Region Of Feasibility Research Articles

Asynchronous time dependent switched model predictive control for nonlinear systems considering feasibility constraints

AbstractThis paper presents a model predictive control for nonlinear asynchronous switched systems, aiming to achieve H∞ performance and addressing feasibility issues. The method proposed guarantees the recursive feasibility of each sub‐system after switching moments in the presence of exogenous disturbances and unknown matched and mismatched time intervals due to asynchronous switching. The boundaries of the feasibility region for each sub‐system are determined in order to impose constraints on decision parameters and switching signals. These constraints aim to maximize the mentioned region while ensuring stability. Additionally, by identifying the common region of feasibility among different sub‐systems, conditions are established for initializing the sub‐systems at the switching moments to ensure that the system states remain within this feasibility region even under the worst switching scenario. Therefore, by ensuring the initial feasibility at the switching moments and demonstrating recursive feasibility, the overall feasibility of the developed MPC is guaranteed at all times. The benefits of the proposed approach are thoroughly investigated through the simulation of a chemical system. The results demonstrate the effectiveness of the proposed method.

The methodological approach to determination of the optimal content of excipients in the composition of tablets

Aim. To determine the algorithm of the optimal amount of excipients in the composition of tablets based on common ginger. Materials and methods. The study object was the regression equations determining the quantitative effect of excipients in the composition of the dosage form on the target pharmacopeial characteristics. The mathematical processing of these equations was carried out using the Mathcad 15 computer program according to the algorithm proposed. Results and discussion. It has been proposed to use the approximation function to determine the level of optimization. The approximation function is the sum of the squares of deviations of the objective functions from their optimal values. It has been proven that identification of mathematical models in pharmaceutical studies with three dependent factors, which total value is determined by the quantitative composition of a dosage form and is fixed at a certain level, is difficult to perform due to the complicated interpretation of multiple regression parameters as characteristics of factors in an isolated form through their correlation. The region for the optimal solution has been proposed with respect to the values of factors and effective indicators of a multiple regression model. The methodological approach to determining the optimal content of excipients in the composition of the given dosage form has been proposed. Conclusions. The optimal content of excipients – neusilin and colidone – has been determined while developing the composition of tablets based on common ginger with the necessary pharmacological and technological indicators that meet the requirements of the State Pharmacopoeia of Ukraine. The approach to the formation of the region offeasibility in two-way studies has been considered. Using the theory of multi-vector optimization a criterion has been developed; it allows determining the optimal feasible solution in the region under conditions of restrictions both by factors and target indicators.

Statistical design of sustainable composites from poly(lactic acid) and grape pomace

AbstractBiocomposites from poly(lactic acid) (PLA) and grape pomace (GP) were created via injection molding to examine the effects of GP in a PLA matrix. To optimize the mechanical performance the biocomposites were compatibilized with maleic anhydride grafted PLA (MA‐g‐PLA). The objective of this work was to create a model that could accurately predict the mechanical properties of GP/PLA biocomposites. A region of feasibility for the biocomposites was determined using a statistical design of experiments. Linear regression was used to model the mechanical performance and predicted results with an error of 10% for both tensile and flexural strength and 16% for impact strength. The model was verified with a biocomposite of PLA/GP/MA‐g‐PLA with a ratio of 62/36/2. This biocomposite had a tensile strength, flexural modulus, and impact strength of 25.8 MPa, 40.0 MPa, and 18.4 J/m, respectively. It was found that a linear model can accurately predict the mechanical properties of PLA/GP/MA‐g‐PLA biocomposites.

