scholarly journals Optimal Control of Gene Mutation in DNA Replication

2012 ◽  
Vol 2012 ◽  
pp. 1-26
Author(s):  
Juanyi Yu ◽  
Jr-Shin Li ◽  
Tzyh-Jong Tarn
Keyword(s):  
Optimal Control ◽  
Dna Replication ◽  
Dna Sequences ◽  
Dynamic Programming Algorithm ◽  
Gene Mutations ◽  
Global Optimum ◽  
Programming Algorithm ◽  
State Variables ◽  
Level Control ◽  
Finite State

We propose a molecular-level control system view of the gene mutations in DNA replication from the finite field concept. By treating DNA sequences as state variables, chemical mutagens and radiation as control inputs, one cell cycle as a step increment, and the measurements of the resulting DNA sequence as outputs, we derive system equations for both deterministic and stochastic discrete-time, finite-state systems of different scales. Defining the cost function as a summation of the costs of applying mutagens and the off-trajectory penalty, we solve the deterministic and stochastic optimal control problems by dynamic programming algorithm. In addition, given that the system is completely controllable, we find that the global optimum of both base-to-base and codon-to-codon deterministic mutations can always be achieved within a finite number of steps.

scholarly journals Study on Indefinite Stochastic Linear Quadratic Optimal Control with Inequality Constraint

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Guiling Li ◽  
Weihai Zhang
Keyword(s):  
Optimal Control ◽  
Dynamic Programming Algorithm ◽  
Inequality Constraint ◽  
Terminal State ◽  
State Feedback Control ◽  
Programming Algorithm ◽  
Necessary Condition ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Lq Optimal Control

This paper studies the indefinite stochastic linear quadratic (LQ) optimal control problem with an inequality constraint for the terminal state. Firstly, we prove a generalized Karush-Kuhn-Tucker (KKT) theorem under hybrid constraints. Secondly, a new type of generalized Riccati equations is obtained, based on which a necessary condition (it is also a sufficient condition under stronger assumptions) for the existence of an optimal linear state feedback control is given by means of KKT theorem. Finally, we design a dynamic programming algorithm to solve the constrained indefinite stochastic LQ issue.

Motorway Path Planning for Automated Road Vehicles Based on Optimal Control Methods

2018 ◽  
Vol 2672 (19) ◽  
pp. 112-123 ◽  
Author(s):  
Konstantinos Makantasis ◽  
Markos Papageorgiou
Keyword(s):  
Optimal Control ◽  
Path Planning ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Dynamic Programming Algorithm ◽  
Weighting Factor ◽  
Initial Guess ◽  
Programming Algorithm ◽  
Road Vehicles ◽  
Planning Algorithm

A path-planning algorithm for automated road vehicles on multi-lane motorways is derived from the opportune formulation of an optimal control problem. In this framework, the objective function to be minimized contains appropriate respective terms to reflect: the goals of the vehicle advancement; passenger comfort; prevailing traffic rules (e.g., overtaking only from left); and the avoidance of obstacles (other moving vehicles) and of the vehicle departing from the road. Each term is coupled with a weighting factor that reflects its comparative importance. For the numerical solution of the optimal control problem, a very efficient feasible direction algorithm is used. To avoid local minima, a simplified dynamic programming algorithm is also conceived to deliver the initial guess trajectory for the optimal control algorithm. With low computation times, the approach is readily executable within a model-predictive control frame. The performance of the proposed algorithm is illustrated using two typical driving scenarios.

REDUCING THE SEARCH SPACE AND TIME COMPLEXITY OF NEEDLEMAN-WUNSCH ALGORITHM (GLOBAL ALIGNMENT) AND SMITH-WATERMAN ALGORITHM (LOCAL ALIGNMENT) FOR DNA SEQUENCE ALIGNMENT

2015 ◽  
Vol 77 (20) ◽  
Author(s):  
F. N. Muhamad ◽  
R. B. Ahmad ◽  
S. Mohd. Asi ◽  
M. N. Murad
Keyword(s):  
Dynamic Programming ◽  
Dna Sequences ◽  
Sequence Comparison ◽  
Dynamic Programming Algorithm ◽  
Search Space ◽  
Programming Algorithm ◽  
Local Alignment ◽  
Global Alignment ◽  
Main Research ◽  
Dna Sequence Alignment

The fundamental procedure of analyzing sequence content is sequence comparison. Sequence comparison can be defined as the problem of finding which parts of the sequences are similar and which parts are different, namely comparing two sequences to identify similarities and differences between them. A typical approach to solve this problem is to find a good and reasonable alignment between the two sequences. The main research in this project is to align the DNA sequences by using the Needleman-Wunsch algorithm for global alignment and Smith-Waterman algorithm for local alignment based on the Dynamic Programming algorithm. The Dynamic Programming Algorithm is guaranteed to find optimal alignment by exploring all possible alignments and choosing the best through the scoring and traceback techniques. The algorithms proposed and evaluated are to reduce the gaps in aligning sequences as well as the length of the sequences aligned without compromising the quality or correctness of results. In order to verify the accuracy and consistency of measurements obtained in Needleman-Wunsch and Smith-Waterman algorithms the data is compared with Emboss (global) and Emboss (local) with 600 strands test data.

A Constraining Hyperplane Technique for State Variable Constrained Optimal Control Problems

1973 ◽  
Vol 95 (4) ◽  
pp. 380-389 ◽  
Author(s):  
K. Martensson
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Control Variable ◽  
Dynamic Programming Algorithm ◽  
Inequality Constraints ◽  
Programming Algorithm ◽  
Control Problems ◽  
State Control ◽  
Constrained Optimal Control ◽  
State Variable

A new approach to the numerical solution of optimal control problems with state-variable inequality constraints is presented. It is shown that the concept of constraining hyperplanes may be used to approximate the original problem with a problem where the constraints are of a mixed state-control variable type. The efficiency and the accuracy of the combination of constraining hyperplanes and a second-order differential dynamic programming algorithm are investigated on problems of different complexity, and comparisons are made with the slack-variable and the penalty-function techniques.

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