马中静，南开大学本科、加拿大麦吉尔大学硕士和博士，美国密歇根大学安娜堡分校博士后。现为自动化学院副教授、博士生导师、电气工程研究所所长、自动化（全英文）专业责任教授。讲授《※优与鲁棒控制》、《自动控制原理》等全英文课程，主持了国家自然科学基金项目插电式电动汽车※优充电控制策略研究和基于交替方向乘子法的大规模多能耦合系统优化问题研究、科技部国际合作专项分布式可再生能源控制及优化利用技术的联合研发以及国家电网等多项课题。在优化、※优控制、博弈论、新能源优化利用等方面取得了丰富的科研成果，在IEEE Trans. on Automatic Control、Automatica、IEEE Trans. on Control Systems Technology等发表高水平SCIEI论文50余篇，GoogleScholar引用1000 次。为知名SCI期刊《Nonlinear Analysis：Hybrid Systems》编委、副编辑，IEEE高级会员。
Many systems, like electrical,mechanical, chemical, aerospace, eco-nomical, and so on, can bemathematically modeled as linearnonlinear deterministicstochastic dierentialdi erence state equations. The state systems evolve with time andpossibly with other variables under certain speci ed dynamical relations witheach other.
The underlying systems mightbe driven from a speci c state to another one by applying some externalcontrols. In case that there exist many di erent ways to implement the samegiven task, one of them may be best in some sense. For instance, there may bea typical way to drive a vehicle from an initial place to the destination ina minimum time or with a minimum consumed fuel. The applied controlcorresponding to the best solution is called an optimal control. The measureof the performance is called cost function.
We have briey introduced anoptimal control problem by putting the above together. This book mainlyfocuses on how to implement the optimal control problems via the variationalmethod. More speci cally It studies how to implement the extrema offunctional by applying the variational method. It covers the extrema offunctional with di erent boundary conditions, involving multiple functionsand with certain constraints etc.
It gives the necessary and sucient condition for the continuous-time optimal control solution via thevariational method, solves the optimal control problems with di erentboundary conditions, and ana-lyzes the linear quadratic regulator andtracking problems respectively in detail.
It gives the solution ofoptimal control problems with state constraintsby applying the Pontryagin''sminimum principle which is developed based upon the calculus of variations.And the developed results are applied to implement several classes of popularoptimal control problems, say minimum-time, minimum-fuel, minimum-energyproblems and so on.
This book is aimed at seniorundergraduate students or graduate students in electrical, mechanical,chemical, and aerospace engineering, operation research and appliedmathematics etc. This book contains the stu swhich can be covered in aone-semester course and it requires the students to have the background oncontrol systems or linear systems theory. This book can also be used byprofessional researchers and engineers working in a variety of elds.
School of Automation
Beijing Institute of Technology, Beijing
Zhongjing Ma and Suli Zou
February, 2020
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