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Large-Signal Stability Analysis of Two-Stage Cascaded DC/DC Converter Systems Using sum-of-squares programming

IEEE TRANSACTIONS ON POWER ELECTRONICS 2024年第2期39卷 2076-2085页

作者： Song, Qingchao Chen, Jiawei Loo, Ka-Hong Chen, Jie Chen, Pengwei Hong Kong Polytech Univ Dept Elect & Elect Engn Hong Kong Peoples R China Chongqing Univ Sch Automat Chongqing 400044 Peoples R China Nanjing Univ Aeronaut & Astronaut Coll Automat Engn Ctr More Elect Aircraft Power Syst Minist Ind & Informat Technol Nanjing 211106 Peoples R China Nanjing Univ Aeronaut & Astronaut Coll Automat Engn Nanjing 211106 Peoples R China

The large-signal stability analysis of two-stage cascaded dc-dc converter systems is still a troublesome problem due to various limitations of existing stability analysis methods. To address this problem, a large-signal stability analysis method based on Lyapunov's stability theory and the sum-of-squares programming technique is proposed. With the proposed method, one can not only obtain the maximum stability boundary of the system under large disturbances, which helps understand the system's transient behaviors, but also can analyze the influences of system parameters on the stability region and identify the dominant parameters. The proposed stability analysis method could provide a practical guide for designing system parameters. The effectiveness of the large-signal stability analyzing results is verified by experimental results.

关键词： Cascaded dc-dc converter system constant power load large-signal stability analysis sum-of-squares programming the largest estimated domain of attraction

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Nonlinear state-feedback design for vehicle lateral control using sum-of-squares programming

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VEHICLE SYSTEM DYNAMICS 2022年第3期60卷 743-769页

作者： Ribeiro, A. M. Fioravanti, A. R. Moutinho, A. de Paiva, E. C. Univ Estadual Campinas Sch Mech Engn Campinas Brazil Univ Lisbon Inst Super Tecn IDMEC Lisbon Portugal

This work addresses the lateral stabilisation problem of four-wheels ground vehicles. The objective is to estimate the largest state-space region such that the closed-loop vehicle lateral stability can be guaranteed. sum-of-squares (SOS) programming technique is applied to find these maximum invariant sets while accounting for steering and yaw moment input saturations. The algorithm allows the region of attraction (RoA) to be approximated by a level set of a Lyapunov function (LF) and the computation of polynomial state feedback control laws. The method is applied for both straight-line motion and cornering manoeuver. Finally, a Monte-Carlo analysis is presented to show that the proposed SOS-based methodology can be used as a valid analysis and design tool considering a real vehicle application.

关键词： Region of attraction vehicle dynamics nonlinear control design sum-of-squares programming vehicle lateral stability polynomial systems

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Local stability analysis using simulations and sum-of-squares programming

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AUTOMATICA 2008年第10期44卷 2669-2675页

作者： Topcu, Ufuk Packard, Andrew Seiler, Peter Univ Calif Berkeley Dept Mech Engn Berkeley CA 94720 USA Honeywell Technol Ctr Minneapolis MN 55418 USA

The problem of computing bounds on the region-of-attraction for systems with polynomial vector fields is considered. Invariant subsets of the region-of-attraction are characterized as sublevel sets of Lyapunov functions. Finite-dimensional polynomial parametrizations for Lyapunov functions are used. A methodology utilizing information from simulations to generate Lyapunov function candidates satisfying necessary conditions for bilinear constraints is proposed. The suitability of Lyapunov function candidates is assessed solving linear sum-of-squares optimization problems. Qualified candidates are used to compute invariant subsets of the region-of-attraction and to initialize various bilinear search strategies for further optimization. We illustrate the method on small examples from the literature and several control oriented systems. (c) 2008 Elsevier Ltd. All rights reserved,

关键词： Local stability Region-of attraction Nonlinear dynamics sum-of-squares programming Simulations

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Region of attraction analysis for nonlinear vehicle lateral dynamics using sum-of-squares programming

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VEHICLE SYSTEM DYNAMICS 2018年第7期56卷 1118-1138页

作者： Masouleh, Mehdi Imani Limebeer, David J. N. Univ Oxford Dept Engn Sci Oxford England

In this study we will estimate the region of attraction (RoA) of the lateral dynamics of a nonlinear single-track vehicle model. The tyre forces are approximated using rational functions that are shown to capture the nonlinearities of tyre curves significantly better than polynomial functions. An existing sum-of-squares (SOS) programming algorithm for estimating regions of attraction is extended to accommodate the use of rational vector fields. This algorithm is then used to find an estimate of the RoA of the vehicle lateral dynamics. The influence of vehicle parameters and driving conditions on the stability region are studied. It is shown that SOS programming techniques can be used to approximate the stability region without resorting to numerical integration. The RoA estimate from the SOS algorithm is compared to the existing results in the literature. The proposed method is shown to obtain significantly better RoA estimates.

