A New Approach to the Control Design of Fuzzy Dynamical Systems

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Ye-Hwa Chen
Keyword(s):  
Dynamical Systems ◽  
Optimization Problem ◽  
Closed Form Solution ◽  
Control Design ◽  
Form Solution ◽  
Bottom Line ◽  
New Approach ◽  
Fuzzy Dynamical System ◽  
The Cost ◽  
Fuzzy Dynamical Systems

A new approach to the control design for fuzzy dynamical systems is proposed. For a fuzzy dynamical system, the uncertainty lies within a fuzzy set. The desirable system performance is twofold: one deterministic and one fuzzy. While the deterministic performance assures the bottom line, the fuzzy performance enhances the cost consideration. Under this setting, a class of robust controls is proposed. The control is deterministic and is not if-then rules-based. An optimal design problem associated with the control is then formulated as a constrained optimization problem. We show that the problem can be solved and the solution exists and is unique. The closed-form solution and cost are explicitly shown. The resulting control is able to guarantee the prescribed deterministic performance and minimize the average fuzzy performance.

A SIMPLE SOLUTION METHOD FOR THE FINITE HORIZON EOQ MODEL FOR DETERIORATING ITEMS WITH COST CHANGES

2011 ◽  
Vol 28 (06) ◽  
pp. 689-704 ◽  
Author(s):  
HORNG-JINH CHANG ◽  
WEN-FENG LIN
Keyword(s):  
Closed Form Solution ◽  
Minimum Cost ◽  
Form Solution ◽  
Inventory System ◽  
Finite Horizon ◽  
Eoq Model ◽  
Ordering Policy ◽  
Optimal Ordering Policy ◽  
Cost Parameters ◽  
The Cost

In this article, we generalize Lev and Weiss's (1990) finite horizon economic order quantity (EOQ) model with cost change to the inventory system with deterioration. Supplier announces some or all of cost parameters may change after a decided time. Depending on whether the inventory is depleted at the time of the last opportunity to purchase before some or all of the cost parameters may change, there are two types of inventory models to be discussed. The main objective of this paper is to identify the optimal ordering policy of the inventory system by comparing the minimum cost of the two types of models. We suggest a finite horizon EOQ model to combine the above two types and propose a theorem that can quickly identify the optimal policy of the suggested model. In considering temporary price discount problem and discrete-time EOQ problem, in general, there are integer operators in mathematical models, but our approach offers a closed-form solution to these kinds of problems. Numerical examples are presented to demonstrate the results of the proposed properties and theorem.

Equations of Motion for Nonholonomic, Constrained Dynamical Systems via Gauss’s Principle

1993 ◽  
Vol 60 (3) ◽  
pp. 662-668 ◽  
Author(s):  
R. E. Kalaba ◽  
F. E. Udwadia
Keyword(s):  
Dynamical Systems ◽  
Closed Form ◽  
Programming Problem ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Closed Form Solution ◽  
Nonholonomic Constraints ◽  
Form Solution ◽  
Constrained Motion ◽  
Constraint Forces

In this paper we develop an analytical set of equations to describe the motion of discrete dynamical systems subjected to holonomic and/or nonholonomic Pfaffian equality constraints. These equations are obtained by using Gauss’s Principle to recast the problem of the constrained motion of dynamical systems in the form of a quadratic programming problem. The closed-form solution to this programming problem then explicitly yields the equations that describe the time evolution of constrained linear and nonlinear mechanical systems. The direct approach used here does not require the use of any Lagrange multipliers, and the resulting equations are expressed in terms of two different classes of generalized inverses—the first class pertinent to the constraints, the second to the dynamics of the motion. These equations can be numerically solved using any of the standard numerical techniques for solving differential equations. A closed-form analytical expression for the constraint forces required for a given mechanical system to satisfy a specific set of nonholonomic constraints is also provided. An example dealing with the position tracking control of a nonlinear system shows the power of the analytical results and provides new insights into application areas such as robotics, and the control of structural and mechanical systems.

Rupture Instability of Plane Membranes and Solids

1960 ◽  
Vol 27 (3) ◽  
pp. 501-504
Author(s):  
S. F. Borg
Keyword(s):  
Closed Form ◽  
Continuum Mechanics ◽  
Closed Form Solution ◽  
Practical Interest ◽  
Form Solution ◽  
Compatibility Conditions ◽  
New Approach ◽  
Conservation Equations ◽  
Dynamic Phenomena

A fundamentally new approach to the rupture-fracture problem is presented. Because of the particular type of dynamic phenomena being investigated, the formulation is given in terms of the conservation equations of continuum mechanics instead of in the usual elasticity-plasticity relations. The introduction of a similarity co-ordinate permits a complete closed-form solution to a particular problem of practical interest subject to certain compatibility conditions which depend upon the specific properties of the material under consideration.

The Proximal Bootstrap for Finite-Dimensional Regularized Estimators

2021 ◽  
Vol 111 ◽  
pp. 616-620
Author(s):  
Jessie Li
Keyword(s):  
Optimization Problem ◽  
Closed Form Solution ◽  
Form Solution ◽  
Support Vector ◽  
Computationally Efficient ◽  
L1 Norm ◽  
Efficient Manner ◽  
Finite Dimensional ◽  
Consistent Estimators ◽  
Nuclear Norm Regularization

We propose a proximal bootstrap that can consistently estimate the limiting distribution of sqrt(n)-consistent estimators with nonstandardasymptotic distributions in a computationally efficient manner by formulating the proximal bootstrap estimator as the solution to aconvex optimization problem, which can have a closed-form solution for certain designs. This paper considers the application to finite-dimensionalregularized estimators, such as the lasso, l1-norm regularized quantile regression, l1-norm support vector regression, and trace regression via nuclear norm regularization.

