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Noniterative convex programming-Based Optimal Guidance With Field-of-View and Acceleration Limits

IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS 2025年第2期61卷 5477-5487页

作者： Jung, Cheol-Goo Kim, Boseok Lee, Chang-Hun Korea Adv Inst Sci & Technol KAIST Dept Aerosp Engn Daejeon 34141 South Korea

In this study, a noniterative, convex programming-based optimal guidance is proposed to address field-of-view and acceleration constraints while achieving terminal impact angles. To circumvent the problems of successive convex programming, such as convergence stability and local optimality, the original guidance problem is reformulated as a quadratic programming problem by employing a limited approximation of look angle. Furthermore, a range-to-go weighted cost function is utilized, which allows the acceleration profile to be shaped based on the gain of the weighting function. A pseudo-spectral method is adopted in the transcription process due to its high solution accuracy. The proposed method rapidly provides optimal guidance solutions without iterations and convergence issues, which makes it suitable for real-time implementation. The performance and utility of the proposed method are demonstrated via extensive simulations.

关键词： convex functions Aerodynamics Cost function Aerospace and electronic systems Nonlinear dynamical systems Convergence Real-time systems Missile guidance Line-of-sight propagation Trajectory optimization Computational guidance convex programming field-of-view and acceleration limits impact angle control optimal guidance

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Max-Linear Regression by convex programming

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IEEE TRANSACTIONS ON INFORMATION THEORY 2024年第3期70卷 1897-1912页

作者： Kim, Seonho Bahmani, Sohail Lee, Kiryung Ohio State Univ Dept Elect & Comp Engn Columbus OH 43220 USA Georgia Inst Technol Sch Elect & Comp Engn Atlanta GA 30332 USA

We consider the multivariate max-linear regression problem where the model parameters beta(1),& mldr;,beta(k )is an element of R-p need to be estimated from n independent samples of the (noisy) observations y = max(1 <= j <= k)beta(T)(j)x + noise . The max-linear model vastly generalizes the conventional linear model, and it can approximate any convex function to an arbitrary accuracy when the number of linear models k is large enough. However, the inherent nonlinearity of the max-linear model renders the estimation of the regression parameters computationally challenging. Particularly, no estimator based on convex programming is known in the literature. We formulate and analyze a scalable convex program given by anchored regression (AR) as the estimator for the max-linear regression problem. Under the standard Gaussian observation setting, we present a non-asymptotic performance guarantee showing that the convex program recovers the parameters with high probability. When the k linear components are equally likely to achieve the maximum, our result shows a sufficient number of noise-free observations for exact recovery scales as k(4)p up to a logarithmic factor. This sample complexity coincides with that by alternating minimization (Ghosh et al., 2021). Moreover, the same sample complexity applies when the observations are corrupted with arbitrary deterministic noise. We provide empirical results that show that our method performs as our theoretical result predicts, and is competitive with the alternating minimization algorithm particularly in presence of multiplicative Bernoulli noise. Furthermore, we also show empirically that a recursive application of AR can significantly improve the estimation accuracy.

关键词： Nonlinear regression convex programming max-linear model empirical processes sample complexity

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Robust optimal powered descent guidance via model predictive convex programming

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AEROSPACE SCIENCE AND TECHNOLOGY 2025年 159卷

作者： Xiao, Yizheng Gong, Youmin Mei, Jie Ma, Guangfu Wu, Weiren Harbin Inst Technol Sch Aerosp Sci Shenzhen 518055 Guangdong Peoples R China Harbin Inst Technol Sch Intelligence Sci & Engn Shenzhen 518055 Guangdong Peoples R China Deep Space Explorat Lab Beijing 100089 Peoples R China

This paper investigates the robust fuel-optimal guidance problem for powered descent landing under uncertainty. A robust optimal control problem (OCP) with stochastic dynamics and constraints is first constructed to ensure both optimality and safety. The polynomial chaos expansion (PCE)-based uncertainty quantification technique is then employed to convert the stochastic OCP into a high-dimensional deterministic OCP, which, while tractable, involves a large number of decision variables and is computationally intensive. To mitigate this issue, the dynamics are convexified within the model predictive convex programming (MPCP) framework, reducing the number of decision variables by establishing the sensitivity relationship between state and control corrections. Furthermore, convexification techniques including lossless convexification and successive convexification are applied to convexify the nonlinear inequality constraints. To enhance computational efficiency, a dimension reduction method is also introduced. After solving the robust OCP through convex optimization, a closed-loop guidance algorithm based on receding horizon strategy is proposed to address navigational errors. Numerical simulations demonstrate the advantages of this guidance algorithm.

