Parametric variational solution of linear-quadratic optimal control problems with control inequality constraints

A parametric variational principle and the corresponding numerical algo- rithm are proposed to solve a linear-quadratic （LQ） optimal control problem with control inequality constraints. Based on the parametric variational principle, this control prob- lem is transformed into a set of Hamiltonian canonical equations coupled with the linear complementarity equations, which are solved by a linear complementarity solver in the discrete-time domain. The costate variable information is also evaluated by the proposed method. The parametric variational algorithm proposed in this paper is suitable for both time-invariant and time-varying systems. Two numerical examples are used to test the validity of the proposed method. The proposed algorithm is used to astrodynamics to solve a practical optimal control problem for rendezvousing spacecrafts with a finite low thrust. The numerical simulations show that the parametric variational algorithm is ef- fective for LQ optimal control problems with control inequality constraints.

Novel Method to Handle Inequality Constraints for Nonlinear Programming

By redefining the multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, say, u2_i, i=1, 2, ..., m, nonnegative constraints imposed on inequality constraints in Karush-Kuhn-Tucker necessary conditions are removed. For constructing the Lagrange neural network and Lagrange multiplier method, it is no longer necessary to convert inequality constraints into equality constraints by slack variables in order to reuse those results dedicated to equality constraints, and they can be similarly proved with minor modification. Utilizing this technique, a new type of Lagrange neural network and a new type of Lagrange multiplier method are devised, which both handle inequality constraints directly. Also, their stability and convergence are analyzed rigorously.

NECESSARY CONDITIONS FOR OPTIMAL CONTROLS OF SEMILINEAR ELLIPTIC VARIATIONAL INEQUALITIES INVOLVING STATE CONSTRAINT

This paper deals with maximum principle for some optimal control problem governed by some elliptic variational inequalities. Some state constraints are discussed. The basic techniques used here are based on those in [1] and a new penalty functional defined in this paper.

A VARIATIONAL-HEMIVARIATIONAL INEQUALITY IN CONTACT PROBLEM FOR LOCKING MATERIALS AND NONMONOTONE SLIP DEPENDENT FRICTION

We study a new class of elliptic variational-hemivariational inequalities arising in the modelling of contact problems for elastic ideally locking materials. The contact is described by the Signorini unilateral contact condition and the friction is modelled by the nonmonotone multivalued subdifferential condition which depends on the slip. The problem is governed by a nonlinear elasticity operator, the subdifferential of the indicator function of a convex set which describes the locking constraints and a nonconvex locally Lipschitz friction potential. The result on existence and uniqueness of solution to the inequality is shown. The proof is based on a surjectivity result for maximal monotone and pseudomonotone operators combined with the application of the Banach contraction principle.

OPTIMAL CONTROL OF HYPERBOLIC H-HEMIVARIATIONAL INEQUALITIES WITH STATE CONSTRAINTS

The optimal control problems of hyperbolic H-hemivariational inequalities with the state constraints and nonnomotone multivalued mapping term are considered.The optimal solutions are obtained.In addition,their approximating problems are also studied.

OPTIMAL CONTROL OF PARABOLIC VARIATIONAL INEQUALITIES WITH STATE CONSTRAINT

The optimal control problem of parabolic variational inequalities with the state constraint and nonlinear, discontinuous nonmonotone multivalued mapping term and its approximating problem are studied, which generalizes some obtained results.

A GLOBALLY CONVERGENT QP-FREE ALGORITHM FOR INEQUALITY CONSTRAINED MINIMAX OPTIMIZATION

Although QP-free algorithms have good theoretical convergence and are effective in practice,their applications to minimax optimization have not yet been investigated.In this article,on the basis of the stationary conditions,without the exponential smooth function or constrained smooth transformation,we propose a QP-free algorithm for the nonlinear minimax optimization with inequality constraints.By means of a new and much tighter working set,we develop a new technique for constructing the sub-matrix in the lower right corner of the coefficient matrix.At each iteration,to obtain the search direction,two reduced systems of linear equations with the same coefficient are solved.Under mild conditions,the proposed algorithm is globally convergent.Finally,some preliminary numerical experiments are reported,and these show that the algorithm is promising.

Some new fixed point results under constraint inequalities in comparable complete partially ordered Menger PM-spaces

In this paper,we introduce the concept of comparable T-completeness of a partially ordered Menger PM-space and discuss the existence of fixed points for mappings satisfying certain conditions in the framework of a comparable T-complete partially ordered Menger PM-space.We obtain some new results which generalize many known ones in the literature.Moreover,we derive some consequent results and give an example to illustrate our main result.

