An optimal discrete control strategy for interplanetary guidance

The problem of guiding one state of a linear dynamical system to a prescribed rms terminal accuracy in the presence of injection, measurement, as well as engine-mechanization errors with a minimum average effort, is considered. Orbit corrections are assumed to be mechanized in the form of discrete velocity increments whose areas are proportional to the predicted miss distance. Equations are derived for computing the feedback gains as a function of the correction times. It is then shown how the spacings between successive corrections can be optimized. This is done by outlining a computation procedure based on the theory of dynamic programming. The optimum solution includes the effect of the loss of information caused by the mechanization error. The results are applied to a simple but illustrative example that approximates the terminal phase of an interplanetary trip. A numerical study is made relating the number of corrections and the required amount of propellant for various terminal accuracies and mechanization errors with typical initial errors. The computer results make evident the improvement of the multiple correction strategy over the design of using only one correction, and seem to indicate that the improvement obtained using more than three to four corrections is negligible. Moreover, it shows that there is an optimum number of corrections for a given size of mechanization error.     

An optimal guidance approximation theory

Synthesis of optimal guidance approximations is undertaken by means of a perturbation theory approach and a scheme for obtaining linear, quadratic and higher order feedback approximations to the optimal control presented. Mechanization is carried out in terms of state deviations from an optimal reference trajectory with the comparison point along the reference selected so that the state comparison is approximately transverse. A simple example is treated analytically, linear and quadratic feedback expressions obtained, and some digital computer simulation results presented which permit a comparison of system performance and accuracy between various approximations.     

Precision program guidance of an nonrigid orbital telescope

New capabilities of direct numerical technology for calculation of open-loop controls for nonlinear objects are considered. The modification of direct algorithm closed with respect to the output of the complete model predicting the state of a nonrigid controlled object is presented. According to this algorithm the control law is iteratively calculated using a reduced system with the order considerably lower than the complete model. The new algorithm provides calculation of high accuracy and low-sensitive to inaccuracy of initial data (Tikhonov stable, or robust) open-loop control for dynamic models with high dimensionality. The operation of the modified algorithm is demonstrated for the calculation of the open-loop control for the regime of reorientation of an orbital telescope whose dynamic model takes into account the flexibility of its structural elements as an example. The objective of the numerical experiment is the analysis of the influence on dynamics of the programmed controlled process of essential perturbations of the model: changes in its structure (due to the account offlexibility of solar panels), parameters (spread of moments of partial tones of solar panels, coefficients of inertial coupling of partial tones of solar panels and the telescope frame, and eigenfrequencies of solar panels) was considered. Results of calculations testify that the theoretically established property of stability of direct algorithm to errors of initial data (well conditioned algorithm) provides robustness and, at the same time, a high accuracy open-loop control according to laws calculated using the direct method.     

Three-dimensional optimal path planning for waypoint guidance of an autonomous underwater vehicle

In this paper, optimal three-dimensional paths are generated offline for waypoint guidance of a miniature Autonomous Underwater Vehicle (AUV). Having the starting point, the destination point, and the position and dimension of the obstacles, the AUV is intended to systematically plan an optimal path toward the target. The path is defined as a set of waypoints to be passed by the vehicle. Four criteria are considered for evaluation of an optimal path; they are “total length of path”, “margin of safety”, “smoothness of the planar motion” and “gradient of diving”. A set of Pareto-optimal solutions is found where each solution represents an optimal feasible path that cannot be outrun by any other path considering all four criteria. Then, a proposed three-dimensional guidance system is used for guidance of the AUV through selected optimal paths. This system is inspired from the Line-of-Sight (LOS) guidance strategy; the idea is to select the desired depth, presumed proportional to the horizontal distance of the AUV and the target. To develop this guidance strategy, the dynamic modeling of this novel miniature AUV is also derived. The simulation results show that this guidance system efficiently guides the AUV through the optimal paths.     