Design of an actuator fault-tolerant controller for an air vehicle with nonlinear dynamics

2018 ◽  
Vol 233 (10) ◽  
pp. 3534-3546 ◽  
Author(s):  
Sajad Roshanravan ◽  
Behnam Sobhani Gendeshmin ◽  
Saeed Shamaghdari
Keyword(s):  
Nonlinear Model ◽  
Optimization Problem ◽  
Closed Loop ◽  
Fault Tolerant ◽  
Control Design ◽  
Actuator Fault ◽  
Nonlinear Dynamic Model ◽  
New Approach ◽  
Air Vehicle ◽  
Novel Method

In this paper, a novel method is presented to design an autopilot for an air vehicle with a polynomial nonlinear model. This method employs the nonlinear model directly in the control design process without the need for local linearization about an operating point. It is shown that the control design problem can be formulated as a sum-of-squares optimization problem. This method guarantees exponential stability of the closed-loop nonlinear system by introducing a polynomial Lyapunov function. The nonlinear dynamic model of air vehicles can usually be represented in the polynomial form. Therefore, the proposed method can widely be applied to design an air vehicle autopilot. Besides using the proposed method along with the projection based and online redesign methods, a fault-tolerant controller is designed for the air vehicle. Furthermore, a new approach is developed by combination of these methods to fault-tolerant control system design. The proposed method is applied to design a fault-tolerant controller for a nonlinear pitch-axis model of an air vehicle subject to loss of effectiveness actuator fault. The simulation results show the efficiency of the proposed method.

scholarly journals Tsallis Entropy of Fuzzy Dynamical Systems

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 264
Author(s):  
Dagmar Markechová
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Conditional Entropy ◽  
Tsallis Entropy ◽  
Positive Real ◽  
Fuzzy Dynamical System ◽  
Fuzzy Partitions ◽  
Definition Of ◽  
Mathematical Behavior ◽  
Fuzzy Dynamical Systems

This article deals with the mathematical modeling of Tsallis entropy in fuzzy dynamical systems. At first, the concepts of Tsallis entropy and Tsallis conditional entropy of order where is a positive real number not equal to 1, of fuzzy partitions are introduced and their mathematical behavior is described. As an important result, we showed that the Tsallis entropy of fuzzy partitions of order satisfies the property of sub-additivity. This property permits the definition of the Tsallis entropy of order of a fuzzy dynamical system. It was shown that Tsallis entropy is an invariant under isomorphisms of fuzzy dynamical systems; thus, we acquired a tool for distinguishing some non-isomorphic fuzzy dynamical systems. Finally, we formulated a version of the Kolmogorov–Sinai theorem on generators for the case of the Tsallis entropy of a fuzzy dynamical system. The obtained results extend the results provided by Markechová and Riečan in Entropy, 2016, 18, 157, which are particularized to the case of logical entropy.

scholarly journals Non-Abelian firewall

2020 ◽  
Vol 29 (14) ◽  
pp. 2043003
Author(s):  
Douglas Singleton
Keyword(s):  
Energy Density ◽  
Equivalence Principle ◽  
Closed Form Solution ◽  
Information Loss ◽  
Form Solution ◽  
Field Equations ◽  
Yang Mills ◽  
Information Loss Paradox ◽  
The Cost ◽  
Mills Field

A simple, closed-form solution to the Yang-Mills field equations is presented which has a non-Abelian firewall — a spherical “horizon” where the energy density diverges. By the gravity/gauge duality, this non-Abelian firewall implies the existence of a gravitational firewall. Gravitational firewalls have been proposed as a way of resolving the information loss paradox, but at the cost of violating the equivalence principle.

scholarly journals Closed form solution in buckling optimization problem of twisted rod

2021 ◽  
Author(s):  
Vladimir Kobelev
Keyword(s):  
Closed Form ◽  
Cross Section ◽  
Cross Sections ◽  
Optimization Problem ◽  
Closed Form Solution ◽  
Form Solution ◽  
Optimal Shape ◽  
Actual Problem ◽  
The Cross ◽  
Simply Connected

Abstract The applications of this method for stability problems are illustrated in this manuscript. In the context of twisted rods, the counterpart for Euler’s buckling problem is Greenhill's problem, which studies the forming of a loop in an elastic bar under torsion (Greenhill, 1883). We search the optimal shape of the rod along its axis. A priori form of the cross-section remains unknown. For the solution of the actual problem the stability equations take into account all possible convex, simply connected shapes of the cross-section. Thus, we drop the assumption about the equality of principle moments of inertia for the cross-section. The cross-sections are similar geometric figures related by a homothetic transformation with respect to a homothetic center on the axis of the rod and vary along its axis. The distribution of material along the length of a twisted rod is optimized so that the rod is of the constant volume T and will support the maximal moment without spatial buckling. The cross section that delivers the maximum or the minimum for the critical eigenvalue must be determined among all convex, simply connected domains. We demonstrate at the beginning the validity of static Euler’s approach for simply supported rod (hinged), twisted by the conservative moment. The applied method for integration of the optimization criteria delivers different length and volumes of the optimal twisted rods. Instead of the seeking for the twisted rods of the fixed length and volume, we directly compare the twisted rods with the different lengths and cross-sections using the invariant factors. The solution of optimization problem for twisted rod is stated in closed form in terms of the higher transcendental functions. In the torsion stability problem, the optimal shape of cross-section is the equilateral triangle.

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