关键词： Powered descent guidance convex programming Trajectory optimization Uncertainty propagation Robust optimization

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Dispersion Sensitive Optimal Control: A Conditional Value-at-Risk-Based Tail Flattening Approach via Sequential convex programming

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IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY 2024年第6期32卷 2468-2475页

作者： Echigo, Kazuya Sheridan, Oliver Buckner, Samuel Acikmese, Behcet Univ Washington William E Boeing Dept Aeronaut & Astronaut Seattle WA 98195 USA

In this brief, we propose a sequential convex programming (SCP) framework for minimizing the terminal state dispersion of a stochastic dynamical system about a prescribed destination-an important property in high-risk contexts such as spacecraft landing. Our proposed approach seeks to minimize the conditional value-at-risk (CVaR) of the dispersion, thereby shifting the probability distribution away from the tails. This approach provides an optimization framework that is not overly conservative and can accurately capture more information about true distribution, compared with methods which consider only the expected value, or robust optimization methods. The main contribution of this brief is to present an approach that: 1) establishes an optimization problem with CVaR dispersion cost 2) approximated with one of the two novel surrogates which is then 3) solved using an efficient SCP algorithm. In 2), two approximation methods, a sampling approximation (SA) and a symmetric polytopic approximation (SPA), are introduced for transforming the stochastic objective function into a deterministic form. The accuracy of the SA increases with sample size at the cost of problem size and computation time. To overcome this, we introduce the SPA, which avoids sampling by using an alternative approximation and thus offers significant computational benefits. Monte Carlo simulations indicate that our proposed approaches minimize the CVaR of the dispersion successfully.

关键词： Dispersion Cost function Optimization Optimal control Gaussian distribution Tail Uncertainty convex programming nonlinear programming stochastic programming

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Deep Reinforcement Learning-Assisted convex programming for AC Unit Commitment and Its Variants

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IEEE TRANSACTIONS ON POWER SYSTEMS 2024年第4期39卷 5561-5574页

作者： Sayed, Ahmed Rabee Zhang, Xian Wang, Guibin Wang, Yi Shaaban, Mostafa Shahidehpour, Mohammad Harbin Inst Technol Sch Mech Engn & Automat Shenzhen 518055 Peoples R China Khalifa Univ Dept Elect Engn & Comp Sci Abu Dhabi 127788 U Arab Emirates Cairo Univ Fac Engn Giza 12613 Egypt Shenzhen Univ Coll Mechatron & Control Engn Shenzhen 518060 Peoples R China Amer Univ Sharjah Dept Elect Engn Sharjah 26666 U Arab Emirates IIT ECE Dept Chicago IL 60616 USA

Unit commitment (UC) is one of the core decisions in electricity markets and system planning. Existing optimization methods either use DC approximation of network constraints or decompose and relax them into subproblems, which may lead to suboptimal/infeasible decisions or require execution times longer than those for the industry. Recent advances in machine learning techniques have proven their ability to find fast near-optimal UC decisions. However, they suffer from the curses of dimensionality and/or lack feasibility guarantees. This paper proposes a new hybrid deep reinforcement learning algorithm for the UC problem with AC network constraints (AC-UC). The problem is formulated as a modified-action Markov decision process model and the fundamental soft actor-critic (SAC) algorithm is enhanced to deal with hybrid action spaces. To ensure the solution feasibility, two action filters are designed based on logic constraints of generation units and sequential convex programming for the discrete and continuous actions, respectively. The hybrid SAC is improved by embedding the two filters and a prioritized experience buffer for fast convergence and stable learning. Simulation results on four test systems verify the effectiveness of the proposed approach and the superiority over traditional methods in computational efficiency and feasibility. Moreover, the presented method is extended to solve stochastic UC and security-constraint UC problems.

关键词： Load flow Generators Uncertainty programming Power systems Computational modeling Mathematical models Reinforcement learning convex programming unit commitment optimal power flow uncertainty

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Multi-step inertial strictly contractive PRSM algorithms for convex programming problems with applications

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2024年 437卷

作者： Deng, Zhao Han, Deren Wuhan Univ Sci & Technol Hubei Prov Key Lab Syst Sci Met Proc Wuhan 430065 Peoples R China Wuhan Univ Sci & Technol Coll Sci Wuhan 430065 Peoples R China Beihang Univ Sch Math Sci Beijing 100191 Peoples R China

The Peaceman-Rachford splitting method (PRSM) has been widely studied in recent years because of its excellent numerical performance, especially with inertial acceler-ation. In this paper, we propose a multi-step inertial strictly contractive PRSM (shortly, MISCPRSM) for solving convex optimization problems, which has not been studied before. This paper aims to give an exhaustive analysis of the value relationship between multiple inertial parameters. The second subproblem utilizes an additional customized indefinite proximal term in order to obtain a closed-form solution. The global conver-gence and complexity result of the introduced method are analyzed by using variational inequality and basic inequalities. Finally, through simulation and computed tomography experiments, the effectiveness and robustness of the MISCPRSM are proved, and the detailed values of inertial parameters are given.& COPY;2023 Elsevier B.V. All rights reserved.