A study of ellipse packing in the high-dimensionality problems

The problems of optimum ellipse packing belong to the class of NP-hard problems. The issues of development of efficient algorithms based on application of local and global optimization methods, construction of adequate mathematical models based on the analytical description of the ellipse interrelations taking into account their continuous translations and rotations are of vital importance. In this article, the problem of packing of sets of ellipses in a given region taking into account conditions of nonintersection and technological restraints which are concretized in the conditions of the applied problem is formulated. The model of packing of a set of ellipses in a rectangle of minimum dimensions is constructed. Continuous ellipse rotations and translations are allowed, the possibility of availability of minimum admissible distances between them is assumed. New quasi-phi-functions are constructed for modeling of the relations of ellipse nonintersection and to define belonging of an ellipse to the container. The algorithm of search for locally optimal solutions is modified. It consists of two stages: generation of the regions of feasibility which contain the starting point and local optimization in the constructed region of feasibility. Only the algorithm step concerning construction of quasi-phi-functions is subjected to modification. It is necessary to notice that the algorithm have shown its efficiency when the quantity of ellipses does not exceed the value of 400. The model of the individual-and-flow movement of individuals approximated by ellipses with specification of technological restraints is constructed. The method of local optimization is given. Examples of computer modeling of the problems assigned in the work are given.

An LMI approach to robust model predictive control of nonlinear systems with state-dependent uncertainties

The design of robust model predictive controller (RMPC) for uncertain nonlinear system is a challenging problem in the area of nonlinear control, yet. A new approach to RMPC is presented here for nonlinear systems with state-dependent uncertainties. The nonlinear system is considered as comprised of a linear part, a nonlinear term, and a bounded additive uncertainty. A state feedback control law is obtained via solving an optimization problem of an infinite horizon quadratic cost function in the framework of linear matrix inequalities (LMIs). To solve the optimization problem, the nonlinear and uncertain terms of the system are supposed to be bounded by a quadratic function that is obtained by solving a sum of squares (SOS) optimization problem. Moreover, the sufficient state feedback synthesis condition guarantees the robust stability of the system in the presence of unknown bounded uncertainties. In this context, a LMI-based optimization problem is solved to obtain the maximum region of stability which is desired to be a subset of the region of feasibility. The simulation examples are reported to indicate the applicability and effectiveness of the proposed approach with different uncertainty scenarios.

Operational Feasibility Analysis of Stand-Alone Methanol Fuel Processors with Flexible Waste Heat Recovery Schemes

To develop a compact and portable fuel processor, two types of stand-alone methanol fuel processor using a combination of an autothermal methanol reformer, a high-temperature water–gas shift reactor, and an internal burner are presented. On the basis of different waste heat recovery schemes, designs 1 and 2, a flexible waste heat recovery design (design 2) by utilizing the split waste heat flow is verified to reduce the waste heat loss. The specific optimization algorithm for maximizing hydrogen yield is taken into account to determine the optimum operating conditions of designs 1 and 2. Through the feasibility analysis at different operational scenarios, the conflict between the optimum operating conditions and the region of operational feasibility can be found. The simulations show that the flexible waste heat recovery design with additional operating variables can raise 11% hydrogen yield and reduce 3.3% waste heat loss.

Stability analysis of constrained MPC with CLF applied to discrete-time nonlinear system

The model predictive control (MPC) strategy with a control Lyapunov function (CLF) as terminal cost is commonly used for its guaranteed stability. In most of the cases, CLF is locally designed, and the region of attraction is limited, especially when under control constraints. In this article, the stability and the region of attraction of constrained MPC that is applied to the discrete-time nonlinear system are explicitly analyzed. The region of feasibility is proposed to substitute the region of attraction, which greatly reduces the calculation burden of terminal constraints inequalities and guarantees the stability of the MPC algorithm. Also, the time-variant terminal weighted factor is proposed to improve the dynamic performance of the close-loop system. Explicit experiments verify the effectiveness and feasibility of the relative conclusions, which provide practically feasible ways to stabilize the unstable and/or fast-dynamic systems.

