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robust model predictive control with sliding mode for constrained non-linear systems

IET control THEORY AND APPLICATIONS 2020年第17期14卷 2592-2599页

作者： Fesharaki, Shekoofeh Jafari Kamali, Marzieh Sheikholeslam, Farid Talebi, Heidar Ali Isfahan Univ Technol Dept Elect & Comp Engn Esfahan *** Iran Amirkabir Univ Technol Dept Elect Engn Tehran Iran

This study proposes a tractable robust non-linear model predictive control for constrained continuous-time uncertain systems with stability guarantees. First, a sampled-data model predictive control for the nominal system is designed to provide a desired performance. Then, a sliding mode control is designed to recover the nominal performance for the uncertain system. The sampled-data model predictive control that is solved online includes the initial state of the model employed in the problem as a decision variable. By merging sampled-data model predictive control and sliding mode control in between samples, the effect of the uncertainty, which is matched with the input, is reduced efficiently. The computational complexity of the proposed robust model predictive control is the same as for the model predictive control while the input and state constraints satisfaction and asymptotic stability of the closed-loop system are achieved. To illustrate the effectiveness of the proposed approach, the controller is applied to a vehicle platooning system.

关键词： control system synthesis asymptotic stability closed loop systems nonlinear control systems predictive control robust control continuous time systems variable structure systems uncertain systems discrete time systems stability linear systems sampled-data model predictive control sliding mode control robust model predictive control nonlinear systems nonlinear model predictive control constrained continuous-time uncertain systems

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robust model predictive control for multirate systems with model uncertainties and circular scheduling

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INTERNATIONAL JOURNAL OF robust AND NONLINEAR control 2020年第18期30卷 8206-8227页

作者： Wang, Jianhua Song, Yan Wei, Guoliang Univ Shanghai Sci & Technol Dept Control Sci & Engn Shanghai 200093 Peoples R China Univ Shanghai Sci & Technol Sch Sci Shanghai Peoples R China

In this article, the robust model predictive control (RMPC) problem on the basis of output feedback (OF) is dealt with for a class of multirate time-varying systems with polyhedral uncertainties and limited-bandwidth channels. For alleviating the communication burden caused by the limited transmission capacity, the Round-Robin (RR) protocol is exploited to allocate transmission permissions in a pre-scheduled order. Meanwhile, in order to reduce the communication cost while ensuring the system performance, the multirate mechanism is presented to govern the update rate of the plant and the sampling rate of the sensors. By means of the lifting technique, given a uniform sampling rate, a comprehensive augmentation system is established on the fixed moving horizon. The objective of the addressed RMPC problem is to design a set of OF-based RMPC controllers such that, in the presence of the multirate scheme and the RR transmission protocol, the desirable performance is guaranteed. Then, the desired RMPC gains are directly obtained, with the help of inequality analysis technique and RR-dependent Lyapunov-like approach, to ensure the asymptotic convergence of system states. Two illustrative examples are given, which include a DC motor system and a numerical simulation example, to demonstrate the effectiveness of the proposed protocol-based RMPC controller design strategy.

关键词： circular scheduling multirate systems polyhedral uncertainties robust model predictive control Round-Robin protocol

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robust model predictive control of a micro machine tool for tracking a periodic force signal

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OPTIMAL control APPLICATIONS & METHODS 2020年第6期41卷 2037-2047页

作者： Wang, Yuzhang Geng, Yanquan Yan, Yongda Wang, Jiqiang Fang, Zhuo Harbin Inst Technol Robot Inst State Key Lab Robot & Syst Harbin Peoples R China Harbin Inst Technol Ctr Precis Engn Harbin Peoples R China

The micro machine tool that can produce nanostructures by force modulation approach plays a significant role in nanotechnology. In this paper, to guarantee fast and high-precision cutting subject to external disturbances and input saturation, a robust model predictive control (MPC) using a tube-based method is exploited to develop a controller for the machining system consisting of a piezoelectric tube (PZT) actuator, a force sensor and a cutting tool, which updates the state of the art. In particular, the dynamic model of the machining system, with the voltage fed into PZT being input and the cutting force being output, is identified by incorporating the map between the cutting force and the displacement of PZT. Based on the voltage-force dynamic model, a tube-based MPC controller that consists of two optimizers is used to make PZT actuator track a desired periodic force signal. Finally, the effectiveness of the MPC method for force signal tracking under different frequencies is validated and advantages over the conventional proportional integral controller are also shown in the presence of the constraints of saturated input and external disturbances via numerical simulations.

