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A global linearization approach to solve nonlinear nonsmooth constrained programming problems

COMPUTATIONAL & APPLIED MATHEMATICS 2011年第2期30卷 427-443页

作者： Vaziri, A. M. Kamyad, A. V. Jajarmi, A. Effati, S. Ferdowsi Univ Mashhad Dept Appl Math Mashhad Iran Ferdowsi Univ Mashhad Dept Elect Engn Mashhad Iran

In this paper we introduce a new approach to solve constrained nonlinear non-smooth programming problems with any desirable accuracy even when the objective function is a non-smooth one. In this approach for any given desirable accuracy, all the nonlinear functions of original problem (in objective function and in constraints) are approximated by a piecewise linear functions. We then represent an efficient algorithm to find the global solution of the later problem. The obtained solution has desirable accuracy and the error is completely controllable. One of the main advantages of our approach is that the approach can be extended to problems with non-smooth structure by introducing a novel definition of Global Weak Differentiation in the sense of L(1) norm. Finally some numerical examples are given to show the efficiency of the proposed approach to solve approximately constraints nonlinear non-smooth programming problems.

关键词： nonlinear programming problem non-smooth analysis equicontinuity uniform continuity

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Engine Idle Speed Control Using nonlinear Model Predictive Control

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IFAC Proceedings Volumes 2013年第21期46卷 171-176页

作者： F. Xu H. Chen X. Gong Y.F. Hu State Key Laboratory of Automotive Simulation and Control Jilin University Changchun 130025 P.R. China Department of Control Science and Engineering Jilin University Changchun 130025 P.R. China

In this paper, a nonlinear model predictive controller is presented for idle speed control (ISC) problem of spark ignition (SI) engine. The objective is to maintain the engine speed at a prescribed set-point through actuating a electronic throttle, and minimize the effects of load torque disturbances and model uncertainties. The nonlinear programming (NLP) problem formed by nonlinear model predictive control (NMPC) is solved by using particle swarm optimization (PSO) algorithm. Simulation results show that the designed nonlinear model predictive controller can achieve satisfactory performance for ISC.

关键词： Engine idle speed control nonlinear model predictive control nonlinear programming problem uncertainty particle swarm optimization algorithm

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Ascent Trajectory Optimization of Launch Vehicles with Air-Breathing Propulsion

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IFAC-PapersOnLine 2019年第12期52卷 274-279页

作者： Vijith Mukundan Arnab Maity Shashi Ranjan Kumar U P Rajeev

This paper aims to investigate optimization of a highly constrained three-dimensional trajectory of a launch vehicle stage powered by air-breathing engine, with oblate gravitational field. The trajectories of such vehicles are difficult to optimize, owing to strong nonlinear coupling between the thrust, aerodynamics and the vehicle’s states, and stringent constraints on structural load and aerodynamic heating. The objective of trajectory optimization is to impart maximum velocity at a desired altitude and direction, with minimum fuel consumption, using angle of attack and engine throttle as control inputs. Path constraints on dynamic pressure, bending moment, and heat flux as well as control constraints need to be satisfied. Trajectory is optimized using the approach of discretization of control variables, which converts this optimal control problem to a nonlinear programming (NLP) problem. This NLP problem is solved using a metaheuristic method (harmony search optimization), and the sensitivity of the solution with respect to discretization is also analyzed. The versatility of trajectory planning method is demonstrated by solving the problem with different initial conditions, objectives and constraints.

关键词： Trajectory launch vehicle optimization constraints harmony search nonlinear programming problem

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Switched System Optimal Control Based on Parameterizations of the Control Vectors and Switching Instants

Switched System Optimal Control Based on Parameterizations o...

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2011 China Control and Decision Conference(2011中国控制与决策会议 CCDC)

作者： Rui-yan ZHAO Shu-rong LI College of information and control engineering China University of Petroleum Dongying 257061 China

This paper presents a new approach for solving optimal control problems for switched systems with prespecified order of the sequence of subsystems. For such problems, we need to seek both the optimal switching instants and the optimal continuous inputs. The optimal control problem for hybrid systems is transcribed into an equivalent problem parameterized by the switching instants and the control vectors. Through the discretization of the control space, the control vector is approximated by the B-spline functions. In order to search for the optimal switching instants, we introduce the normalized time variable and do normalized treatment for the control arcs. The optimal switching control problem is converted to a nonlinear programming problem. The control profiles and switching instants act as decision variables. Two examples are solved using the proposed method so as to demonstrate the effectiveness of the method proposed.

