Existence Of Feasible Solutions Research Articles

Generalized Variable Gain ADRC for Nonlinear Systems and Its Application to Delta Parallel Manipulators

In this paper, a novel generalized variable gain active disturbance rejection control (VGADRC) method is proposed for the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> -th order nonlinear system. The generalized VGADRC, including generalized variable gain tracking differentiator (VGTD), generalized variable gain extended state observer (VGESO), and generalized variable gain controller (VGC), incorporates error-based variable gains to achieve desired control performance. Moreover, the stability analysis of VGADRC is performed, and the existence of feasible solutions are discussed and expressed explicitly. Finally, the generalized VGADRC method is applied to delta parallel manipulators, and the numerical simulation results and experiment results are presented to illustrate the effectiveness of the proposed method.

Distributed zone MPC of pressure management for water distribution network systems

In the pressure management of large scale water distribution network (WDN), a distributed zone model predictive control (MPC) is proposed to keep the terminal water head in thedesired pressure range for satisfying the customer's demand, avoiding frequently operating of the actuator and reducing the correlation between subsystems. To ensure the existence of feasible solutions of constrained distributed zone MPC, a new reference trajectory of the tank level is introduced as an optimised variable. With the consideration of the desired pressure range constraints on the new reference trajectory and some physical constraints on the corresponding physical variables, a distributed zone MPC is presented to minimise the weighted sum of the three terms in the proposed performance index. To achieve the convergence of distributed zone MPC optimisation problem, an augmented Lagrangian formulation is applied to the distributed coordinated strategy. The proposed distributed zone MPC is applied to the WDN in the Shinan district of Shanghai, and the effectiveness of the method is illustrated.

On boundary optimal control problem for an arterial system: Existence of feasible solutions

We discuss a control constrained boundary optimal control problem for the Boussinesq-type system arising in the study of the dynamics of an arterial network. We suppose that a control object is described by an initial-boundary value problem for 1D system of pseudo-parabolic nonlinear equations with an unbounded coefficient in the principal part and Robin boundary conditions. The main question we discuss in this part of paper is about topological and algebraical properties of the set of feasible solutions. Following Faedo–Galerkin method, we establish the existence of weak solutions to the corresponding initial-boundary value problem and show that these solutions possess some special extra regularity properties which play a crucial role in the proof of solvability of the original optimal control problem.

A comparison of alternative strategies for optimal utilisation of tyre friction forces aimed at vehicle lateral-plane motion control

In this paper, three strategies are analysed and compared for optimal determination of tyre friction forces used for vehicle lateral-plane motion control. The valueability of this determination depends on the feasibility of the solution of a real-time optimisation problem. In strategy (III), the optimisation problem is relaxed from the equality constraints (enforced in strategies (I) and (II)) posed owing to the stabilisation and tracking objectives of the closed loop and instead these objectives are included in the cost function of the optimisation problem. In this way, the problem of the existence of feasible solution encountered in strategy (II) is remedied without infringing the saturation restrictions imposed by the limited physical capability of the tyres and actuators in developing tyre friction forces, which was overlooked in strategy (I). Detailed simulation studies show convincing performance that can be achieved with strategy (III) in physical entire range of operation including mild, moderate and severe manoeuvre conditions.

Scheduling a single vehicle in the just-in-time part supply for a mixed-model assembly line

This paper focuses on the scheduling of a single vehicle, which delivers parts from a storage centre to workstations in a mixed-model assembly line. In order to avoid part shortage and to cut down total inventory holding and travelling costs, the destination workstation, the part quantity and the departure time of each delivery have to be specified properly according to predetermined assembly sequences. In this paper, an optimisation model is established for the configuration that only one destination workstation is involved within each delivery. Four specific properties of the problem are deduced, then a backward-backtracking approach and a hybrid GASA (genetic algorithm and simulated annealing) approach are developed based on these properties. Both two approaches are applied to several groups of instances with real-world data, and results show that the GASA approach is efficient even in large instances. Furthermore, the existence of feasible solutions (EOFS) is analysed via instances with different problem settings, which are obtained by an orthodox experimental design (ODE). An analysis of variance (ANOVA) shows that the buffer capacity is the most significant factor influencing the EOFS. Besides this, both the assembly sequence length and distances to workstations also have noticeable impacts.