Stability of singular networked control systems with control constraint

Based on bounded network-induced time-delay, the networked control system is modeled as a linear time-variant singular system. Using the Lyapunov theory and the linear matrix inequality approach, the criteria for delay-independent stability and delay-dependent stability of singular networked control systems are derived and transformed to a feasibility problem of linear matrix inequality formulation, which can be solved by the Matlab LMI toolbox, and the feasible solutions provide the maximum allowable delay bound that makes the system stable. A numerical example is provided, which shows that the analysis method is valid and the stability criteria are feasible.

Robust Fuzzy Tracking Control for Nonlinear Networked Control Systems with Integral Quadratic Constraints

This paper investigates the robust tracking control problcm for a class of nonlinear networked control systems （NCSs） using the Takagi-Sugeno （T-S） fuzzy model approach. Based on a time-varying delay system transformed from the NCSs, an augmented Lyapunov function containing more useful information is constructed. A less conservative sufficient condition is established such that the closed-loop systems stability and time-domain integral quadratic constraints （IQCs） are satisfied while both time-varying network- induced delays and packet losses are taken into account. The fuzzy tracking controllers design scheme is derived in terms of linear matrix inequalities （LMIs） and parallel distributed compensation （PDC）. Furthermore, robust stabilization criterion for nonlinear NCSs is given as an extension of the tracking control result. Finally, numerical simulations are provided to illustrate the effectiveness and merits of the proposed method.

Fault detection for networked systems subject to access constraints and packet dropouts

This paper addresses the problem of fault detection（FD） for networked systems with access constraints and packet dropouts.Two independent Markov chains are used to describe the sequences of channels which are available for communication at an instant and the packet dropout process,respectively.Performance indexes H∞ and H_ are introduced to describe the robustness of residual against external disturbances and sensitivity of residual to faults,respectively.By using a mode-dependent fault detection filter（FDF） as residual generator,the addressed FD problem is converted into an auxiliary filter design problem with the above index constraints.A sufficient condition for the existence of the FDF is derived in terms of certain linear matrix inequalities（LMIs）.When these LMIs are feasible,the explicit expression of the desired FDF can also be characterized.A numerical example is exploited to show the usefulness of the proposed results.

Suboptimal reliable guaranteed cost control for continuous-time systems with multi-criterion constraints

The suboptimal reliable guaranteed cost control （RGCC） with multi-criterion constraints is investigated for a class of uncertain continuous-time systems with sensor faults. A fauk model in sensors, which considers outage or partial degradation of sensors, is adopted. The influence of the disturbance on the quadratic stability of the closed-loop systems is analyzed. The reliable state-feedback controller is developed by a linear matrix inequalities （LMIs） approach, to minimize the upper bound of a quadratic cost fimction under the conditions that all the closed-loop poles be placed in a specified disk, and that the prescribed level of H∞ disturbance attenuation and the upper bound constraints of control inputs＇ magnitudes be guaranteed. Thus, with the above muki-criterion constraints, the resulting closed-loop system can provide satisfactory stability, transient property, a disturbance rejection level and minimized quadratic cost performance despite possible sensor faults.

A SELF-ADAPTIVE ALGORITHM FOR NONLINEAR LEAST SQUARES WITH LINEAR CONSTRAINTS

An algorithm for solving nonlinear least squares problems with general linear inequality constraints is described.At each step,the problem is reduced to an unconstrained linear least squares problem in a subs pace defined by the active constraints,which is solved using the quasi-Newton method.The major update formula is similar to the one given by Dennis,Gay and Welsch (1981).In this paper,we state the detailed implement of the algorithm,such as the choice of active set,the solution of subproblem and the avoidance of zigzagging.We also prove the globally convergent property of the algorithm.

A GENERALIZED PENALTY METHOD FOR DIFFERENTIAL VARIATIONAL-HEMIVARIATIONAL INEQUALITIES

We consider a differential variational-hemivariational inequality with constraints,in the framework of reflexive Banach spaces.The existence of a unique mild solution of the inequality,together with its stability,was proved in[1].Here,we complete these results with existence,uniqueness and convergence results for an associated penalty-type method.To this end,we construct a sequence of perturbed differential variational-hemivariational inequalities governed by perturbed sets of constraints and penalty coefficients.We prove the unique solvability of each perturbed inequality as well as the convergence of its solution to the solution of the original inequality.Then,we consider a mathematical model which describes the equilibrium of a viscoelastic rod in unilateral contact.The weak formulation of the model is in a form of a differential variational-hemivariational inequality in which the unknowns are the displacement field and the history of the deformation.We apply our abstract penalty method in the study of this inequality and provide the corresponding mechanical interpretations.