Reconfigurable predictive control for redundantly actuated systems with parameterised input constraints

A method is proposed for on-line reconfiguration of the terminal constraint used to provide theoretical nominal stability guarantees in linear model predictive control (MPC). By parameterising the terminal constraint, its complete reconstruction is avoided when input constraints are modified to accommodate faults. To enlarge the region of feasibility of the terminal control law for a certain class of input faults with redundantly actuated plants, the linear terminal controller is defined in terms of virtual commands. A suitable terminal cost weighting for the reconfigurable MPC is obtained by means of an upper bound on the cost for all feasible realisations of the virtual commands from the terminal controller. Conditions are proposed that guarantee feasibility recovery for a defined subset of faults. The proposed method is demonstrated by means of a numerical example.

Oxidation kinetics of n-decane in the presence of an inhibiting composition: A mathematical model

We designed an algorithm and software for inverse kinetic problem solving by conditional global minimization of the deviation of calculated data from experimental data. This approach allows use of more complete information on the process, which narrows the region of feasibility and increases the quality of mathematical simulation of chemical reactions. The algorithms designed were tested in the kinetic description of a complex liquid-phase chain reaction, specifically, the oxidation of n-decane in the presence of an inhibiting composition, viz., para-oxydiphenylamine + n-decanol.

Region of Feasibility of Interference Alignment in Underwater Sensor Networks

To enable underwater applications such as coastal and tactical surveillance, undersea explorations, and real-time picture/video acquisition, there is a need to achieve high data-rate and reliable communications underwater, which translates into attaining high acoustic channel spectral efficiencies. Interference alignment (IA), which has been recently proposed for radio-frequency multiple-input-multiple-output (MIMO) terrestrial communication systems, aims at improving the spectral efficiency by enabling nodes to transmit data simultaneously at a rate equal to half of the interference-free channel capacity. The core of IA in the space domain lies in designing transmit precoding matrices for each transmitter such that all the interfering signals align at the receiver along a direction different from that of the desired signal. While promising, however, there are still challenges to solve for the practical use of IA underwater, i.e., imperfect acoustic channel knowledge, high computational complexity, and high communication delay. In this paper, a feasibility study on the employment of IA underwater is presented. A novel distributed computing framework for sharing processing resources in the network so to parallelize and speed IA algorithms up is proposed; also, such framework enables “ensemble learning” of various precoding matrices computed using different (competing) IA algorithms so to achieve efficient alignment of the interference at the receiver. The robustness of the IA technique against imperfect acoustic channel knowledge is also quantified by estimating precoding matrices based on predicted channel coefficients. Finally, the performance of an algorithm to predict the underwater acoustic channel impulse response is presented using real data sets.

The economic assessment of micro wind turbines for South Australia

Micro wind generation is becoming a favorable form of renewable energy, in and around urban centers as it is able to discretely supplement energy drawn off the national grid without requiring large infrastructural costs. The paper describes a method to identify regions of potential profitability based upon the assessment of its net present value (NPV). By modeling the wind conditions with the 2-parameter Weibull function the wind conditions required to ensure economic feasibility of a turbine is represented using the shape factor-scale factor (SF/SCF) mapping concept. These calculations are then superimposed to a geographical map to delimit the regional boundary of interest. When applying this method to the Australian city of Adelaide, the present concept evidences that a government fiscal policy directed at supplementing a gross energy tariff will be more effective than discounting the initial capital invested by the end user to enlarge the local region of economic feasibility.

On the region of feasibility of interference alignment for underwater acoustic communication

To enable underwater applications such as coastal and tactical surveillance, undersea explorations, and picture/video acquisition, there is a need to achieve high data-rate underwater acoustic communications, which translates into attaining high acoustic channel spectral efficiencies. Interference Alignment (IA) technique, which has recently been proposed for radio-frequency MIMO terrestrial communication systems, aims at improving the spectral efficiency by enabling nodes to transmit data simultaneously at a rate equal to half of the interference-free channel capacity. The core of IA lies in designing transmit precoding matrices for each transmitter such that all the interfering signals align at the receiver along a direction different from the desired signal. To decode, the receiver projects the received signal onto a decoding vector that is orthogonal to the data vector of interfering signal. While promising, there are challenges to be solved for the use of IA underwater, i.e., 1) imperfect acoustic channel knowledge, 2) high computational complexity, and 3) high communication delay. We study the feasibility of IA in underwater environment under these challenges; we also propose a distributed computational framework to parallelize the iterative IA algorithm and determine to what extent we can parallelize it among neighboring nodes under different channel coherence times.

