Penalty function method for the minimal time crisis problem

In this note, we propose a new method to approximate the minimal time crisis problem using an auxiliary control and a penalty function, and show its convergence to a solution to the original problem. The interest of this approach is illustrated on numerical examples for which optimal trajectories can leave and enter the crisis set tangentially.

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Applications of the penalty function method in constrained optimal control problems

Journal of Applied Mathematics and Simulation ◽

10.1155/s1048953389000201 ◽

1989 ◽

Vol 2 (4) ◽

pp. 251-265 ◽

Cited By ~ 4

Author(s):

An-qing Xing

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Penalty Function ◽

Function Method ◽

Optimal Control Problems ◽

Control Problems ◽

Penalty Function Method ◽

Constrained Optimal Control ◽

Numerical Examples ◽

Constrained Optimal Control Problem

This paper uses the penalty function method to solve constrained optimal control problems. Under suitable assumptions, we can solve a constrained optimal control problem by solving a sequence of unconstrained optimal control problems. In turn, the constrained solution to the main problem can be obtained as the limit of the solutions of the sequence. In using the penalty function method to solve constrained optimal control problems, it is usually assumed that each of the modified unconstrained optimal control problems has at least one solution. Here we establish an existence theorem for those problems. Two numerical examples are presented to demonstrate the findings.

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An exact penalty function method for optimising QAP formulation in facility layout problem

International Journal of Production Research ◽

10.1080/00207543.2016.1229068 ◽

2016 ◽

Vol 55 (10) ◽

pp. 2913-2929 ◽

Cited By ~ 7

Author(s):

Jingyang Zhou ◽

Peter E.D. Love ◽

Kok Lay Teo ◽

Hanbin Luo

Keyword(s):

Penalty Function ◽

Function Method ◽

Facility Layout ◽

Exact Penalty Function ◽

Penalty Function Method ◽

Exact Penalty ◽

Layout Problem ◽

Facility Layout Problem

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Penalty Function Method for Peer Selection over Wireless Mesh Network

2010 IEEE 72nd Vehicular Technology Conference - Fall ◽

10.1109/vetecf.2010.5594219 ◽

2010 ◽

Cited By ~ 4

Author(s):

Mohammad Zulhasnine ◽

Changcheng Huang ◽

Anand Srinivasan

Keyword(s):

Penalty Function ◽

Function Method ◽

Wireless Mesh Network ◽

Mesh Network ◽

Penalty Function Method ◽

Peer Selection ◽

Wireless Mesh

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Robust optimum design of SAW filters by using penalty function method

2004 IEEE International Conference on Industrial Technology, 2004. IEEE ICIT '04. ◽

10.1109/icit.2004.1490169 ◽

2005 ◽

Author(s):

K. Tagawa ◽

T. Ohtani ◽

T. Igaki ◽

S. Seki

Keyword(s):

Optimum Design ◽

Penalty Function ◽

Function Method ◽

Penalty Function Method ◽

Robust Optimum Design

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Nonlinear model predictive control for systems with autonomous state jumps using a penalty function method

2017 11th Asian Control Conference (ASCC) ◽

10.1109/ascc.2017.8287503 ◽

2017 ◽

Cited By ~ 2

Author(s):

Sotaro Katayama ◽

Yasuyuki Satoh ◽

Masahiro Doi ◽

Toshiyuki Ohtsuka

Keyword(s):

Model Predictive Control ◽

Predictive Control ◽

Nonlinear Model ◽

Penalty Function ◽

Function Method ◽

Nonlinear Model Predictive Control ◽

Penalty Function Method ◽

Autonomous State

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An objective penalty function method for biconvex programming

Journal of Global Optimization ◽

10.1007/s10898-021-01064-5 ◽

2021 ◽

Author(s):

Zhiqing Meng ◽

Min Jiang ◽

Rui Shen ◽

Leiyan Xu ◽

Chuangyin Dang

Keyword(s):

Penalty Function ◽

Function Method ◽

Penalty Function Method ◽

Objective Penalty Function

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Solving some optimal control problems using the barrier penalty function method

System Modelling and Optimization - Lecture Notes in Control and Information Sciences ◽

10.1007/bfb0008387 ◽

2005 ◽

pp. 358-367 ◽

Cited By ~ 1

Author(s):

Pekka Neittaanmäki ◽

Andrzej Stachurski

Keyword(s):

Optimal Control ◽

Penalty Function ◽

Function Method ◽

Optimal Control Problems ◽

Control Problems ◽

Penalty Function Method

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Nonlinear Model Predictive Control for Systems with State-Dependent Switches and State Jumps Using a Penalty Function Method

2018 IEEE Conference on Control Technology and Applications (CCTA) ◽

10.1109/ccta.2018.8511448 ◽

2018 ◽

Cited By ~ 2

Author(s):

Sotaro Katayama ◽

Yasuyuki Satoh ◽

Masahiro Doi ◽

Toshiyuki Ohtsuka

Keyword(s):

Model Predictive Control ◽

Predictive Control ◽

Nonlinear Model ◽

Penalty Function ◽

Function Method ◽

Nonlinear Model Predictive Control ◽

Penalty Function Method ◽

State Dependent

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Application of penalty function method to computation of reachable sets for control systems with state constraints

10.1063/1.4964973 ◽

2016 ◽

Cited By ~ 5

Author(s):

M. I. Gusev

Keyword(s):

Control Systems ◽

Penalty Function ◽

Function Method ◽

State Constraints ◽

Reachable Sets ◽

Penalty Function Method

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Smoothing Approximation to the Square-Root Exact Penalty Function

Journal of Systems Science and Information ◽

10.1515/jssi-2016-0087 ◽

2016 ◽

Vol 4 (1) ◽

pp. 87-96

Author(s):

Yaqiong Duan ◽

Shujun Lian

Keyword(s):

Penalty Function ◽

Original Problem ◽

Optimal Solution ◽

Penalty Functions ◽

Exact Penalty Functions ◽

Exact Penalty ◽

Square Root ◽

Inequality Constrained Optimization ◽

Numerical Examples ◽

Mild Conditions

AbstractIn this paper, smoothing approximation to the square-root exact penalty functions is devised for inequality constrained optimization. It is shown that an approximately optimal solution of the smoothed penalty problem is an approximately optimal solution of the original problem. An algorithm based on the new smoothed penalty functions is proposed and shown to be convergent under mild conditions. Three numerical examples show that the algorithm is efficient.

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