Multi-Objecitve Control of Dynamical Systems

1995 ◽  
Author(s):  
Petros Voulgaris
Keyword(s):  
Exact Solution ◽  
Duality Theory ◽  
Closed Loop ◽  
Finite Impulse Response ◽  
Optimal Solution ◽  
Standard Methods ◽  
Continuity Properties ◽  
Step Procedure ◽  
Quadratic Programming Problems ◽  
Finite Step

Abstract In this paper we consider the problem of minimizing the H2-norm of the closed loop map while maintaining its ℓ1-norm at a prescribed level. The problem is analyzed in the case of discrete-time, SISO closed loop maps. Utilizing duality theory, it is shown that the optimal solution is unique and has a finite impulse response. A finite step procedure is given for the construction of the exact solution. This procedure consists of solving a finite number of quadratic programming problems which can be performed using standard methods. Finally, continuity properties of the optimal solution with respect to changes in the ℓ1-constraint are established.

Generalized Transient Leveque Problem

1996 ◽  
Vol 61 (9) ◽  
pp. 1267-1284
Author(s):  
Ondřej Wein
Keyword(s):  
Mass Transfer ◽  
Exact Solution ◽  
Shear Rate ◽  
Transfer Problem ◽  
Numerical Data ◽  
Wall Shear Rate ◽  
Response Operator ◽  
Mass Transfer Problem ◽  
Finite Step ◽  
General Response

Response of an electrodiffusion friction sensor to a finite step of the wall shear rate is studied by numerically solving the relevant mass-transfer problem. The resulting numerical data on transient currents are treated further to provide reasonably accurate analytical representations. Existing approximations to the general response operator are checked by using the obtained exact solution.

The Location Problem of Given and Indivisible Different Units

1970 ◽  
Vol 2 (3) ◽  
pp. 341-356
Author(s):  
G. Jándy
Keyword(s):  
Exact Solution ◽  
Heuristic Algorithm ◽  
Network Flow ◽  
Location Problem ◽  
Optimal Solution ◽  
Type Problem ◽  
Distribution Problem ◽  
Enumeration Algorithm ◽  
Weighted Distribution ◽  
Partial Enumeration

In cases where certain simplifications are allowed, the location optimisation of given and indivisible different economic units may be modelled as a bi-value weighted distribution problem. The paper presents a heuristic algorithm for this network-flow-type problem and also a partial enumeration algorithm for deriving the exact solution. But it is also pointed out that an initial sub-optimal solution can quickly be improved with a derivation on a direct line only, if the exact solution is not absolutely essential. A numerical example is used to illustrate the method of derivation on a direct line starting with an upper bound given by a sub-optimal solution.

scholarly journals Robust and Optimal Output-Feedback Control for Interval State-Space Model: Application to a Two-Degrees-of-Freedom Piezoelectric Tube Actuator

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Mounir Hammouche ◽  
Philippe Lutz ◽  
Micky Rakotondrabe
Keyword(s):  
State Space ◽  
Output Feedback ◽  
Degrees Of Freedom ◽  
Closed Loop ◽  
State Space Model ◽  
Output Feedback Control ◽  
Optimal Solution ◽  
Loop System ◽  
Closed Loop System ◽  
Optimal Output

The problem of robust and optimal output feedback design for interval state-space systems is addressed in this paper. Indeed, an algorithm based on set inversion via interval analysis (SIVIA) combined with interval eigenvalues computation and eigenvalues clustering techniques is proposed to seek for a set of robust gains. This recursive SIVIA-based algorithm allows to approximate with subpaving the set solutions [K] that satisfy the inclusion of the eigenvalues of the closed-loop system in a desired region in the complex plane. Moreover, the LQ tracker design is employed to find from the set solutions [K] the optimal solution that minimizes the inputs/outputs energy and ensures the best behaviors of the closed-loop system. Finally, the effectiveness of the algorithm is illustrated by a real experimentation on a piezoelectric tube actuator.

