Application of stochastic optimal control to the suboptimal design of thrust-mass profiles

Stochastic optimal control techniques are applied to compare the performance of identical medium-range air-to-air missiles which have different thrust-mass profiles. The measure of the performance is the probability of reaching a lock-on-point with a favorable range of guidance and flight parameters, during a fixed time interval [0,t _f ], given that, during the flight, the trajectories of the missile are subjected to a variety of constraints including dynamic pressure constraints.     

Game of two cars: Case of variable speed

A stochastic version of Isaacs's (Ref. 1) game of two cars is dealt with here. In this version, the pursuer, owing to thrust and drag forces, has a variable speed, whereas the evader's speed is constant. Also, the pursuer can maneuver as long as his speed is bounded by some lower and upper limits. The probability of interception, corresponding to optimal (saddle-point) feedback strategies, is computed and serves as a reference for evaluating the performance of four different versions of the proportional navigation pursuit law as well as two other strategies.     

Computation of suboptimal randomized strategies for steering the random motion of a point under partial observation

Consider the random motion in the plane of a pointM, whose velocityv=(v ₁,v ₂) is perturbed by an ²-valued Gaussian white noise. Only noisy nonlinear observations taken on the point location (state) are available toM. The velocityv is of the formv(y)= _u (u ₁,u ₂) _y (du), wherey denotes the value of the observed signal,U is the range of the velocity, and, for eachy, _y is a probability measure on (U). Using the available observations, the pointM wishes to steer itself into a given target set by choosing a randomized strategy ={ _y :y ²}. Sufficient conditions on weak optimal randomized strategies are derived. An algorithm for computing weak suboptimal randomized strategies is suggested, and the strategies are computed for a variety of cases.This work was partially supported by a grant from Control Data.     

Optimal controls that maximize the probability of hitting a set of targets: A numerical study

A two-dimensional random motion of a point is dealt with. The point velocity (v cos ?,v sin ?) is subjected to two different kinds of perturbations, the first represented by a vector of independent standard Wiener processes and the second by a generalized type of Poisson process. The control function is ?, whilev is kept fixed. We assume given a configuration ofn+1 target sets,A ₀,...,A _n , in the plane, all of these sets being surrounded by an open and bounded setD. We denote by ? _x (?(?)∈A _i the probability thatX _t , the location of the point, whereX ₀=x∈D, will reach the setA _i beforeX _i reaches any other setA _j ,i≠j, and before it leavesD. The problem dealt with here is to find an optimal control law ?*, ?*=?*(x),x∈D, such that the function $$V\left( {x;\theta } \right) = \sum\limits_{i = 0}^n {\lambda _i \mathbb{P}_x \left( {X_\tau \left( \theta \right) \in A_i } \right),}$$ where λ₁,i=0,...,n, are given nonnegative numbers, will be maximized on a given class of admissible control laws. Sufficient conditions on optimal controls, of a dynamic programming type, are derived. These conditions require the existence of a smooth solution to a nonlinear partial integrodifferential equation, which is solved here by applying a finite-difference scheme. Two examples are dealt with numerically.     

Parametric study of ship maneuverability in laterally restricted waters: Stochastic control approach

A stochastic control approach is used in a parametric study of ship maneuverability in a restricted channel of prescribed geometry. A realistic method, based on some empirical data, is used for the mathematical modelling of the ship motion in deep water.The authors are grateful to Mr. Lodewyk Wessels, Department of Electrical and Electronic Engineering, University of Pretoria, for generating the plots in this article.     

Closed-Loop Control of the Motion of a Disk–Rod System

This work deals with the guidance and control of a system which is composed of a rolling disk and a controlled slender rod that is pivoted, through its center of mass, about the disk center. There are given N points P _i, i=1, ..., N, in the horizontal plane, a set of angles _2i , i=1, ..., N, a finite-time interval [0, t _f], and a sequence of times ₁=0<₂<...< _N =t _f. Using the concept of path controllability, a closed-loop control law is derived to steer the system in such a manner that the disk center and the rod angle of rotation ₂ will pass through (P _i, _2i ) at the times _i , i=1,...,N, respectively. This system serves as a model for the motion of a simple mobile robot.     

Stochastic pursuit-evasion differential games in 3D

A stochastic version of Isaacs's homicidal chauffeur game in the (x, y, z)-space is considered. This is used to solve a pursuit-evasion problem in the (x, y, z)-space in which the pursuer has incomplete information on the evader motion. Optimal feedback strategies for the game, and optimal feedback guidance laws for the pursuer, which uses only the measurements available to the pursuer, are computed. A simple suboptimal guidance law for the pursuer is suggested.     

Modelling the motion of a disk Rolling on a curve in R: The case where the motion is driven by using two overhead rotors

This work deals with the modelling of the motion of a disk rolling without slipping ona regular curve in R³. The disk's motion is driven by a pedalling torque and by using two overhead rotors.     

Response functions of 58Ni, 116Sn AND 208Pb to the excitation of intermediate-energy α-particles

Inelastic scattering of 340 MeV and 480 MeV α-particles has been measured on ⁵⁸Ni, ¹¹⁶Sn and ²⁰⁸Pb up to 60 MeV excitation energy. Consistent background subtraction and multipole analysis has provided the repartition of multipole strength for all three nuclei. The so-obtained response functions show the already known low-energy giant resonances in a detailed way, as well as new giant resonances at high energy.