The Infinite Time Quadratic Control Problem for Linear Systems with State and Control Delays: An Evolution Equation Approach

1981 ◽  
Vol 19 (1) ◽  
pp. 139-153 ◽  
Author(s):  
R. B. Vinter ◽  
R. H. Kwong
Keyword(s):  
Evolution Equation ◽  
Control Problem ◽  
Linear Systems ◽  
Equation Approach ◽  
Infinite Time ◽  
And Control ◽  
Control Delays

Design of performance robustness for uncertain linear systems with state and control delays

1998 ◽  
Vol 43 (11) ◽  
pp. 1593-1596 ◽  
Author(s):  
J.S. Luo ◽  
P.P.J. Van Den Bosch ◽  
S. Weiland ◽  
A. Goldenberge
Keyword(s):  
Linear Systems ◽  
And Control ◽  
Uncertain Linear Systems ◽  
Control Delays ◽  
Performance Robustness

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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