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Approximate Closed-Loop robust model predictive control With Guaranteed Stability and Constraint Satisfaction

IEEE control SYSTEMS LETTERS 2020年第3期4卷 719-724页

作者： Paulson, Joel A. Mesbah, Ali Ohio State Univ Dept Chem & Biomol Engn Columbus OH 43210 USA Univ Calif Berkeley Dept Chem & Biomol Engn Berkeley CA 94720 USA

The real-time implementation of closed-loop robust model predictive control (MPC) schemes is an important challenge for fast systems, as their solution complexity depends strongly on the system size, control policy parametrization, and prediction horizon. We look to address this problem by approximating the implicitly-defined MPC controller using deep learning. Although the resulting neural network approximation has a small memory footprint and can be efficiently computed, it does not guarantee robust constraint satisfaction or stability. We propose a novel projection-based strategy that is capable of providing a certificate of robust feasibility and input-to-state stability in real-time. We also show how this projection operator can be formulated as a parametric quadratic program that is solvable offline. The advantages of the proposed approach are demonstrated on a benchmark case study.

关键词： robustness Stability analysis Numerical stability Real-time systems Neural networks Optimization Asymptotic stability robust model predictive control deep neural networks input-to-state stability safe invariant sets

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Offline robust model predictive control for Lipschitz Non-Linear Systems Using Polyhedral Invariant Sets

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ASIAN JOURNAL OF control 2020年第1期22卷 288-296页

作者： Shokrollahi, Ali Shamaghdari, Saeed Iran Univ Sci & Technol Dept Elect Engn Tehran Iran

In this paper the concept of maximal admissible set (MAS) for linear systems with polytopic uncertainty is extended to non-linear systems composed of a linear constant part followed by a non-linear term. We characterize the maximal admissible set for the non-linear system with unstructured uncertainty in the form of polyhedral invariant sets. A computationally efficient state-feedback RMPC law is derived off-line for Lipschitz non-linear systems. The state-feedback control law is calculated by solving a convex optimization problem within the framework of linear matrix inequalities (LMIs), which leads to guaranteeing closed-loop robust stability. Most of the computational burdens are moved off-line. A linear optimization problem is performed to characterize the maximal admissible set, and it is shown that an ellipsoidal invariant set is only an approximation of the true stabilizable region. This method not only remarkably extends the size of the admissible set of initial conditions but also greatly reduces the on-line computational time. The usefulness and effectiveness of the method proposed here is verified via two simulation examples.

关键词： robust model predictive control Lipschitz non-linear systems polyhedral invariant sets linear matrix inequalities off-line control design

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robust nonlinear model predictive control based on nominal predictions with piecewise constant references and bounded disturbances

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INTERNATIONAL JOURNAL OF robust AND NONLINEAR control 2022年第6期32卷 3944-3968页

作者： Cunha, Victor M. Santos, Tito L. M. Univ Fed Bahia Dept Engn Elect & Comp Escola Politecn Rua Prof Aristides Novis 02 BR-40210630 Salvador BA Brazil

This article presents a robust nonlinear model predictive control (NMPC) strategy for constrained systems with piecewise constant references and bounded disturbances based on nominal predictions. An artificial target is employed to avoid feasibility loss due to target change and to provide a potentially enlarged domain of attraction. Recursive feasibility and input-to-state stability are ensured. Recursive feasibility is guaranteed due to the tighter constraints that are recursively computed offline based on the disturbance reachable sets. The zonotopic approach from the mean-value theorem extension is applied to compute these tighter constraints. In the presence of stochastic disturbances with known distribution, individual chance constraints can be considered in the proposed NMPC algorithm. Furthermore, simplified stabilizing ingredients are proposed in order that the robust assumptions hold based on standard algorithms. Case studies based on the continuous stirred tank reactor and buck-boost control benchmarks are presented to illustrate the main properties of the proposed approach.

关键词： Bounded disturbances constrained systems nonlinear systems robust model predictive control zonotopes

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A novel dual-mode robust model predictive control approach via alternating optimizations

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AUTOMATICA 2021年 133卷 109857-109857页

作者： Yang, Weilin Xu, Dezhi Jiang, Bin Shi, Peng Jiangnan Univ Sch Internet Things Engn Wuxi 214122 Jiangsu Peoples R China Nanjing Univ Aeronaut & Astronaut Coll Automat Engn Nanjing 211106 Peoples R China Univ Adelaide Sch Elect & Elect Engn Adelaide SA 5005 Australia

The minimal robust positively invariant (mRPI) set plays an important role in robust model predictive control (RMPC). However, the exact computation of the mRPI set is generally intractable. This paper proposes a novel H-infinity-type RMPC approach for linear systems with additive disturbances. This approach enables users to compute an ellipsoidal RPI set that approximates the minimal one in online implementations. Considering that a bilinear matrix inequality is involved in the problem formulation, an alternating optimization method is proposed in this work to ensure that the optimization problem to be solved online is always convex. Furthermore, a novel dual-mode control strategy is introduced that consists of two modes, i.e., with, and without alternating optimizations. The "classic mode"achieves fast convergence of the control algorithm, while the "alternating mode"can precisely approximate the mRPI set. None of the proposed approaches requires any off-line design, which makes practical applications more convenient. Simulations are conducted to demonstrate the effectiveness of the proposed approaches. (C) 2021 Published by Elsevier Ltd.