关键词： Region of attraction vehicular lateral dynamics nonlinear stability analysis sum-of-squares programming rational tyre model Lyapunov stability

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Off-equilibrium linearisation-based nonlinear control of turbojet enginese with sum-of-squares programming

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AERONAUTICAL JOURNAL 2020年第1282期124卷 1879-1895页

作者： Tang, Y. Li, Y. Cui, T. Zheng, Y. Zhejiang Univ Sch Aeronaut & Astronaut Hangzhou 310027 Peoples R China China Aerosp Sci & Ind Corp Beijing Power Machinery Res Inst Beijing 100074 Peoples R China Northwestern Polytech Univ Sch Astronaut Xian 710072 Peoples R China

In conventional linear parameter-varying (LPV) modelling and gain scheduling control design for turbojet engines, the linearisation is performed at a set of equilibrium points, and the validity of such LPV models is ensured near the equilibria. However, the linear model can only provide an approximate description of the engine's state when the system operates away from equilibrium. In this paper, it is suggested that such linearisation should be carried out not only at equilibrium states but also in transient (off-equilibrium) operating regimes. This will result in a global approximation to the system states whether equilibrium or off-equilibrium. Theoretically, the transient control performance can be improved by introducing such an offequilibrium linearisation-based control procedure. Subsequently, a gain scheduling control procedure based on off-equilibrium linearisation models is proposed by using sum-of-squares (SOS) programming, which, compared with many convex programming methods, can provide less conservative results. The resulting off-equilibrium linearisation-based nonlinear control procedure with SOS programming can capture a wide range of transient engine dynamics with better accuracy, and further achieve better control performance.

关键词： turbojet engine linearisation sum-of-squares programming

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Designing Transient Stability Controllers for Power Systems via sum-of-squares programming 9

Designing Transient Stability Controllers for Power Systems ...

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9th International Conference on Power and Renewable Energy

作者： Qin, Yingjie Liu, Yu Chen, Deyang Wang, Xinwei Miao, Lu Fan, Wei Chen, Zengjie Zhang, Yuhan Liao, Jiemin Guangdong Power Grid Corp Elect Dispatching & Control Ctr Guangzhou Peoples R China South China Univ Technol Sch Elect Power Engn Guangzhou Peoples R China

ISBN: (纸本)9798350377477;9798350377460

Traditional stability controllers are constructed based on the equilibrium points of power systems and fail to meet the performance criteria under large disturbances. In this paper, an algorithm has been proposed to design transient stability controllers for power system using sum-of-squares (SOS) programming which is a powerful technique able to answer many analysis questions for nonlinear systems. Since the SOS programming only deals with polynomial systems, first we recast the power system model into polynomial form. Then we derive the algorithm from the Lyapunov Theory to search for stability controllers of power systems, by introducing the so-called target region and expanding the estimated stability region. The effectiveness of our algorithm is demonstrated on the IEEE 3-machine-9-bus power system.

关键词： power systems transient stability nonlinear controllers sum-of-squares programming

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Optimal Control for a Class of Chaotic Systems Using sum-of-squares programming 38

Optimal Control for a Class of Chaotic Systems Using Sum-of-...

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第三十八届中国控制会议

作者： ZHU Gui LOU Xuyang QIU Fang School of Internet of Things Engineering Jiangnan University College of Science Binzhou University

ISBN: (纸本)9781728123295;9789881563972

This paper proposes a new computational approach for optimal control of chaotic systems based on the polynomial model and Hamilton-Jacobi inequality. Firstly, a class of chaotic systems under a state feedback controller are described as a polynomial model. Secondly, the optimal control problem for the class of chaotic systems is transformed into a state-dependent linear matrix inequality(SDLMI) problem using the Hamilton-Jacobi inequality. Then, by using the sum-of-squares programming method, a feasible solution to the SDLMI problem is obtained with an upper bound on the optimal value and the state feedback law. Finally, numerical simulations are given to illustrate the validity of the proposed method.

