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Iterative distributed model predictive control for nonlinear systems with coupled non-convex constraints and costs

INTERNATIONAL JOURNAL OF ROBUST AND nonLINEAR CONTROL 2024年第11期34卷 7220-7244页

作者： Wu, Jinxian Dai, Li Xia, Yuanqing Beijing Inst Technol Sch Automat Beijing 100081 Peoples R China

This paper proposes a distributed model predictive control (DMPC) algorithm for dynamic decoupled discrete-time nonlinear systems subject to nonlinear (maybe non-convex) coupled constraints and costs. Solving the resulting nonlinear optimal control problem (OCP) using a DMPC algorithm that is fully distributed, termination-flexible, and recursively feasible for nonlinear systems with coupled constraints and costs remains an open problem. To address this, we propose a fully distributed and globally convergence-guaranteed framework called inexact distributed sequential quadratic programming (IDSQP) for solving the OCP at each time step. Specifically, the proposed IDSQP framework has the following advantages: (i) it uses a distributed dual fast gradient approach for solving inner quadratic programming problems, enabling fully distributed execution;(ii) it can handle the adverse effects of inexact (insufficient) calculation of each internal quadratic programming problem caused by early termination of iterations, thereby saving computational time;and (iii) it employs distributed globalization techniques to eliminate the need for an initial guess of the solution. Under reasonable assumptions, the proposed DMPC algorithm ensures the recursive feasibility and stability of the entire closed-loop system. We conduct simulation experiments on multi-agent formation control with non-convex collision avoidance constraints and compare the results against several benchmarks to verify the performance of the proposed DMPC method.

关键词： distributed model predictive control non-convex constraints sequential quadratic programming

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Global optimization method with dual Lipschitz constant estimates for problems with non-convex constraints

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SOFT COMPUTING 2020年第16期24卷 11853-11865页

作者： Strongin, Roman Barkalov, Konstantin Bevzuk, Semen Lobachevsky State Univ Nizhni Novgorod Nizhnii Novgorod 603950 Russia

This paper considers the constrained global optimization problems, in which the functions are of the "black-box" type and satisfy the Lipschitz condition. The algorithms for solving the problems of this class require the use of adequate estimates of the a priori unknown Lipschitz constants for the problem functions. A novel approach presented in this paper is based on a simultaneous use of two estimates of the Lipschitz constant: an overestimated and an underestimated one. The upper estimate provides the global convergence, whereas the lower one reduces the number of trials necessary to find the global optimizer with the required accuracy. The considered algorithm for solving the constrained problems does not use the ideas of the penalty function method;each constraint of the problem is accounted for separately. The convergence conditions of the proposed algorithm are formulated in the corresponding theorem. The results of the numerical experiments on a series of multiextremal problems with non-convex constraints demonstrating the efficiency of the proposed scheme of dual Lipschitz constant estimates are presented.

关键词： Global optimization Multiextremal problems non-convex constraints Lipschitz constant estimates Dimensionality reduction Numerical methods

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Computation of the maximal invariant set of discrete-time linear systems subject to a class of non-convex constraints

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AUTOMATICA 2021年 125卷 109463-109463页

作者： Wang, Zheming Jungers, Raphael M. Ong, Chong Jin UCLouvain ICTEAM Inst B-1348 Louvain La Neuve Belgium Natl Univ Singapore Dept Mech Engn Singapore 117576 Singapore

We consider the problem of computing the maximal invariant set of discrete-time linear systems subject to a class of non-convex constraints that admit quadratic relaxations. These non-convex constraints include semialgebraic sets and other smooth constraints with Lipschitz gradient. With these quadratic relaxations, a sufficient condition for set invariance is derived and it can be formulated as a set of linear matrix inequalities. Based on the sufficient condition, a new algorithm is presented with finite-time convergence to the actual maximal invariant set under mild assumptions. This algorithm can be also extended to switched linear systems and some special nonlinear systems. The performance of this algorithm is demonstrated on several numerical examples. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Invariant sets non-convex constraints Switched linear systems Semi-algebraic sets

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Real-time critical safety curve and predictive control based trajectory planning for complex shaped rotating spacecraft proximity

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ADVANCES IN SPACE RESEARCH 2025年第4期75卷 3891-3913页

作者： Wang, Jingxian Chen, Zhijun Chen, Rong Zhao, Yong Bai, Yuzhu Natl Univ Def Technol Coll Aerosp Sci & Engn Changsha 410073 Peoples R China