关键词： Switched systems Optimal control problem B-spline functions nonlinear programming problem

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Minimum Jerk Trajectory Generation of a Quadrotor Based on the Differential Flatness

Minimum Jerk Trajectory Generation of a Quadrotor Based on t...

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2014中国制导、导航与控制学术会议

作者： Jing Yu Zhihao Cai Yingxun Wang Science and Technology on Aircraft Control Laboratory Beihang UniversityBeijing100191 China National Key Laboratory of Science and TechnologyBeihang UniversityBeijing100191 China National Key Laboratory of Science and TechnologyBeihang UniversityBeijing100191China

ISBN: (纸本)9781479946983

In order to improve smoothness of task trajectories,this paper describe algorithms to generate smooth-optimal trajectories based on the differential flatness of quadrotor.B-spline is used to parameterize the selected flat outputs,and the dynamic constraints or kinematical constraints on quadrotor are transferred to the control point constraints of *** trajectory generation is then considered an optimal control problem by adopting the integral of squared *** then the optimal solution is solved by transforming the optimal control problem into a nonlinear programming *** last the smoothness-optimal trajectories are *** results show that,this method can smooth out movements and minimize the accumulative jerk which can decrease trajectory tracking errors effectively.

关键词： helicopters nonlinear programming optimal control splines (mathematics) trajectory control B-spline differential flatness dynamic constraints kinematical constraints minimum jerk trajectory generation nonlinear programming problem optimal control problem quadrotor smooth-optimal trajectories trajectory tracking errors Aerospace electronics Equations Optimal control programming Splines (mathematics) Trajectory Vectors

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Time-Optimal Attitude Maneuver for Underactuated Spacecraft based on Pseudospectral Method

Time-Optimal Attitude Maneuver for Underactuated Spacecraft ...

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2014中国制导、导航与控制学术会议

作者： Dongxia Wang Jinxian Zhao Caibo Hu Department of Operating Control and Technology Beijing Satellite Navigation CenterBeijing100094China

ISBN: (纸本)9781479946983

the time-optimal attitude maneuver problem of a rigid spacecraft with only two control torques along its principal axes is studied using Radau Pseudospectral Method (RPM).The asymmetric and symmetric spacecraft have been considered in ***,we establish the attitude dynamical models of asymmetric and symmetric spacecraft with two controls,and use (w,z) parameter to describe the attitude ***,according to the general optimal control problem like Bloza form,the maneuver time minimum as the performance index is selected to be optimized,simultaneously considered the control inputs and angular velocities boundary in the practical application of ***,the optimal maneuver problem is discretized based on the Radau Pseudospectral Method and then converted into a nonlinear programming *** for asymmetric and symmetric system are carried out based on GPOPS toolbox and the analysis results illustrate the feasibility the proposed algorithm.

关键词： angular velocity control attitude control motion control nonlinear programming optimal control space vehicles torque control Bloza form GPOPS toolbox RPM Radau pseudospectral method angular velocities boundary asymmetric spacecraft attitude dynamical models attitude motion control torques maneuver time nonlinear programming problem optimal control problem performance index rigid spacecraft symmetric spacecraft time-optimal attitude maneuver problem underactuated spacecraft Actuators Angular velocity Attitude control Interpolation Optimal control Polynomials Space vehicles Space vehicles attitude control Optimal control Rigid spacecraft Torque control angular velocity control performance indicators ANGULAR VELOCITY revolutions per minute Attitude maneuvers nonlinear programming Motor Control actuators Polynomial Interpolation

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Cooperative Trajectory Planning for Multi-UCAV Performing Air-to-Ground Target Attack Missions

Cooperative Trajectory Planning for Multi-UCAV Performing Ai...

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2013 3rd International Conference on Advanced Measurement and Test(AMT 2013)

作者： Xueqiang Gu Yu Zhang Shaofei Chen Jing Chen College of Mechatronics and Automation National University of Defense Technology

The problem of planning flight trajectories is studied for multiple unmanned combat aerial vehicles(UCAVs)performing a cooperated air-to-ground target attack(CA/GTA)*** constraints including individual and cooperative constraints are modeled,and an objective function is ***,the cooperative trajectory planning problem is formulated as a cooperative trajectory optimal control problem(CTP-OCP).Moreover,in order to handle the temporal constraints,a notion of the virtual time based strategy is ***,a planning algorithm based on the differential flatness theory and B-spline curves is developed to solve the ***,the proposed approach is demonstrated using a typical CA/GTA mission scenario,and the simulation results show that the proposed approach is feasible and effective.

关键词： Multi-UCAV air-to-ground attack Cooperative trajectory planning Differential flatness B-spline curve nonlinear programming problem

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Robust control design method for uncertain system using a set of measurements

Robust control design method for uncertain system using a se...