On the optimal pure strategy sets for a mixed missile guidance lawsynthesis

The terminal phase of a missile-versus-aircraft engagement in a noise-corrupted environment is formulated as an imperfect information zero-sum differential game. The payoff of the game is the single shot kill probability of the missile to be maximized by its designer and minimized by the pilot of the evading aircraft. In the past, it was shown that in such a game the optimal strategy of the evader is mixed. The proposed formulation allows a mixed strategy for the pursuer. The mathematical basis for such an analysis is provided, and a constructive methodology for the synthesis of missile guidance laws based on the concept of mixed strategies is outlined     

Learning to transfer optimal navigation policies

Autonomous agents that act in the real world utilizing sensory input greatly rely on the ability to plan their actions and to transfer these skills across tasks. The majority of path-planning approaches for mobile robots, however, solve the current navigation problem from scratch, given the current and goal configuration of the robot. Consequently, these approaches yield highly efficient plans for the specific situation, but the computed policies typically do not transfer to other, similar tasks. In this paper, we propose to apply techniques from statistical relational learning to the path-planning problem. More precisely, we propose to learn relational decision trees as abstract navigation strategies from example paths. Relational abstraction has several interesting and important properties. First, it allows a mobile robot to imitate navigation behavior shown by users or by optimal policies. Second, it yields comprehensible models of behavior. Finally, a navigation policy learned in one environment naturally transfers to unknown environments. In several experiments with real robots and in simulated runs, we demonstrate that our approach yields efficient navigation plans. We show that our system is robust against observation noise and can outperform hand-crafted policies.     

Neighbouring extremals for nonlinear systems with control constraints

In this paper, we consider a class of nonlinear optimal control problems subject to control constraints. We assume that an initial condition for the dynamical system is specified. Then, we can easily compute an openloop optimal control using any convenient optimal control software package. Now, suppose the optimal trajectory is perturbed due to a change in initial conditions or uncertainty in the model equations. If the perturbations are not too large, it is known that the neighbouring extremal approach can be used to obtain a feedback law which adjusts the open-loop optimal control accordingly provided there are no bounds on the control variables. In this paper, our aim is to develop a computational method for the more general case of fixed-time problems with control constraints.     

Optimal guidance law for cooperative attack of multiple missiles based on optimal control theory

This article considers the problem of optimal guidance laws for cooperative attack of multiple missiles based on the optimal control theory. New guidance laws are presented such that multiple missiles attack a single target simultaneously. Simulation results show the effectiveness of the proposed algorithms.     

On-line optimal autonomous reentry guidance based on improved Gauss pseudospectral method

The on-line optimal autonomous reentry guidance of the hypersonic vehicle is proposed based on the improved Gauss pseudospectral method （IGPM）. The autonomous reentry guidance requires the hypersonic vehicle can generate the optimal trajectory for the latest flight mission on line and track the new trajectory well under the uncertainty. These two problems are simplified into a nonlinear optimal control problem with nonlinear constraints. The IGPM is introduced to solve the above two problems. The trajectory has to change according to the flight mission and therefore the new optimal trajectory can be obtained by IGPM within about 10 s. The optimal feedback guidance law is used to track the reference trajectory to handle the uncertainty. In order to deal with the CPU time delay, which comes from optimizing the new trajectory, the new on-line optimal autonomous reentry guidance is depicted. Finally, the numerical simulation shows that the proposed autonomous guidance can generate optimal trajectory for the new flight mission and have a high tracking accuracy     

Loop transfer recovery techniques for discrete-time optimal regulators using prediction estimators

For discrete-time LQG optimal regulators using current estimators, it has been shown that perfect recoveries of the loop transfer matrices at the input or at the output are possible for square minimum-phase systems. However, current estimators cannot be used when the processing time of the controller is significant. In this note, the loop transfer recoveries using prediction estimators for square minimum-phase systems are considered. It is shown that, although the perfect recoveries are impossible, the feedback properties obtained by the recovery techniques are those that can be recovered best in the presence of the delay in the controller.     

Unprejudiced optimal open loop input design for identification of transfer functions

The problem to estimate transfer functions of linear systems is considered. The quality of the resulting estimate depends, among other things, on the input used during the identification experiment. We measure the quality using a quadratic norm in the frequency domain. The problem to determine optimal inputs, i.e. inputs that minimize the chosen norm, subject to constrained input variance, has long been studied. We point out that such procedures may involve a prejudice (that the system is to be found in a certain model set) that may have some surprising effects. We discuss how such a prejudice can be reduced by allowing the possibility that the true system cannot be exactly described in the chosen model set. We also calculate explicit expressions for the resulting “unprejudiced” optimal inputs. These expressions relate the signal-to-noise ratio (as a function of frequency) to the chosen weighting function in the quadratic norm. We also point out the role of the employed noise model for the design.     

