Exact solutions to some minimum time problems with inequality state constraints

1989 ◽  
Vol 2 (2) ◽  
pp. 137-169 ◽  
Author(s):  
Daniel R. Baker
Keyword(s):  
Exact Solutions ◽  
State Constraints ◽  
Minimum Time ◽  
Inequality State ◽  
Minimum Time Problems

scholarly journals The Mayer and Minimum Time Problems with Stratified State Constraints

2017 ◽  
Vol 26 (3) ◽  
pp. 643-662 ◽  
Author(s):  
C. Hermosilla ◽  
P. R. Wolenski ◽  
H. Zidani
Keyword(s):  
State Constraints ◽  
Minimum Time ◽  
Minimum Time Problems

Maximum Correntropy Criterion Constrained Kalman Filter

2017 ◽  
Author(s):  
Seyed Fakoorian ◽  
Mahmoud Moosavi ◽  
Reza Izanloo ◽  
Vahid Azimi ◽  
Dan Simon
Keyword(s):  
Kalman Filter ◽  
Gaussian Noise ◽  
State Constraints ◽  
Statistical Information ◽  
Second Order ◽  
System Model ◽  
Error Covariance ◽  
Inequality State ◽  
Maximum Correntropy Criterion ◽  
Non Gaussian

Non-Gaussian noise may degrade the performance of the Kalman filter because the Kalman filter uses only second-order statistical information, so it is not optimal in non-Gaussian noise environments. Also, many systems include equality or inequality state constraints that are not directly included in the system model, and thus are not incorporated in the Kalman filter. To address these combined issues, we propose a robust Kalman-type filter in the presence of non-Gaussian noise that uses information from state constraints. The proposed filter, called the maximum correntropy criterion constrained Kalman filter (MCC-CKF), uses a correntropy metric to quantify not only second-order information but also higher-order moments of the non-Gaussian process and measurement noise, and also enforces constraints on the state estimates. We analytically prove that our newly derived MCC-CKF is an unbiased estimator and has a smaller error covariance than the standard Kalman filter under certain conditions. Simulation results show the superiority of the MCC-CKF compared with other estimators when the system measurement is disturbed by non-Gaussian noise and when the states are constrained.

Vehicular Optimal Control

2018 ◽  
pp. 391-426
Author(s):  
David J. N. Limebeer ◽  
Matteo Massaro
Keyword(s):  
Optimal Control ◽  
Minimization Problem ◽  
Optimization Problems ◽  
Structural Features ◽  
Minimum Time ◽  
Time Of Arrival ◽  
Hybrid Powertrain ◽  
Multi Stage ◽  
Time Minimization ◽  
Minimum Time Problems

Chapter 9 deals with the solution of minimum-time and minimum-fuel vehicular optimal control problems. These problems are posed as fuel usage optimization problems under a time-of-arrival constraint, or minimum-time problems under a fuel usage constraint. The first example considers three variants of a simple fuel usage minimization problem under a time-of-arrival constraint. The first variant is worked out theoretically, and serves to highlight several of the structural features of these problems; the other two more complicated variants are solved numerically.The second example is also a multi-stage fuel usage minimization problem under a timeof- arrival constraint.More complicated track and vehicle models are then employed; the problem is solved numerically. The third problem is a lap time minimization problem taken from Formula One and features a thermoelectric hybrid powertrain. The fourth and final problem is a minimum-time closed-circuit racing problem featuring a racing motorcycle and rider.

A Fast and Robust Algorithm for General Inequality/Equality Constrained Minimum-Time Problems

1999 ◽  
Vol 121 (3) ◽  
pp. 337-345 ◽  
Author(s):  
B. J. Driessen ◽  
N. Sadegh ◽  
G. G. Parker ◽  
G. R. Eisler
Keyword(s):  
Maximum Principle ◽  
Quadratic Programming ◽  
Sequential Quadratic Programming ◽  
Joint Angle ◽  
Minimum Time ◽  
Robotic Arm ◽  
General Inequality ◽  
Constrained Problems ◽  
Ill Conditioning ◽  
Minimum Time Problems

This work has developed a new robust and reliable O(N) algorithm for solving general inequality/equality constrained minimum-time problems. To our knowledge, no one has ever applied an O(N) algorithm for solving such minimum time problems. Moreover, the algorithm developed here is new and unique and does not suffer the inevitable ill-conditioning problems that pre-existing O(N) methods for inequality-constrained problems do. Herein we demonstrate the new algorithm by solving several cases of a tip path constrained three-link redundant robotic arm problem with torque bounds and joint angle bounds. Results are consistent with Pontryagin’s Maximum Principle. We include a speed/robustness/complexity comparison with a sequential quadratic programming (SQP) code. Here, the O(N) complexity and the significant speed, robustness, and complexity improvements over an SQP code are demonstrated. These numerical results are complemented with a rigorous theoretical convergence proof of the new O(N) algorithm.

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