Flowsheet simulation of aqueous two‐phase extraction systems for protein purification

AbstractBACKGROUND: Aqueous two‐phase extraction (ATPE) has many advantages as an efficient, inexpensive large‐scale liquid–liquid extraction technique for protein separation. However, the realization of ATPE as a protein separation technology at industrial scales is rather limited due to the large, multidimensional design space and the paucity of design approaches to predict phase and product behavior in an integrated fashion with overall system performance. This paper describes a framework designed to calculate suitable flowsheets for the extraction of a target protein from a complex protein feed using ATPE. The framework incorporated a routine to set up flowsheets according to target protein partitioning behavior in specific ATPE systems and a calculation of the amounts of phase‐forming components needed to extract the target protein. The thermodynamics of phase formation and partitioning were modeled using Flory‐Huggins theory and calculated using a Gibbs energy difference minimization approach.RESULTS: As a case study, suitable flowsheets to recover phosphofructokinase from a simple model feedstock using poly(ethylene glycol)‐dextran (PEG6000‐DxT500) and poly(ethylene glycol)‐salt (PEG6000‐Na3PO4) two‐phase systems were designed and the existence of feasible solutions was demonstrated. The flowsheets were compared in terms of product yield, product purity, phase settling rate and scaled process cost. The effect of the mass flowrates of phase‐forming components on product yield and purity was also determined.CONCLUSION: This framework is proposed as a basis for flowsheet optimization for protein purification using ATPE systems. Copyright © 2010 Society of Chemical Industry

A method for parametrized contingency‐constrained optimal power flow (PCCOPF)

AbstractThis paper presents a method for Parametrized Contingency Constrained Optimal Power Flow (PCCOPF) whose formulation can discriminate unpreventable contingencies, determine the existence of feasible solutions for postcontingencies, and analyze the feasible solution for the contingencies in terms of static sense. The proposed formulation is based on parametrized contingency constraints in which each contingency parameter represents the achievement ratio of each selected contingency. In the formulation, not only parametrized contingency constraints are given by a set of equality constraints which is modified power flow equations, but also the objective is maximization of the sum of the achievement ratios of selected contingencies. Since contingency parameters are treated as decision variables in the proposed method, the information on unsolvability with respect to each contingency can be efficiently obtained. The feasibility and effectiveness of the proposed method are demonstrated on test problems with 4‐bus and 71‐bus systems. © 2003 Wiley Periodicals, Inc. Electr Eng Jpn, 144(1): 21–31, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.10182

Unified Approach for Optimization of Vehicle Motion

AbstractA direct‐search approach for time and energy optimization of vehicles (V) in point‐to‐point operation is developed. The test control functions are consistent with the Pontryagin maximum principle and conform to the control and state constraints. After appropriate input‐output pairing, the control synthesis task is transformed into a set of parameter optimization problems. Under a weak condition, existence of feasible solutions can be guaranteed. The optimization procedure is demonstrated on a full dynamic model of an electrically driven underwater V.

On the Optimal Placement of Robot Manipulators and Work Stations

Abstract A direct-search control synthesis procedure for robots in point-to-point operation is, at first, proposed. The performance index is the mixed time energy loss functional. The procedure uses a set of simple, linear spline parameterized control functions and a weak conditions given to ensure existence of feasible solutions. On the base of the procedure above proposed, the problem of optimal placement is converted into a problem of nonlinear programming. An illustrative example is given to show how sensitive is the movement execution time with respect to the layout of the manipulator

フレキシブルロボットアームの逆動力学に関する有効解の存在条件とアームの設計基準

フレキシブルロボットアームの逆動力学に関する有効解の存在条件とアームの設計基準

Zur kepplimg eines exakten verfahrens mit einem heuristiscieb verfahren für die lösung ganzzahliger linearer optimierungsprobleme

Combining an exact method with a heuristic approach possibilities for solving linear mixed integer optimization problems are investigated. For the considered exact method numerical results with problems from the practice are given. Proper heuristic methods are the interior path methods [2] for which numerical experiences are well-known or the so-called geometric approach [8], Deriving of sufficient conditions for the existence of feasible solutions is possible.