An Infrastructure to Support Closed Loop Product Development Practice Coupled With Rapid Prototyping

1998 ◽  
Author(s):  
Shuichi Fukuda ◽  
Ping-Yu Jiang
Keyword(s):  
Product Development ◽  
Rapid Prototyping ◽  
Quality Function Deployment ◽  
Closed Loop ◽  
Design Procedure ◽  
Optimal Solution ◽  
Chain Process ◽  
Process Chain ◽  
Rp Process ◽  
Development Practice

Abstract This paper deals with a methodology to use rapid prototyping and tooling to aid the product development practice. Under the support of the distributive activity scheduling mechanism and the unified product data model, a closed loop is described, which consists of design-phase-oriented requirement analysis of RP/RT applications, multi-criterion decision-making mechanism for selecting the combination of materials, RP method, and RP process chain, process planning for rapid prototyping and tooling, data collections from RP manufacturing, design evaluations based on manufactured prototypes, as well as case-based learning from RP process chain. Here, quality function deployment is used for quality control and assurance of such a design closed cycle. Several such closed loops during product design procedure will make the product go to a optimal solution. In addtion, concurrence and competence issues inside a closed loop design evaluation cycle are also discussed. Finally, a conclusion about this methodology is drawn.

Design of Low Order Controllers for Decoupled MIMO Systems With Time Response Specifications

2018 ◽  
pp. 90-128
Author(s):  
Maher Ben Hariz ◽  
Wassila Chagra ◽  
Faouzi Bouani
Keyword(s):  
Convex Optimization ◽  
Optimization Problem ◽  
Closed Loop ◽  
Mimo Systems ◽  
Design Method ◽  
Optimal Solution ◽  
Time Response ◽  
Convex Optimization Problem ◽  
Tito Systems ◽  
Low Order

The design of a low order controller for decoupled MIMO systems is proposed. The main objective of this controller is to guarantee some closed loop time response performances such as the settling time and the overshoot. The controller parameters are obtained by resolving a non-convex optimization problem. In order to obtain an optimal solution, the use of a global optimization method is suggested. In this chapter, the proposed solution is the GGP method. The principle of this method consists of transforming a non-convex optimization problem to a convex one by some mathematical transformations. So as to accomplish the fixed goal, it is imperative to decouple the coupled MIMO systems. To approve the controllers' design method, the synthesis of fixed low order controller for decoupled TITO systems is presented firstly. Then, this design method is generalized in the case of MIMO systems. Simulation results and a comparison study between the presented approach and a PI controller are given in order to show the efficiency of the proposed controller. It is remarkable that the obtained solution meets the desired closed loop time specifications for each system output. It is also noted that by considering the proposed approach the user can fix the desired closed loop performances for each output independently.

scholarly journals Proximity measures based on KKT points for constrained multi-objective optimization

2020 ◽  
Author(s):  
Gabriele Eichfelder ◽  
Leo Warnow
Keyword(s):  
Evolutionary Algorithms ◽  
Optimal Solution ◽  
Necessary Optimality Conditions ◽  
Kkt Conditions ◽  
Test Problems ◽  
Numerical Verification ◽  
Termination Criteria ◽  
Continuity Properties ◽  
Optimal Solution Set ◽  
Proximity Measures

AbstractAn important aspect of optimization algorithms, for instance evolutionary algorithms, are termination criteria that measure the proximity of the found solution to the optimal solution set. A frequently used approach is the numerical verification of necessary optimality conditions such as the Karush–Kuhn–Tucker (KKT) conditions. In this paper, we present a proximity measure which characterizes the violation of the KKT conditions. It can be computed easily and is continuous in every efficient solution. Hence, it can be used as an indicator for the proximity of a certain point to the set of efficient (Edgeworth-Pareto-minimal) solutions and is well suited for algorithmic use due to its continuity properties. This is especially useful within evolutionary algorithms for candidate selection and termination, which we also illustrate numerically for some test problems.

A Simple Structure for Bilateral Transparent Teleoperation Systems With Time Delay

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Alireza Alfi ◽  
Mohammad Farrokhi
Keyword(s):  
Time Delay ◽  
Closed Loop ◽  
Simple Structure ◽  
Finite Impulse Response ◽  
Structure Design ◽  
Loop System ◽  
Bilateral Teleoperation ◽  
Closed Loop System ◽  
The Stability ◽  
Teleoperation Systems

This paper presents a simple structure design for bilateral teleoperation systems with uncertainties in time delay in communication channel. The goal is to achieve complete transparency and robust stability for the closed-loop system. For transparency, two local controllers are designed for the bilateral teleoperation systems. One local controller is responsible for tracking the master commands, and the other one is in charge of force tracking as well as guaranteeing the stability of the closed-loop system in the presence of uncertainties in time delay. The stability analysis will be shown analytically for two cases: (I) the possibly stability and (II) the intrinsically stability. Moreover, in Case II, in order to generate the proper inputs for the master controller in the presence of uncertainties in time delay, an adaptive finite impulse response (FIR) filter is designed to estimate the time delay. The advantages of the proposed method are threefold: (1) stability of the closed-loop system is guaranteed under some mild conditions, (2) the whole system is transparent, and (3) design of the local controllers is simple. Simulation results show good performance of the proposed method.