关键词： Chaotic system polynomial model optimal control sum-of-squares programming state-dependent linear matrix inequality

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Hamiltonian-driven adaptive dynamic programming for mixed H₂/H_∞ performance using sum-of-squares

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2021年第6期31卷 1941-1963页

作者： Yang, Yongliang Mazouchi, Majid Modares, Hamidreza Univ Sci & Technol Beijing Sch Automat & Elect Engn Key Lab Knowledge Automat Ind Proc Minist Educ Beijing Peoples R China Michigan State Univ Dept Mech Engn E Lansing MI 48824 USA

In this article, the mixed H-2/H-infinity performance optimization is first formulated as a nonzero-sum game, of which the sufficient condition guaranteeing the existence of the Nash equilibrium is derived using the Hamilton-Jacobi (HJ) theory. Then, Hamiltonian-driven inequalities are presented to evaluate the H-2 and H-infinity performances. Using this Hamiltonian-inequality driven approach, the coupled HJ equations arising from finding the Nash equilibrium are relaxed to the HJ inequality constraints. A novel mixed policy iteration (PI) algorithm is developed that uses sum-of-squares (SOS) program in policy evaluation step, and consists of an H-2 performance improvement step and an H-infinity performance guarantee step. This constrained-driven approach allows us to present a PI algorithm that takes into account both robustness and performance objectives. Finally, a numerical simulation is carried out to highlight the efficacy of the proposed framework.

关键词： adaptive dynamic programming Hamiltonian-driven framework mix H-2/H-infinity performance nonzero-sum game sum-of-squares programming

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Exponential Stability and Input-to-State Stability of Polynomial Systems via an Observer with Sporadic Measurements

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CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2025年 1-18页

作者： Cai, Xu Lou, Xuyang Sid, Mohanmed Amine Hohai Univ Coll Artificial Intelligence & Automat Changzhou 213000 Peoples R China Jiangnan Univ Sch IoT Engn Wuxi 214122 Peoples R China Univ Setif 1 Fac Technol Dept Elect Engn Setif 19000 Algeria

In this article, we address the problem of estimating the state of a class of polynomial systems with sporadically available measurements and external disturbance. To begin with, an observer with sporadically available measurements is designed to estimate the states of the polynomial system. We introduce a timer variable to initiate the arrival of new measurements and examine the whole system in a hybrid systems framework. Then, we establish conditions for exponential stability of the polynomial system by employing the observer. Additionally, the designed observer ensures the exponential input-to-state stability for the hybrid error system in the presence of external disturbances. Finally, we provide an illustrative example to demonstrate the validity of the designed observer in estimating the states of the polynomial system and guaranteeing input-to-state stability under external disturbance.

关键词： Polynomial systems sum-of-squares programming Observer Hybrid system Input-to-state stability

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Model-Free Inverse Optimal Control for Completely Unknown Nonlinear Systems by Adaptive Dynamic programming

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2025年

作者： Ahmadi, Peyman Rahmani, Mehdi Shahmansoorian, Aref Imam Khomeini Int Univ Elect Engn Dept Qazvin *** Iran

This article presents an inverse optimal control (IOC) approach for nonlinear polynomial systems based on adaptive dynamic programming (ADP). First, a novel model-based algorithm is presented which provides a control policy, a suboptimal Lyapunov function, and an objective function, that is, minimized by applying the control policy. It is then extended to a model-free approach for systems with a completely unknown model using only the measured input/output data. Compared with existing ADP-based algorithms for nonlinear continuous-time systems, the proposed algorithm is data-based and does not rely on numerical solutions for model approximation. Additionally, it is an off-policy algorithm and avoids the repeat of experiments for control design. Instead, an ADP-based sum-of-squares programming is presented which is computationally tractable. The theoretical guarantee for the stability of the proposed IOC is established using the Lyapunov technique. The performance and efficacy of the proposed approach are investigated through three simulation examples.

关键词： Optimal control Polynomials Linear programming Mathematical models Computational modeling Nonlinear systems Vectors Trajectory Numerical stability Numerical models Adaptive dynamic programming (ADP) inverse optimal control (IOC) sum-of-squares programming unknown nonlinear systems

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