3期62卷 1403-1410页

作者： Airan, Astha Bhushan, Mani Bhartiya, Sharad Indian Inst Technol Dept Chem Engn Mumbai 400076 Maharashtra India

Linear machine has been recently proposed as an elegant solution for solving the point location problem arising in multi-parametric programming (mp-P) based online optimization. Linearmachine associates a linear discriminant function with each polytopic region in the parametric space. The solution to the point location problem is then obtained by simply evaluating these discriminant functions and finding their maximum value. In this technical note, we rigorously establish the correctness of the linear machine generation procedure and identify a necessary condition for existence of linear machine. A modified procedure, involving systematic subdivision of the parametric space, is proposed when this condition is not satisfied. Analysis of complexity and storage requirements, along with computational experiments on a large sized example, indicate that linear machine can be an efficient tool for solving the point location problem.

关键词： Discriminant functions explicit model predictive control multi-parametric programming online optimization

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Constrained optimal control: an application to semiactive suspension systems

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE 2010年第7期41卷 797-811页

作者： Paschedag, Tina Giua, Alessandro Seatzu, Carla Univ Cagliari Dept Elect & Elect Engn I-09134 Cagliari Italy Tech Univ Munich Inst Automat Control Engn LSR D-80290 Munich Germany

This article applies three different control techniques to the design of a quarter-car semiactive suspension system. The three techniques, originally developed to solve a constrained optimal control problem, are optimal gain switching, discontinuous variable structure control and explicit model predictive control. All of them divide the state space into convex regions and assign a linear or affine state feedback controller to each region. The partition of the state space is computed off-line. During the on-line phase, the controller switches between the subcontrollers according to the current state. All the above techniques gave satisfactory results when applied to the design of semiactive suspension systems. A detailed comparison in terms of computational complexity, performance and simplicity of the design is proposed in the article.

关键词： semiactive suspensions constrained optimal control optimal gain switching discontinuous variable structure control explicit model predictive control

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Robust region elimination for piecewise affine control laws

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AUTOMATICA 2019年 99卷 333-337页

作者： Maddalena, Emilio Tanowe Harrop Galvao, Roberto Kawakami Magalhaes Afonso, Rubens Junqueira Inst Tecnol Aeronaut Elect Engn Div BR-12228900 Sao Jose Dos Campos Brazil

This paper is concerned with uncertain linear discrete-time systems controlled by a piecewise affine feedback law defined on a polyhedral domain. Assuming the initial state is contained in a given set, a novel algorithm is proposed to identify regions of the polyhedral partition which are guaranteed not to be visited during real-time operation. By dispensing with the need to store the aforementioned regions and associated control functions, the proposed method enables a reduction in both storage and on-line computational demands. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Piecewise affine system explicit model predictive control Region elimination Computational complexity

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