Synthesis of Controllers for MIMO Systems with Time Response Specifications

2014 ◽  
Vol 3 (3) ◽  
pp. 25-52 ◽  
Author(s):  
Maher Ben Hariz ◽  
Wassila Chagra ◽  
Faouzi Bouani
Keyword(s):  
Global Optimization ◽  
Optimization Problem ◽  
Closed Loop ◽  
Controller Design ◽  
Mimo Systems ◽  
Optimal Solution ◽  
Optimization Method ◽  
Time Response ◽  
Step Response ◽  
Global Optimization Method

This paper proposes the design of fixed low order controllers for Multi Input Multi Output (MIMO) decoupled systems. The simplified decoupling is used as a decoupling system technique due to its advantages compared to other decoupling methods. The main objective of the proposed controllers is to satisfy some desired closed loop step response performances such as the settling time and the overshoot. The controller design is formulated as an optimization problem which is non convex and it takes in account the desired closed loop performances. Therefore, classical methods used to solve the non convex optimization problem can generate a local solution and the resulting control law is not optimal. Thus, the thought is to use a global optimization method in order to obtain an optimal solution which will guarantee the desired time response specifications. In this work the Generalized Geometric Programming (GGP) is exploited as a global optimization method. The key idea of this method consists in transforming an optimization problem, initially, non convex to a convex one by some mathematical transformations. Simulation results and a comparison study between the presented approach and a Proportional Integral (PI) controller are given in order to shed light the efficiency of the proposed controllers.

scholarly journals Optimality Conditions for Fuzzy Number Quadratic Programming with Fuzzy Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Xue-Gang Zhou ◽  
Bing-Yuan Cao ◽  
Seyed Hadi Nasseri
Keyword(s):  
Quadratic Programming ◽  
Objective Function ◽  
Optimality Conditions ◽  
Fuzzy Number ◽  
Duality Theory ◽  
Quadratic Function ◽  
Linear Functions ◽  
Duality Results ◽  
Constraint Set ◽  
Quadratic Programming Problems

The purpose of the present paper is to investigate optimality conditions and duality theory in fuzzy number quadratic programming (FNQP) in which the objective function is fuzzy quadratic function with fuzzy number coefficients and the constraint set is fuzzy linear functions with fuzzy number coefficients. Firstly, the equivalent quadratic programming of FNQP is presented by utilizing a linear ranking function and the dual of fuzzy number quadratic programming primal problems is introduced. Secondly, we present optimality conditions for fuzzy number quadratic programming. We then prove several duality results for fuzzy number quadratic programming problems with fuzzy coefficients.

scholarly journals Decision Analysis of E-commerce Closed-loop Supply Chain with Different Recycling Modes

2021 ◽  
Vol 257 ◽  
pp. 02019
Author(s):  
Sijia Liu ◽  
Yanting Huang
Keyword(s):  
Supply Chain ◽  
Optimal Strategy ◽  
Mixed Mode ◽  
Closed Loop ◽  
Optimal Solution ◽  
The Other ◽  
Price Sensitivity ◽  
Closed Loop Supply Chain ◽  
Closed Loop Supply Chains ◽  
The Game Theory

According to an e-commerce closed-loop supply chain dominated by manufacturers, which is composed of manufacturers and e-commerce platforms, divided into three different recovery mode: manufacturers recycling mode alone, electric business platform recycling mode alone, and manufacturers and electric business platform mixed mode, using the game theory to solve, compares three closed-loop supply chains found: (1)When the recycling price sensitivity is high, the optimal strategy of the manufacturer is the manufacturers recycling mode alone; when the price sensitivity of recycling is low, the manufacturer’s best strategy is the independent recycling mode of the e-commerce platform. No matter how sensitive the recycling price is, the profits of the manufacturer under the mixed recycling mode are always lower than those under the other two recycling modes. (2) When the recycling price sensitivity is high, the optimal strategy of the electric business platform is the mixed recycling mode; when the price sensitivity of recycling is low, the optimal solution of the electric business platform is the independent recycling mode of the electric business platform. (3) When the recovery price sensitivity is low, the best strategy of both is the separate recycling mode of the electric business platform.

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