scholarly journals Set Stability and Set Stabilization of Boolean Control Networks Avoiding Undesirable Set

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2864
Author(s):  
Wen Liu ◽  
Shihua Fu ◽  
Jianli Zhao
Keyword(s):  
Tensor Product ◽  
Design Method ◽  
Boolean Networks ◽  
Control Networks ◽  
State Subset ◽  
Time Optimal ◽  
Set Stabilization ◽  
Optimal Set

The traditional set stability of Boolean networks (BNs) refers to whether all the states can converge to a given state subset. Different from the existing results, the set stability investigated in this paper is whether all states in a given initial set can converge to a given destination set. This paper studies the set stability and set stabilization avoiding undesirable sets of BNs and Boolean control networks (BCNs), respectively. First, by virtue of the semi-tensor product (STP) of matrices, the dynamics of BNs avoiding a given undesirable set are established. Then, the set reachability and set stability of BNs from the initial set to destination set avoiding an undesirable set are investigated, respectively. Furthermore, the set stabilization of BCNs from the initial set to destination set avoiding a given undesirable set are investigated. Finally, a design method for finding the time optimal set stabilizer is proposed, and an example is provided to illustrate the effectiveness of the results.

Constrained Optimization of Multi-Degree-of-Freedom Mechanisms for Near-Time Optimal Motions

1992 ◽  
Author(s):  
Satish Sundar ◽  
Zvi Shiller
Keyword(s):  
Constrained Optimization ◽  
Design Method ◽  
Close Correlation ◽  
Optimization Methods ◽  
Pattern Search ◽  
Degree Of Freedom ◽  
Design Parameters ◽  
Maximum Acceleration ◽  
Time Optimal ◽  
Order Of Magnitude

Abstract This paper presents a design method of multi-degree-of-freedom mechanisms for near-time optimal motions. The design objective is to select system parameters, such as link lengths and actuator sizes, so as to minimize the optimal motion time of the mechanism along a given path. The exact time optimization problem is approximated by a simpler procedure that maximizes the acceleration near the end points. Representing the directions of maximum acceleration with the acceleration lines, and the reachability constraints as explicit functions of the design parameters, we transform the constrained optimization to a simpler curve fitting problem that can be formulated analytically. This allows the use of efficient gradient type optimizations, instead of the pattern search optimization that is otherwise required. Examples for optimizing the dimensions of a five-bar planar mechanism demonstrate close correlation of the approximate with the exact solutions, and an order of magnitude better computational efficiency than the previously developed unconstrained optimization methods.

Direct Optimization of Multi-Degree-of-Freedom Mechanisms for Near Time Optimal Motions Along Specified Paths

1991 ◽  
Author(s):  
Satish Sundar ◽  
Zvi Shiller
Keyword(s):  
Design Method ◽  
Close Correlation ◽  
Optimization Methods ◽  
Degree Of Freedom ◽  
Design Parameters ◽  
Direct Optimization ◽  
Fitting Procedure ◽  
Time Optimal ◽  
Approximate Cost ◽  
The Given

Abstract A design method for selecting system parameters of multi-degree-of-freedom mechanisms for near minimum time motions along specified paths is presented. The time optimization problem is approximated by a simple curve fitting procedure that fits, what we call, the acceleration lines to the given path. The approximate cost function is explicit in the design parameters, facilitating the formulation of the design problem as a constrained optimization. Examples for optimizing the dimensions of a five-bar planar mechanism demonstrate close correlation between the approximate and the exact solutions and better computational efficiency than the previous unconstrained optimization methods.

Sign in / Sign up

Export Citation Format

Share Document