This paper presents a real-time trajectory planning and tracking control framework for a complex-shaped chaser to approach a rotating target with complex shapes. The framework is divided into two layers: trajectory planning and tracking control. Firstly, considering the complex shapes and relative attitude constraints of the target and chaser, a real-time critical safety curve (RT-CSC) is proposed as a collision avoidance constraint combined with the rotational motion of the target. Secondly, the multi-constraint improved disturbed fluid method (MCIDFM) is proposed. The flow field velocity is designed by considering proximity time optimization under boundary and chaser thruster performance constraints. Trajectory planning is achieved by making the flow field bypass the non-convex keep-out zone formed by the RT-CSC. Then, the tracking control is implemented using a model predictive control method and the closed-loop asymptotic stability is demonstrated. Simulation results demonstrate the proposed methods' smoothness, safety, and strong approach capabilities. Rapidity and robustness are also reflected in simulation analysis. (c) 2024 Published by Elsevier B.V. on behalf of COSPAR.

关键词： Rotating spacecraft Trajectory planning Complex shape non-convex constraints Collision avoidance

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Optimal control of a solar sail

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OPTIMAL CONTROL APPLICATIONS & METHODS 2024年第6期45卷 2837-2855页

作者： Herasimenka, Alesia Dell'Elce, Lamberto Caillau, Jean-Baptiste Pomet, Jean-Baptiste Univ Cote Azur CNRS Inria LJAD Nice France

Optimal control of a solar sail orbiting around a fixed center of mass is considered. The sail is modelled as a plane surface with two sides having similar optical properties. The control is assumed to be the attitude of the sail and is represented as an element of the projective plane. Mapping this plane into the three dimensional ambient space to compute the actual force generated by a given attitude results in a generally non-convex set of admissible control values. A suitable convex relaxation is introduced to study the optimality system associated with maximising the change of the sail orbital parameters in a given direction along one orbit. Existence for both the relaxed and the original problems are deduced. Building on previous works, a refined analysis of the control structure is given, proving rigorously that it contains only switchings, and a global bound of the number of switchings is obtained. In order to compute effective solutions, a multiple shooting approach is retained that is well suited for systems with a sequence of switchings between various control subarcs. Three issues are addressed: initialization of shooting by means a tailored semi-definite relaxation that takes advantage of good convergence properties of modern convex optimization algorithms;changes in the control structure that are accommodated by coupling shooting with differential continuation;implicit character of the Hamiltonian maximization when using Pontrjagin maximum principle that is taken care of by incorporating the associated equation for the dynamical feedback into the shooting procedure. The method is illustrated on an example from NASA for which the sail inclination is optimally changed over one orbital period. The optimal control of a solar sail is studied, and a numerical case coming from NASA is treated. The problem is solved using an adequate semi-definite relaxation of the problem to initialize a multiple shooting procedure. Changes in the control structure are dealt

关键词： differential continuation multiple shooting non-convex constraints SDP relaxation solar sailing

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SOLVING NET-CONSTRAINED CLUSTERING PROBLEM

JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS

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JOURNAL OF nonLINEAR AND VARIATIONAL ANALYSIS 2024年第6期8卷 987-1012页

作者： Kepalas, Mindaugas Zilinskas, Julius Vilnius Univ Inst Data Sci & Digital Technol Vilnius Lithuania

In this paper, we consider a planar clustering problem with location constraints for cluster centers. A simple adaptation of the k-means algorithm solving the presented problem to local optimality is outlined. We further show that our problem can be stated as a MIQCP (mixed-integer-quadratically-constrained-programming) problem, and some results to solve the formulated problem to global optimality with a popular solver are presented. We also present a specialized enumeration algorithm which can be used to find the global optima of the problem and our numerical experiments indicate that this approach is a better choice in comparison to solving the formulated MIQCP problem with a general solver.