关键词： robust model predictive control Bilinear matrix inequality robust positively invariant set Alternating optimization

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Matrix Inequalities Based robust model predictive control for Vehicle Considering model Uncertainties, External Disturbances, and Time-Varying Delay

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FRONTIERS IN NEUROROBOTICS 2021年 14卷 617293页

作者： Liu, Wenjun Chen, Guang Knoll, Alois Tech Univ Munich Dept Informat Munich Germany Tongji Univ Sch Automot Studies Shanghai Peoples R China

In this paper, we design a robust model predictive control (MPC) controller for vehicle subjected to bounded model uncertainties, norm-bounded external disturbances and bounded time-varying delay. A Lyapunov-Razumikhin function (LRF) is adopted to ensure that the vehicle system state enters in a robust positively invariant (RPI) set under the control law. A quadratic cost function is selected as the stage cost function, which yields the upper bound of the infinite horizon cost function. A Lyapunov-Krasovskii function (LKF) candidate related to time-varying delay is designed to obtain the upper bound of the infinite horizon cost function and minimize it at each step by using matrix inequalities technology. Then the robust MPC state feedback control law is obtained at each step. Simulation results show that the proposed vehicle dynamic controller can steer vehicle states into a very small region near the reference tracking signal even in the presence of external disturbances, model uncertainties and time-varying delay. The source code can be downloaded on https://***/wenjunliu999.

关键词： robust model predictive control vehicle dynamic control matrix inequities robust positively invariant model uncertainties external disturbances time-varying delay

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Fault-Tolerant control for Flexible Air-Breathing Hypersonic Vehicle Based on Tube robust model predictive control 9

Fault-Tolerant Control for Flexible Air-Breathing Hypersonic...

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9th IEEE Data Driven control and Learning Systems Conference (DDCLS)

作者： Yang, Xiaohe Lv, Weijie Hu, Chaofang Hu, Yongtai Tianjin Univ Sch Elect & Informat Engn Tianjin 300072 Peoples R China Facri Aviat Key Lab Sci & Technol Aircraft Control Xian 710065 Peoples R China

ISBN: (纸本)9781728159225

This paper adopts Tube robust model predictive control (RMPC) approach to achieve the trajectory tracking control for flexible air-breathing hypersonic vehicle (FAHV) with lose efficiency fault of actuator. First of all, Jacobian linearization and tensor-product transformation are used to build the polytopic linear parameter varying (LPV) model for FAHV. Then, the FAHV faulty model is obtained by transforming lose efficiency fault of actuator into the additional disturbance term. Thirdly, fault-tolerant control is realized by composite control law. The error system is obtained by the difference between the actual and the nominal system. By designing the minimum robust positive invariant set (mRPI), the error system state is limited to the mRPI set. The additional disturbance term in mRPI set is suppressed by the auxiliary robust feedback control law. The nominal control law provides a reasonable trajectory for the actual system. And it is calculated by the convex optimization problem, which is constrained by linear matrix inequality (LMI). The fault-tolerant controller guarantees that the actual trajectory is located in the mRPI set all the time and centered on the nominal trajectory. Finally, the designed Tube RMPC controller is validated by simulation.

关键词： Flexible Air-breathing Hypersonic Vehicle Fault-Tolerant control Linear Parameter Varying model robust model predictive control

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A frequency control strategy for multimicrogrids with V2G based on the improved robust model predictive control

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ENERGY 2021年 222卷 119963-119963页

作者： Rao, Yingqing Yang, Jun Xiao, Jinxing Xu, Bingyan Liu, Wenjing Li, Yonghui Wuhan Univ Sch Elect Engn & Automat Wuhan 430072 Peoples R China State Grid Shanghai Municipal Elect Power Co State Grid Shanghai 200122 Peoples R China

The microgrid contains many distributed power sources which have great randomness and volatility, so it is difficult to maintain the stable operation. As a mobile energy storage component with the capability of Vehicle-to-Grid (V2G), electric vehicles (EVs) provide a solution for the safe and stable operation of multimicrogrids. First, a microgrid system including micro gas turbines, distributed power and EVs which consider the random behavior of EV users as dynamic limitations is established. A coupled multimicrogrid system is then established. An improved robust model predictive frequency control strategy of multimicrogrids with EVs is proposed, and the whole control process is transformed into linear matrix inequalities (LMIs). A linear quadratic regulator (LQR) is added to further optimize control quantities to ensure the stability of the output. Finally, different scenarios are set up in the microgrids, and the simulation results are compared with other control methods. The simulation results show that the proposed control method can better suppress the frequency fluctuation with a faster response speed than other methods. The regulation of LQR is verified, and the proposed algorithm is shown to be effective in solving the uncertainty of system parameters. The establishment of multimicrogrids in-creases the anti-interference ability of the system. (c) 2021 Elsevier Ltd. All rights reserved.