数字支付能显著降低农户消费不平等吗?

居民消费对实现共同富裕以及推动经济长期稳定发展具有重要意义。以往研究主要关注城乡居民消费差距,较少关注农户内部消费不平等问题。鉴于此,基于2017、2019年中国家庭金融调查数据,采用由农户人均消费支出测算的Kakwani指数构建消费不平等测度指标,使用双向固定效应模型和工具变量法实证分析数字支付对农户消费不平等的影响。研究结果表明,数字支付能够显著降低农户消费不平等;机制分析表明,数字支付通过缓解流动性约束和提高消费可及性,进而降低农户消费不平等;异质性分析表明,数字支付对户主年龄更高、受教育水平更低农户消费不平等的缓解作用更大,对发展型消费不平等的缓解作用大于生存型消费。基于此,本文认为应加大对农村数字支付发展的支持力度,推动农村数字普惠金融发展,提升农村居民数字素养,支持农村发展型消费品产业发展。

平台经济发展促进居民消费潜力释放了吗?

平台经济是一种基于数字技术,由平台支撑、网络协同等构成的新型经济模式,对居民消费潜力的释放具有重要影响。本文在理论分析平台经济对居民消费潜力直接影响机理及间接作用机制的基础上,采用2013—2021年275个地级市面板数据,实证分析平台经济发展对居民消费潜力的释放效应。研究发现:平台经济发展显著促进了居民消费潜力的释放;机制分析发现,平台经济发展可通过提高流通效率、缓解流动性约束和缓解居民收入不平等来促进居民消费潜力释放;异质性分析表明,平台经济发展对具有资源禀赋优势的城市居民消费潜力的促进作用更强;进一步分析表明,产业结构升级对居民消费潜力的释放具有门槛效应。研究结论对提升新质生产力、畅通国内国际双循环的相关政策制定有一定启示作用。

具有H_(∞)性能的输入受限三级倒立摆控制器设计

【目的】针对直线三级倒立摆控制输入受限下的稳摆控制问题,设计了具有H_(∞)性能的输入受限三级倒立摆控制器。【方法】利用线性矩阵不等式(LMI)方法,将控制输入约束问题转化为利用线性矩阵不等式求解优化值的优化问题,经Lyapunov稳定性推导出符合条件的LMI,利用MATLAB中的LMI工具箱求解得到有效的K。进一步在控制输入受限下引入H_(∞)性能指标,使所设计的控制输入受限下的算法具有H_(∞)性能。【结果】仿真结果表明,该控制器对于控制输入受限下的复杂高阶次不稳定系统具有很好的控制效果。【结论】控制输入信号在给定的受限范围内实现了三级倒立摆的稳摆要求,且引入H_(∞)性能指标后控制输入和摆杆波动更小。

机会不平等影响居民消费的机制与效应——基于CFPS数据的经验研究

本文利用中国家庭追踪调查(CFPS)2010—2018年5轮调查数据测度我国机会不平等程度,研究机会不平等对居民消费的影响效应和作用机制。结果表明,机会不平等程度的上升将显著抑制居民家庭消费支出;机制分析表明,机会不平等主要通过社会资本、流动性约束和经济地位渴求影响居民消费。扩展研究发现,机会不平等主要挤出了居民普通消费支出,且这一抑制作用对农村户籍、受教育程度低和体制外的家庭更强;而民生性财政支出和数字普惠金融可以消减机会不平等对居民家庭消费的抑制作用。本文研究结论从机会不平等视角为全面促进居民消费、构建新发展格局和实现共同富裕与共享发展提供了理论和经验证据。

A trust region algorithm for optimization with nonlinear equality and linear inequality constraints

A new algorithm of trust region type is presented to minimize a differentiable function ofmany variables with nonlinear equality and linear inequality constraints. Under the milder conditions, theglobal convergence of the main algorithm is proved. Moreover, since any nonlinear inequality constraint can beconverted into an equation by introducing a slack variable, the trust region method can be used in solving general nonlinear programming problems.

集约束下的变分不等式:像空间分析法

变分不等式是一种数学模型,属于平衡问题的一类,常应用于交通均衡问题、经济均衡问题以及生态产业链问题。像空间分析法(ISA)是研究最优问题与平衡问题非常重要的工具之一。为了丰富ISA在变分不等式问题上的研究,在集约束的假设下,利用ISA研究了在欧氏空间中经典变分不等式问题。首先,验证了问题的线性分离性。然后,通过拉格朗日型函数得到了拉格朗日型鞍点条件。最后,给出了变分不等式的最优性条件。