关键词： Cluster-center-location constraints Constrained minimum sum of squares clustering Constrined multi-souce Weber problem It-means algorithm Location-allocation paradigm non-convex constraints

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Trajectory Planning for Complex Shaped Spacecraft Proximity Based on Critical Safety Curve and Disturbed Fluid

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IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS 2023年第5期59卷 5930-5942页

作者： Wang, Jingxian Chen, Rong Chen, Zhijun Zhao, Yong Bai, Yuzhu Chen, Xiaoqian Natl Univ Def Technol Coll Aerosp Sci & Engn Changsha 410073 Peoples R China Chinese Acad Mil Sci Natl Innovat Inst Def Technol Beijing 100071 Peoples R China

Recent research on on-orbit service rarely considers the complex shapes of servicing spacecraft (chaser) and the target simultaneously, which could cause collision problems in ultraclose-range proximity. This article presents a novel trajectory planning method via critical safety curve (TPCSC). The core of the framework is the construction of collision avoidance constraints called critical safety curve (CSC) using geometrized mathematical methods. CSC has good mathematical properties and innovatively combines the complex shape and relative attitude constraints of two spacecraft. Subsequently, TPCSC proposes an improved disturbed fluid method based on CSC that can handle non-convex constraints to generate smooth approach trajectories. Finally, the framework can achieve ultraclose-range proximity between spacecraft with complex shapes under complex non-convex constraints. The simulation results indicate that the planning of TPCSC is rapid, and the formed trajectory is safe, smooth, and easy to track.

关键词： Shape Space vehicles Trajectory Collision avoidance Trajectory planning Safety Fluids Collision avoidance complex shape non-convex constraints spacecraft proximity trajectory planning

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A Navigation Algorithm for UUVs to Avoid Shape Changeable Obstacles 14

A Navigation Algorithm for UUVs to Avoid Shape Changeable Ob...

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14th International Conference on Computer and Automation Engineering (ICCAE)

作者： Zhang, Yang Zhang, Jian Univ New South Wales Sch Elect Engn & Telecommun Sydney NSW Australia

ISBN: (纸本)9781665483797

In order to guide an undersea unmanned vehicle (UUV) avoiding obstacles in an underwater environment, an navigation algorithm is proposed in this paper. It can be applied to planar environment, the shape of obstacles could be changeable. This method combines local path planning and global path planning together, switching between two modes so as to safely navigate the UUV' s way. In order to show the performance of the proposed algorithm, the simulation results are presented by Matlab. The reason why we promoting this algorithm is that it is a computational efficient algorithm, comparing with the prior ones, the cost could be saved while achieving the expected results successfully.

关键词： undersea unmanned vehicle navigation algorithm obstacle avoidance shape changeable obstacles non-convex constraints

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Energy Efficiency of NOMA Network under Fast Fading Channel 11

Energy Efficiency of NOMA Network under Fast Fading Channel

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11th International Conference on Communications, Circuits and Systems (ICCCAS)

作者： Li, Shuang Wu, Pengfei An, Fuhua Tibet Univ Sch Informat Sci & Technol Lhasa Peoples R China Tibet Univ Sch Sci Lhasa Peoples R China

ISBN: (纸本)9781665469890

For downlink non-orthogonal multiple access (NOMA) systems under fast time-varying fading channels, a power allocation scheme to maximize system energy efficiency (EE) is proposed. Based on satisfying the users' quality of service (QoS), an optimization problem of power allocation among users that maximizes the system energy efficiency is established. Due to the fractional objective function and the non-convex constraints, the optimization problem is non-convex and it is difficult to obtain accurate solutions efficiently. First, we propose an iterative algorithm to solve the power allocation scheme that maximizes energy efficiency within a single subchannel, and then allocate power to users by bisection method. The simulation results show that the proposed scheme has good effect in EE and good convergence performance.

关键词： non-orthogonal multiple access (NOMA) energy efficiency (EE) non-convex constraints

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Parallel Global Search Algorithm with Local Tuning for Solving Mixed-Integer Global Optimization Problems

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LOBACHEVSKII JOURNAL OF MATHEMATICS 2021年第7期42卷 1492-1503页

作者： Barkalov, K. A. Gergel, V. P. Lebedev, I. G. Lobachevskii State Univ Nizhny Novgorod Nizhnii Novgorod 603950 Russia

In this paper, we consider mixed-integer global optimization problems and propose a parallel algorithm for solving problems of this class based on information-statistical approach for solving continuous global optimization problems. Within this algorithm, we suggest using a local tuning scheme based on the assumption that the multiextremality of the discussed problem is weak. We also compare the sequential version of the algorithm with other similar methods. The effectiveness of parallelizing the algorithm has been confirmed by solving a series of mixed-integer global optimization problems on the Lobachevskii supercomputer.

关键词： global optimization non-convex constraints mixed-integer problems local tuning parallel algorithms

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