关键词： force modulation micro machine tool periodic force signal tracking robust model predictive control

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robust model predictive control BASED ON SIGN-PERTURBED SUMS STRATEGY

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INTERNATIONAL JOURNAL OF INNOVATIVE COMPUTING INFORMATION AND control 2022年第2期18卷 463-476页

作者： Jiang, Hong Yan, Xiang Wang, Jianhong Jingdezhen Ceram Univ Sch Mech & Elect Engn 86 Taoyang Rd Jingdezhen 333403 Peoples R China

This paper studies the problem of robust model predictive control, whose state variable in its quadratic penalty function is related with an unknown parameter vector. After formulating the open loop system and closed loop system into their corresponding linear regressor forms, sign-perturbed sums is proposed to construct one guaranteed confidence region for that unknown parameter vector, while relaxing the strict limitation of the external noise, i.e., no probabilistic density function. Only each noise has a symmetric probability distribution about zero. Consider the controller design and confidence region for the parameter vector in model predictive control simultaneously, then robust model predictive control corresponding to one min-max optimization problem, whose max operation means the worst case performance. Generally, robustness is from the uncertainty of the parameter vector, as here this parameter vector is not a scalar vector, but one guaranteed confidence region, which includes the parameter vector with one chosen probability level. Finally, one simulation example is used to prove our considered theories.

关键词： robust model predictive control Sign-perturbed sums Linear regressor Probability level

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robust model predictive control based on recurrent multi-dimensional Taylor network for discrete-time non-linear time-delay systems

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IET control THEORY AND APPLICATIONS 2020年第13期14卷 1806-1818页

作者： Duan, Zheng-Yi Yan, Hong-Sen Zheng, Xiao-Yi Southeast Univ Sch Automat Nanjing 210096 Jiangsu Peoples R China Southeast Univ Key Lab Measurement & Control Complex Syst Engn Minist Educ Nanjing 210096 Jiangsu Peoples R China

This study is concerned with the robust model predictive control (MPC) based on recurrent multi-dimensional Taylor network (RMTN) for the discrete-time non-linear time-delay systems. Regarding the MPC algorithm for the discrete-time time-delay systems, the existing literature only considers the linear case. In this study, by designing the suitable terminal cost and terminal region, the MPC scheme is firstly investigated for the non-linear case. Meanwhile, to reduce the computational burden of MPC using the existing model types (e.g. recurrent neural network) as the identified model, an RMTN possessing the concise structure and high computational efficiency is constructed to approximate the state-space model of the system. After trained by the backpropagation through time algorithm, the RMTN obtaining the high accuracy of prediction over a long-range horizon is capable of serving as the prediction model in the MPC scheme. Furthermore, aiming at alleviating the adverse effect of the inevitable identification error, the tube-based MPC is proposed via leveraging dual-mode MPC to guarantee that actual trajectory is contained within a robust tube. The stability of the considered system is proved theoretically, and numerical simulation is employed to validate the effectiveness of the proposed method.

关键词： recurrent neural nets discrete time systems predictive control backpropagation robust control linear systems delay systems RMTN approximate the state-space model prediction model MPC scheme tube-based MPC robust model predictive control recurrent multidimensional Taylor network discrete-time nonlinear time-delay MPC algorithm discrete-time time-delay systems nonlinear case existing model types recurrent neural network

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robust model predictive control of HVAC systems with uncertainty in building parameters using linear matrix inequalities

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ADVANCES IN BUILDING ENERGY RESEARCH 2020年第3期14卷 338-354页

作者： Nagpal, Himanshu Staino, Andrea Basu, Biswajit Trinity Coll Dublin Dept Civil Struct & Environm Engn Dublin 2 Ireland ALSTOM PHM Ctr Excellence St Ouen France

In this work, a new robust controller is proposed for building climate control in presence of parametric uncertainties. The design of the controller is based on the model predictive control (MPC) framework and it includes time-varying constraints. The robust design is implemented by explicitly considering parametric uncertainty in the synthesis of the control law. Variations of the parameters of the buildings are represented in the form of polytopic uncertainty. The robust control action is obtained by minimizing an appropriate 'worst-case' cost function, which leads to the definition of a min-max optimization problem. This optimization problem is formulated using Linear Matrix Inequalities (LMIs) that allow for efficient numerical computation of the control command. Simulation results show that the proposed approach is successful in keeping the indoor temperature of the building in the desired range even in presence of large model uncertainties. The proposed controller is also compared with a nominal controller synthesized without accounting for parametric uncertainty. Numerical results confirm 24% better performance of the robust design in comparison with the nominal controller with same conditions. Further, simulation results also demonstrate that the robust control system achieves 17% better performance in the case of severe conditions of uncertainty.