Supervisory control for optimal route guidance in intelligent vehicle highway systems based on hybrid network models

This paper is devoted to the problem of optimal route guidance in intelligent vehicle highway systems to provide travellers with information minimizing the travel time as a kind of advanced traveller information systems. In order to deal with this problem, we first introduce a hybrid network model by incorporating the high-level discrete event model with the low-level flow dynamics model. Based on it, two feasible control policies are proposed employing supervisory control theory and then followed by a comparative simulation study.     

A real-time dynamic optimal guidance scheme using a general regression neural network

This paper presents an investigation into the challenges in implementing a hard real-time optimal non-stationary system using general regression neural network (GRNN). This includes investigation into the dynamics of the problem domain, discretisation of the problem domain to reduce the computational complexity, parameters selection of the optimization algorithm, convergence guarantee for real-time solution and off-line optimization for real-time solution. In order to demonstrate these challenges, this investigation considers a real-time optimal missile guidance algorithm using GRNN to achieve an accurate interception of the maneuvering targets in three-dimension. Evolutionary Genetic Algorithms (GAs) are used to generate optimal guidance training data set for a large missile defense space to train the GRNN. The Navigation Constant of the Proportional Navigation Guidance and the target position at launching are considered for optimization using GAs. This is achieved by minimizing the miss distance and missile flight time. Finally, the merits of the proposed schemes for real-time accurate interception are presented and discussed through a set of experiments.     

基于停车诱导信息板的最优停车场推荐的双层目标模型

现有停车诱导信息板的优化显示模型仅从驾车者的时间费用上进行优化,且多数仅支持输出各停车场空满状态.基于此,提出一种新的优化显示双层目标模型,增加诱导区域内各停车场空满程度最相近为第二层优化目标,并将给定目的地的推荐最优停车场作为模型的输出.该模型可在保证待停车辆寻找停车场造成的交通压力最小的前提下,诱导驾驶者的停车行为更加高效.通过算例分析表明:提出的双层目标模型,可以使停车诱导系统将待停车辆向更有利于驾驶者及停车场双方利益的方向诱导,克服了已有单目标模型和以排队长度为目标之一的双层目标模型最优解的不唯一性,同时达到了使总行驶时间最短和各停车场空满程度最相近的诱导目标.     

Weakly supervised semantic segmentation by iteratively refining optimal segmentation with deep cues guidance

Neural Computing and Applications - Weakly supervised semantic segmentation under image-level label supervision has undergone impressive improvements over the past years. These approaches can...     

The direct algorithm for calculating programmed controls of a special form in the problem of guidance of an orbital telescope

The problem is studied for calculating the programmed control of an orbital telescope with two-stage powered gyroscopes as actuators of the control system. Modifications are considered of the direct method for calculating the programmed controls, which is alternative to the method of inverse problems of dynamics. The suggested versions of the algorithm afford either the calculation of smooth controls taking prescribed values at the initial and the finite instant of time or the calculation of piecewise linear programmed controls realizable by the rotation of gyronodes with constant accelerations. The special feature of the dynamic model of an orbital telescope is the availability of the model of an invariant manifold in the space of states. The presented algorithm rebuilds the linearized model at each iteration of the calculation, its boundary conditions, and makes up a collection of independent variables of the state for these conditions.     

On determining optimal fleet size and vehicle transfer policy for a car rental company

This paper considers how to determine the optimal fleet size and vehicle transfer policy for a rental-car company that serves two cities. In each city, there are single-trip and round-trip customers, where the former is given a higher priority. Because of the single-trip traffic, the number of cars at these two cities may become unbalanced. Hence, the central planner in each day needs to decide whether to transfer any cars from one city to the other. We develop a two-stage dynamic programming model, in which we determine the vehicle transfer policy in the second stage and the optimal fleet size in the first stage. Although the objective function could be neither concave nor quasi-concave due to lost sales, we can find the optimal fleet size and vehicle transfer policy by solving a series of linear programming problems. We propose a heuristic solution, which is based on a special case analysis, for the fleet size problem. A numerical study reveals that our heuristic solution for the fleet size performs well. However, if the corresponding vehicle transfer policy is not appropriate, the overall performance can drastically deteriorate even with the optimal fleet size. Several extensions of our basic model are also analyzed.