Optimal Planar Interception with Fixed End Conditions: Approximate Solutions

In a previous paper (Ref. 1), an exact solution of the optimal planar interception with fixed end conditions was derived in closed form. The optimal control was expressed as an explicit function of the state variables and two fixed parameters, obtained by solving a set of nonlinear algebraic equations involving elliptic integrals. In order to facilitate the optimal control implementation, the present paper derives a highly accurate simplified solution assuming that the ratio of the pursuer turning radius to the initial range is small. An asymptotic expansion further reduces the computational workload. Construction of a near-optimal open-loop control, based on the approximations, completes the present paper.     

An Extension of the Coordinate Transformation Method for Open-Loop Nash Equilibria

In Leitmann (Ref. 1), a coordinate transformation method was introduced to obtain global solutions for free problems in the calculus of variations. This direct method was extended and broadened in Carlson (Ref. 2) and later in Leitmann (Ref. 3). The applicability of the original work of Leitmann (Ref. 1) was further developed in Dockner and Leitmann (Ref. 4) to include the class of open-loop dynamic games. In the present work, we improve the results of Ref. 4 in two directions. First, we enlarge the class of open-loop dynamic games to permit coupling among the dynamic equations via the states of the players; second, we incorporate the modifications given in Refs. 2 and 3. Our results greatly increase the applicability of this method. An example arising from the harvesting of a renewable resource is presented to illustrate the utility of our results.     

Sufficiency and game structure in Nash open-loop differential games

This note deals with the following problem inN-player Nash open-loop differential games: Which conditions on the Hamiltonians will simplify the verification of the sufficient conditions? In the class of games with Hamiltonians linear in the state, and where the state is separated from the control of playeri in the Hamiltonian of this player, the first-order and second-order conditions for an extremum of the Hamiltonian of playeri also constitute a set of sufficient conditions.     

THE ALGEBRAIC CRITERION OF UNCONDITIONAL STABILITY OF CONSTANT LINEAR SYSTEMS

1IntroductionandLemmasConsidern-dimentionalconstantlinearcontrolsystemwithdelaywhereA(1)=(ail))...,A(2)=(aj:))...,B(1)=(6j:))...,B(2)~(hi:))...,C=(oil)...areconstantmatrixesandX(t)~(xl(t),''5x.(t))',U(t)=(m(t),...9u.(t))',y(t)=(yi(t),'',y.(t))'arevector…     

Tractable classes of nonzero-sum open-loop Nash differential games: Theory and examples

This paper identifies some classes ofN-person nonzero-sum differential games that are tractable, in the sense that open-loop Nash strategies can be determined, either explicitly or qualitatively in terms of a phase-diagram portrait. The classes are characterized by conditions imposed on the Hamiltonians. Also, the underlying game structures needed to satisfy these conditions are characterized.The authors wish to thank V. Kaitala, Helsinki University of Technology, and the referees.     

Complex differential games of pursuit-evasion type with state constraints,part 1: Necessary conditions for optimal open-loop strategies

Complex pursuit-evasion games with state variable inequality constraints are investigated. Necessary conditions of the first and the second order for optimal trajectories are developed, which enable the calculation of optimal open-loop strategies. The necessary conditions on singular surfaces induced by state constraints and non-smooth data are discussed in detail. These conditions lead to multi-point boundary-value problems which can be solved very efficiently and very accurately by the multiple shooting method. A realistically modelled pursuit-evasion problem for one air-to-air missile versus one high performance aircraft in a vertical plane serves as an example. For this pursuit-evasion game, the barrier surface is investigated, which determines the firing range of the missile. The numerical method for solving this problem and extensive numerical results will be presented and discussed in Part 2 of this paper; see Ref. 1.This paper is dedicated to the memory of Professor John V. Breakwell.The authors would like to express their sincere and grateful appreciation to Professors R. Bulirsch and K. H. Well for their encouraging interest in this work.     

Output feedback stabilization for a class of nonlinear time-evolution systems

A variety of problems in nonlinear time-evolution systems such as communication networks, computer networks, manufacturing, traffic management, etc., can be modelled as min–max-plus systems in which operations of min, max and addition appear simultaneously. Systems with only maximum (or minimum) constraints can be modelled as max-plus system and handled by max-plus algebra which changes the original nonlinear system in the traditional sense into linear system in this framework. Min-max-plus systems are extensions of max-plus systems and nonlinear even in the max-plus algebra view. Output feedback stabilization for min–max-plus systems with min–max-plus inputs and max-plus outputs is considered in this paper. Max-plus projection representation for the closed-loop system with min–max-plus output feedback is introduced and the formula to calculate the cycle time is presented. Stabilization of reachable systems with at least one observable state and a further result for reachable and observable systems are worked out, during which max-plus output feedbacks are used to stabilize the systems. The method based on the max-plus algebra is constructive in nature.     

螺旋天线步进电机控制系统仿真及运行曲线优化

为实现机械相控阵列天线的波束扫描,采用步进电机驱动螺旋天线单元转动来达到预定的辐射相位。为了优化步进电机的开环控制,研究运行曲线对步进电机控制性能的影响,提高步进电机控制速度和精度。根据步进电机及控制系统的工作原理,建立了基于Simulink的步进电机开环控制系统仿真模型,并在此基础上对梯形和抛物线两种运行曲线进行了仿真研究。仿真结果表明,该仿真模型能精确实现两种运行曲线对步进电机的控制,在100 ms的控制周期内,采用梯形运行曲线步进电机的最大无失步转动角度能够达到270°,而采用抛物线运行曲线时其转动角度能够达到360°,抛物线运行曲线在开环控制系统中具有更高的控制速度。     

C波段半波长开路谐振器平行耦合滤波器的研制

采用切比雪夫低通原型滤波器综合法,设计了一种半波长开路谐振器平行耦合滤波器,该类型滤波器具有插入损耗低、结构简单、容易实现等诸多特点。从测试结果看出,实际测试值与理论分析及MWO软件仿真结果基本一致。     

Nonlinear Programming Methods for Real-Time Control of an Industrial Robot

The optimal control of an industrial robot is considered as a parametricnonlinear control problem subject to control and state constraints. Based onrecent stability results for parametric control problems, a robust nonlinearprogramming method is proposed to compute the sensitivity of open-loopcontrol solutions. Real-time control approximations of the perturbedoptimal solutions are obtained by evaluating first-order Taylor expansionsof the optimal solutions with respect to the parameter. The proposednumerical methods are applied to the industrial robot Manutec r3. Thequality of the real-time approximations is illustrated for perturbations inthe transport load.