关键词： robust model predictive control model uncertainty building climate control linear-matrix inequalities

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A robust model predictive control framework for the regulation of anesthesia process with Propofol

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OPTIMAL control APPLICATIONS & METHODS 2021年第4期42卷 965-986页

作者： Ntouskas, Sotiris Sarimveis, Haralambos Natl Tech Univ Athens NTUA Sch Chem Engn 9 Heroon Polytechneiou StZografou Campus Athens 15780 Greece

In this work, we present a robust model predictive control (MPC) strategy based on linear matrix inequalities (LMIs) for the intravenous administration of Propofol, a drug which is used for anesthesia during surgeries. The controller is designed for a population of patients and takes into account constraints on the amount of administered drug and on the drug concentration profile. A detailed compartmental mathematical model available in the literature is adjusted to the available data and provides the future predictions of the process. In the context of the application, only the depth of anesthesia (BIS index) is assumed to be measured-as it is common in practice. The state of the system (drug amount in organs) is estimated in real-time by incorporating a state observer. The derived control scheme, along with the designed state observer are able to deal with major challenges in controlling the depth of anesthesia which are inter- and intra-patient variability, model nonlinearity, and model uncertainty. The controller is able to satisfy the divergent characteristics of the patients of the dataset, while satisfying in parallel all the imposed constraints. Moreover, we show that by considering smaller groups of patients with similar characteristics the corresponding responses are significantly improved.

关键词： compartmental PBPK modeling intravenous anesthesia robust model predictive control

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Observer-based robust model predictive control of switched nonlinear systems with time delay and parametric uncertainties

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JOURNAL OF VIBRATION AND control 2021年第17-18期27卷 1939-1955页

作者： Taghieh, Amin Shafiei, Mohammad Hossein Univ Tabriz Fac Elect & Comp Engn Tabriz Iran Shiraz Univ Technol Dept Elect & Elect Engn Modares Blvd Shiraz 715555313 Iran

In this study, an observer-based robust model predictive control scheme is proposed to control a class of switched nonlinear systems in the presence of time delay and parametric uncertainties under arbitrary switching. Constructing an appropriate Lyapunov-Krasovskii functional in conjunction with an infinite horizon cost function, sufficient conditions are obtained to guarantee the asymptotic stability of the closed-loop switched system in terms of linear matrix inequalities depending on the time delay, the upper bounds of uncertain parameters, and the Lipschitz constant of subsystems. To model the uncertainty of the system, the parametric uncertainty is used to reduce the computational burden and the conservatism of the method. In the proposed method, a predictive state observer and an observer-based controller are synthesized via an online optimization problem to minimize the upper bound of the cost function, while handling the constraints. Finally, the obtained results are validated using practical and numerical simulations.

关键词： Switched nonlinear systems observer-based controller robust model predictive control parametric uncertainties time delay

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Fast System Level Synthesis: robust model predictive control using Riccati Recursions

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IFAC-PapersOnLine 2024年第18期58卷 173-180页

作者： Antoine P. Leeman Johannes Kohler Florian Messerer Amon Lahr Moritz Diehl Melanie N. Zeilinger Institute for Dynamic Systems and Control ETH Zurich Zurich 8053 Switzerland Department of Microsystems Engineering (IMTEK) University of Freiburg 79110 Freiburg Germany Department of Mathematics University of Freiburg 79104 Freiburg Germany

System level synthesis enables improved robust MPC formulations by allowing for joint optimization of the nominal trajectory and controller. This paper introduces a tailored algorithm for solving the corresponding disturbance feedback optimization problem for linear time-varying systems. The proposed algorithm iterates between optimizing the controller and the nominal trajectory while converging q-linearly to an optimal solution. We show that the controller optimization can be solved through Riccati recursions leading to a horizon-length, state, and input scalability of O(N 2 (n x 3 + n u 3 )) for each iterate. On a numerical example, the proposed algorithm exhibits computational speedups by a factor of up to 10 3 compared to general-purpose commercial solvers.

关键词： Optimization and model predictive control robust model predictive control Real-Time Implementation of model predictive control

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Trajectory Tracking for Autonomous Vehicles Using robust model predictive control

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IFAC-PapersOnLine 2024年第10期58卷 94-101页

作者： Dan Shen Yaobin Chen Lingxi Li Jianghai Hu Aptiv Corporation Troy MI 48098 USA Purdue University Indianapolis IN 46202 USA Purdue University West Lafayette IN 47907 USA

This paper proposes a novel trajectory tracking control method using a robust model predictive control (RMPC) design technique based on matrix inequality and the theoretical approach of the hybrid & switched system. Firstly, considering bounded model uncertainties and norm-bounded external disturbances, the system states and control matrices are modified. In addition, vehicle time-varying longitudinal speed is considered, and a vehicle lateral dynamic model based on Linear Parameter Varying (LPV) is established by utilizing a polytope with finite vertices. Then the Min-Max robust MPC state feedback control law is obtained at every timestamp by solving a set of matrix inequalities which are derived from Lyapunov stability and the minimization of the worst-case in infinite-horizon quadratic objective function. The numerical simulation results demonstrated that the proposed robust LPV MPC can effectively track vehicle lateral dynamics on both straight and curved roads with varying longitudinal speeds.

关键词： Trajectory tracking control linear parameter varying robust model predictive control

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