关键词： convex programming Peaceman-Rachford splitting method Inertial step Indefinite proximal term Variational inequality Global convergence

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Optimal Midcourse Guidance for Dual-Pulse Rocket Using Pseudospectral Sequential convex programming

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2023年第7期46卷 1425-1436页

作者： Kim, Boseok Lee, Chang-Hun Korea Adv Inst Sci & Technol Daejeon 34141 South Korea

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A dual-primal balanced augmented Lagrangian method for linearly constrained convex programming

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2023年第1期69卷 1015-1035页

作者： Xu, Shengjie Harbin Inst Technol Dept Math Harbin 150001 Peoples R China Southern Univ Sci & Technol Dept Math Shenzhen 518055 Peoples R China

Most recently, a balanced augmented Lagrangian method (ALM) has been proposed by He and Yuan for the canonical convex minimization problem with linear constraints, which advances the original ALM by balancing its subproblems, improving its implementation and enlarging its applicable range. In this paper, we propose a dual-primal version of the newly developed balanced ALM, which updates the new iterate via a conversely dual-primal iterative order formally. The new algorithm inherits all advantages of the prototype balanced ALM, and it can be extended to more general separable convex programming problems with both linear equality and inequality constraints. The convergence analysis of the proposed method can be well conducted in the context of variational inequalities. In particular, by some application problems, we numerically validate that these balanced ALM type methods can outperform existing algorithms of the same kind significantly.

关键词： Augmented Lagrangian method convex programming Dual-primal Proximal point algorithm Variational inequality

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A Robust Fixed-Time Piecewise Dynamic Network for convex programming

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NEURAL PROCESSING LETTERS 2023年第8期55卷 11541-11558页

作者： Wang, Dan Li, Huiyun Liu, Xin-Wei Hebei Univ Technol Sch Artificial Intelligence Tianjin 300401 Peoples R China Hebei Univ Technol Inst Math Tianjin 300401 Peoples R China

To solve optimization problems in real-time and robustly, we propose a piecewise dynamic network for solving convex programming constrained by inequalities and linear equalities. The network is proposed based on the penalty method and includes two stages. The network in the first stage is a zeroing dynamic network to solve an equation. It makes sure that for any initial point, the state of the network enters the linear equality constraint set within a fixed time. The optimal solution to this convex programming is obtained by the network in the second stage which is a gradient-type dynamic network. A lower bound of the penalty parameter is given to ensure the validity of the network, which makes up for the deficiency of the existing works. A suitable activation function is introduced to promote fixed-time convergence of the network and to improve its anti-interference capability. As a result, the proposed piecewise dynamic network is robust against additional interferences. Some tests are presented to show the effectiveness of our network.

关键词： Piecewise dynamic network convex programming Exact penalty method Fixed-time convergence Robustness

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Rapid sizing of a hydrogen-battery storage for an offshore wind farm using convex programming

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INTERNATIONAL JOURNAL OF HYDROGEN ENERGY 2023年第58期48卷 21946-21958页

作者： Ma, Zetao Tian, Tian Cui, Qiong Shu, Jie Zhao, Jianguang Wang, Hao Chinese Acad Sci Guangzhou Inst Energy Convers Key Lab Renewable Energy Guangzhou 510640 Peoples R China Shanwei Branch Adv Energy Sci & Technol Guangdong Shanwei 529599 Peoples R China

This paper carries out a comprehensive analysis on an offshore wind farm equipped with a hybrid storage comprised of hydrogen and battery, from the perspective of economic effectiveness. To rapidly evaluate the system economy, a computationally efficient convex program that takes the nonlinear storage efficiencies into account is provided, which can simultaneously and synergistically optimize the storage sizing and energy management over a long offshore wind cycle. In the analysis, a case study on the optimal configuration and operation of the hybrid storage is thoroughly investigated, answering what the scalings are and how the storage functions in the offshore wind farm. Comparisons to other offshore wind farms with none or only one storage type further demonstrate the advantage of combining hydrogen plant and battery. Influences of the offshore wind electricity price of grid parity and hydrogen price on the system economies, in the terms of total annual cost, net annual profit and hydrogen production cost, are also discussed, revealing sensitivity and dependency of the scalings. Finally, this paper presents the future potential of applying hydrogen plant in the offshore wind farm, from the angles of hydrogen production cost and energy saving. & COPY;2023 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

关键词： Offshore wind farm Hydrogen storage Optimal sizing Energy management convex programming

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