scholarly journals Numerical Methods for Viscosity Solutions of an Optimal Control Problem and an Obstacle Avoidance Problem for a Wheeled Vehicle

2000 ◽  
Vol 13 (10) ◽  
pp. 458-469 ◽  
Author(s):  
Kei IMAFUKU ◽  
Yuh YAMASHITA ◽  
Hirokazu NISHITANI
Keyword(s):  
Optimal Control ◽  
Numerical Methods ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Obstacle Avoidance ◽  
Viscosity Solutions ◽  
Wheeled Vehicle ◽  
Avoidance Problem

scholarly journals Singular perturbations and optimal control of stochastic systems in infinite dimension: HJB equations and viscosity solutions

2021 ◽  
Author(s):  
Andrzej Swiech
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Stochastic Differential Equation ◽  
Control Problem ◽  
Viscosity Solutions ◽  
Hilbert Spaces ◽  
Stochastic Systems ◽  
Nonlinear Dependence ◽  
Infinite Dimensional

We study a stochastic optimal control problem for a two scale system driven by an infinite dimensional stochastic differential equation which consists of ``slow'' and ``fast'' components. We use the theory of viscosity solutions in Hilbert spaces to show that as the speed of the fast component goes to infinity, the value function of the optimal control problem converges to the viscosity solution of a reduced effective equation. We consider a rather general case where the evolution is given by an abstract semilinear stochastic differential equation with nonlinear dependence on the controls. The results of this paper generalize to the infinite dimensional case the finite dimensional results of O. Alvarez and M. Bardi and complement the results in Hilbert spaces obtained recently by G. Guatteri and G. Tessitore.

scholarly journals Multiaircraft Optimal 4D Trajectory Planning Using Logical Constraints

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Dinesh B. Seenivasan ◽  
Alberto Olivares ◽  
Ernesto Staffetti
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Obstacle Avoidance ◽  
Trajectory Planning ◽  
Model Complexity ◽  
Mixed Integer ◽  
Planning Problem ◽  
Integer Variables ◽  
Logical Constraints

This paper studies the trajectory planning problem for multiple aircraft with logical constraints in disjunctive form which arise in modeling passage through waypoints, distance-based and time-based separation constraints, decision-making processes, conflict resolution policies, no-fly zones, or obstacle or storm avoidance. Enforcing separation between aircraft, passage through waypoints, and obstacle avoidance is especially demanding in terms of modeling efforts. Indeed, in general, separation constraints require the introduction of auxiliary integer variables in the model; for passage constraints, a multiphase optimal control approach is used, and for obstacle avoidance constraints, geometric approximations of the obstacles are introduced. Multiple phases increase model complexity, and the presence of integer variables in the model has the drawback of combinatorial complexity of the corresponding mixed-integer optimal control problem. In this paper, an embedding approach is employed to transform logical constraints in disjunctive form into inequality and equality constraints which involve only continuous auxiliary variables. In this way, the optimal control problem with logical constraints is converted into a smooth optimal control problem which is solved using traditional techniques, thereby reducing the computational complexity of finding the solution. The effectiveness of the approach is demonstrated through several numerical experiments by computing the optimal trajectories of multiple aircraft in converging and intersecting arrival routes with time-based separation constraints, distance-based separation constraints, and operational constraints.

scholarly journals Numerical Methods for Solving Optimal Control Problem Using Scaling Boubaker Function

2020 ◽  
Vol 25 (2) ◽  
pp. 78-89 ◽  
Author(s):  
Eman Hassan Ouda Alfrdji ◽  
Imad Noah Ahmed
Keyword(s):  
Optimal Control ◽  
Numerical Methods ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Approximation Method ◽  
Numerical Examples ◽  
Control Parameterization ◽  
Matlab Program ◽  
And Control

      In this paper, the approximation method was used for solving optimal control problem (OCP), two techniques for state parameterization and control parameterization have been considered with the aid of Scaling Polynomials (SBP) represent a new important technique for solving (OCP’s). The algorithms were illustrated by several numerical examples using Matlab program. The results were evaluated and graphed to show the accuracy  of the methods.

A Multi-Stage Optimization Formulation for MPC-Based Obstacle Avoidance in Autonomous Vehicles Using a LIDAR Sensor

2014 ◽  
Author(s):  
Jiechao Liu ◽  
Paramsothy Jayakumar ◽  
Jeffrey L. Stein ◽  
Tulga Ersal
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Obstacle Avoidance ◽  
High Speed ◽  
Optimal Solution ◽  
Multi Stage ◽  
Lift Off ◽  
And Control ◽  
Control Delays

The dynamics of an autonomous unmanned ground vehicle (UGV) that is at least the size of a passenger vehicle are critical to consider during obstacle avoidance maneuvers to ensure vehicle safety. Methods developed so far do not take vehicle dynamics and sensor limitations into account simultaneously and systematically to guarantee the vehicle’s dynamical safety during avoidance maneuvers. To address this gap, this paper presents a model predictive control (MPC) based obstacle avoidance algorithm for high-speed, large-size UGVs that perceives the environment only through the information provided by a sensor, takes into account the sensing and control delays and the dynamic limitations of the vehicle, and provides smooth and continuous optimal solutions in terms of minimizing travel time. Specifically, information about the environment is obtained using an on-board Light Detection and Ranging (LIDAR) sensor. Ensuring the vehicle’s dynamical safety is translated into avoiding single tire lift-off. The obstacle avoidance problem is formulated as a multi-stage optimal control problem with a unique optimal solution. To solve the optimal control problem, it is transcribed into a nonlinear programming (NLP) problem using a pseudo-spectral method, and solved using the interior-point method. Sensing and control delays are explicitly taken into consideration in the formulation. Simulation results show that the algorithm is capable of generating smooth control commands to avoid obstacles while guaranteeing dynamical safety.

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