关键词： Frequency control robust model predictive control Electric vehicle Multimicrogrids V2G

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robust model predictive control with randomly occurred networked packet loss in industrial cyber physical systems

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Journal of Central South University 2019年第7期26卷 1921-1933页

作者： CAI Hong-bin LI Ping SU Cheng-li CAO Jiang-tao School of Automation Northwestern Polytechnical University Xi'an 710072 China School of Information and Control Engineering Liaoning Shihua University Fushun 113001 China

For a class of linear discrete-time systems that is subject to randomly occurred networked packet loss in industrial cyber physical systems, a novel robust model predictive control method with active compensation mechanism was proposed. The probability distribution of packet loss is described as the Bernoulli distributed white sequences. By using the Lyapunov stability theory, the existing sufficient conditions of the controller are derived from solving a group of linear matrix inequalities. Moreover, dropout-rate with uncertainty and unknown dropout-rate are also considered, which can greatly reduce the conservativeness of the controller. The designed robust model predictive control method not only efficiently eliminates the negative effects of the networked data loss in industrial cyber physical systems but also ensures the stability of closed-loop system. Two examples were provided to illustrate the superiority and effectiveness of the proposed method.

关键词： robust model predictive control networked control system packet loss linear matrix inequalities (LMIs)

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A fast dissipative robust nonlinear model predictive control procedure via quasi-linear parameter varying embedding and parameter extrapolation

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INTERNATIONAL JOURNAL OF robust AND NONLINEAR control 2021年第18期31卷 9619-9651页

作者： Morato, Marcelo Menezes Normey-Rico, Julio E. Sename, Olivier Univ Fed Santa Catarina Dept Automacao & Sistemas Florianopolis SC Brazil Univ Grenoble Alpes Grenoble INP GIPSA Lab CNRSInst Engn Grenoble France

In this article, a robust model predictive control (MPC) procedure for quasi-linear parameter varying (qLPV) systems is proposed. The novelty resides in considering a recursive extrapolation algorithm to estimate the values of the scheduling parameters along the prediction horizon Np, which fastens the sluggish performances achieved with the robust qLPV MPCs from the literature. The bounds on the estimation errors of the scheduling parameters through Np are taken into account by the robust MPC, which solves an online min-max problem: first, a constrained convex program is resolved in order to determine the worst-case bound on the cost function and, subsequently, a second constrained quadratic program is solved to minimize this worst-case cost function with respect to a control sequence vector. Since the bounds on the estimation error for the scheduling parameters are usually much smaller than the bounds on the actual scheduling parameter, the conservativeness of the solution is quite reduced. Recursive feasibility and stability of the proposed algorithm are demonstrated with dissipativity arguments given in the form of a linear matrix inequality remedy, which determines the zone of attraction for which input-to-state stability is ensured. The nonlinear temperature regulation problem of a flat solar collector is considered as a case study. Using a realistic simulation benchmark, the proposed technique is compared to other robust min-max LPV MPC algorithms from the literature, proving itself efficient while achieving good performances.

关键词： dissipativity linear parameter varying systems quadratic programming robust model predictive control solar collectors

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robust H∞ model predictive control for constrained Lipschitz non-linear systems

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JOURNAL OF PROCESS control 2021年 104卷 101-111页

作者： Shokrollahi, Ali Shamaghdari, Saeed Iran Univ Sci & Technol Sch Elect Engn Tehran Iran

This paper is concerned with the robust H-infinity model predictive control problem for a class of non-linear systems subject to state and input constraints and with norm bounded disturbances. It is well known that the disturbance degrades the control performance remarkably and can cause system instability. As well as, design the H-infinity model predictive control based on the non-linear model is much more challenging, because the control problem changes to a non-convex non-linear problem. The main contribution is the introduction of the novel robust controller to stabilize the perturbed Lipschitz non-linear systems. The objective is to minimize the L2 gain between the disturbance input and the controlled output. The non-convex control problem is formulated as a linear matrix inequality optimization problem. The designed controller guarantees the closed-loop asymptotic stability with a prescribed H-infinity disturbance attenuation level. In order to reduce conservatism, a sum of squares optimization problem is proposed to obtain the optimal value of Lipschitz coefficient. The proposed algorithm is applied to two non-linear systems, a laboratory tank and a DC/AC converter to evaluate its applicability and effectiveness. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： robust model predictive control H-infinity norm Lipschitz non-linear system Laboratory tank DC/AC converter

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