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American Control Conference

作者： S. Khadraoui H. Nounou M. Nounou A. Datta S. P. Bhattacharyya Department of Electrical and Computer Engineering Texas A&M University at Qatar Doha Qatar Department of Chemical Engineering Texas A&M University at Qatar Doha Qatar Department of Electrical and Computer Engineering Texas A&M University College Station TX USA 77843

ISBN: (纸本)9781479901777

This work deals with the design of robust fixed-structure controllers for uncertain systems based on a finite set of measured data. This set of measurements is given in the frequency domain. In the current control design approaches, controllers are usually designed based on plant models obtained on the basis of measured data. However, due to various forms of uncertainties such as: plant parameter variations, external disturbances, measurement noise, etc, such models are unable to perfectly describe the behavior of the physical system. Hence, degradation in the controller performance is expected due to such uncertainties and errors associated with the identification process. For that, we propose a new control technique that uses the uncertain measurements to directly design robust controllers, for a class of uncertainties, without going through the use of identification process. In such a proposed design method, interval techniques are introduced to bound plant uncertainties. Its main principle is to find the set of admissible values of the controller parameters so that the family of all possible frequency responses of the closed-loop system lies between an upper and lower bounds of a desired frequency response. This problem is formulated as a nonlinear programming problem which can easily be solved to characterize the solution set of the controller parameters. The main feature of our proposed approach is that it enables to design robust fixed-structure controllers by taking into account the plant uncertainties. Moreover, since no mathematical model is needed in the controller synthesis, the design process does not depend on the increasing order and complexity of the system. A simulation example is presented to illustrate and validate the efficacy of the proposed method.

关键词： Data-based control Robust controller Plant uncertainty Interval analysis Frequency response template nonlinear programming problem Robust controllers Uncertainty Controllers design approach frequency response uncertain systems Control technology plant models Plant uncertain Set (Psychology) Set Database Frequency-domain analysis

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Comparison of LPM,GPM and RPM for Optimization of Low-Thrust Earth-Mars Rendezvous Trajectories

Comparison of LPM,GPM and RPM for Optimization of Low-Thrust...

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2014中国制导、导航与控制学术会议

作者： Yukai Wang Yongsheng Zhu Xiuqiang Jiang Shuang Li College of Astronautics Nanjing University of Aeronautics and AstronauticsNanjing 210016China Shanghai Engineering Center for MicrosatellitesShanghai 201203China

ISBN: (纸本)9781479946983

The performance comparison is performed among Legendre (LPM),Gauss (GPM),and Radau (RPM) pseudospectral methods,which are utilized to optimize the low-thrust Earth-Mars rendezvous *** order to provide a fair comparison condition,a shape-based approach is implemented to provide equivalent initial guesses for all the next accurate optimization,and the SQP algorithm is used to solve the resulting nonlinear programming problem for each of the *** behavior and performance of the three pseudospectral methods are compared on the mission of Earth-Mars Rendezvous in 2013.

关键词： Earth Mars quadratic programming trajectory optimisation (aerospace) GPM Gauss pseudospectral methods LPM Legendre pseudospectral methods RPM Radau pseudospectral methods SQP algorithm low-thrust Earth-Mars rendezvous trajectory optimization nonlinear programming problem sequential quadratic programming algorithm shape-based approach Approximation methods Optimal control Optimization Polynomials Space vehicles Trajectory Vectors

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The reflector shape adjusting methods for cable mesh deployable antenna

The reflector shape adjusting methods for cable mesh deploya...

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Systems and Control in Aerospace and Astronautics, 2006. ISSCAA 2006. 1st International Symposium on

作者： Jiejian Di Baoyan Duan Fei Zheng School of Electromechanical Engineering Xidian University Xi'an China

ISBN: (纸本)0780393953

Considering the characteristics of mesh reflector antenna, two adjusting methodologies are proposed in this paper. One is to search for highest reflector precision whilst satisfying nonlinear constrains, such as eigen frequency, material strength and sides by finding the optimum adjusting cables' increment. The other is to search for the highest reflector precision and the minimum adjusting cable numbers whilst satisfying the same constraints as the above by finding out two kinds of variables, i.e., number of adjusting cables and increment of adjusting cables' length. Obviously the latter is a nonlinear programming problem with two objectives and both continuous and discrete design variables. The numerical simulation of a 17 m cable mesh antenna is carried out to demonstrate the methodology given in this paper.

关键词： constraint theory nonlinear programming numerical analysis reflector antennas 17 m cable mesh antenna continuous design variables deployable antenna discrete design variables eigenfrequency material strength nonlinear programming problem reflector antenn

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