Generation of feasible set points and control of a cable robot

Cable-suspended robots are structurally similar to parallel-actuated robots, but with the fundamental difference that cables can only pull the end-effector, but not push it. These input constraints make feedback control of cable-suspended robots a lot more challenging than their counterpart parallel-actuated robots. In this paper, we present a computationally efficient control design procedure for a cable robot with six cables, which is kinematically determined as long as all cables are in tension. The control strategy is based on dynamic aspects of statically feasible workspace. The basic idea suggested in this paper is to represent the reachable domain in terms of achievable set points under a specified control law that respects the input constraints. This computational framework is recursively used to find a set of reachable domains, using which, we are able to expand the region of feasibility by connecting adjacent domains through common points. The salient feature of the technique is that it is computationally efficient, or online implementable, for the control of a cable robot with positive input constraints. However, due to the complexity of the dynamics of general motion of a cable robot, we consider only translations. No cable interference is considered in this paper. Finally, the effectiveness of the proposed method is illustrated by numerical simulations and laboratory experiments on a six-degree-of-freedom cable-suspended robot.

Performance Optimization of Critical Nets Through Active Shielding

We propose the concept of active shields-shields that switch concurrently with a signal wire of interest. Active shields aid signal transitions through the coupling between the signal wire and shields. For RC dominated wires, the active shields switch in the same phase as the signal wire since capacitive coupling is the dominant coupling mechanism. For wires with dominant inductive coupling, active shields switch in the opposite phase of the signal wire. We show that under fixed area and input capacitance constraints, in-phase active shielding outperforms traditional (passive) shielding and wire sizing/spacing techniques for minimizing delays and transition times on RC-dominated wires. For RLC wires, we demonstrate a region of feasibility (in terms of signal wire widths) for which opposite-phase active shielding outperforms the passive shielding technique. Opposite-phase active shielding suppresses ringing behavior to a greater degree than passive shields, providing similar performance to differential signaling while maintaining the simplicity of single ended signaling. The benefits of opposite-phase active shielding as compared to passive shielding are shown in the context of various clock net optimizations where reductions in ringing behavior (up to 4.5X) and transition times (up to 40% reduction) are achieved.

Sectional and overall reachability for systems with S-shaped distillation lines

Total and minimum reflux bounds serve as limiting case scenarios for determining feasibility in azeotropic distillation columns. Specifically, all reachable feed compositions in a staged rectifying or stripping section have been reported as the union of points enclosed by the distillation and pinch-point curves through a desired product. By eigenvalue considerations of pinch bifurcations and geometric analysis of fundamental region structures, the region of all reachable compositions has seemingly been identified. Additional insights are needed to fully characterize the feasible compositions in a subset of azeotropic mixtures. This article describes how sectional profiles can actually cross pinch-point curves and generate a region of additional feasibility outside the one previously reported. It also demonstrates how a substantially larger region between the distillation line and pinch-point curve after the intersection is only accessible by composition profiles going through the extended region. This extended reachable region is explained by evaluating the conditions for a fixed point in composition space. The effect on sectional profiles is illustrated for both an artificially parametric VLE manifold and a nonideal azeotropic system with more than one simple distillation region. Sectional profiles extended beyond the traditional bounds affect coupled sections in a distillation cascade.

Maximizing regions of attraction via backstepping and CLFs with singularities

When a nonlinear control law contains a singularity (that is, becomes unbounded on a set of points in the state space), the region of attraction is often only a subset of the region of feasibility of this control law. A method which is well known to suffer from this difficulty is feedback linearization. We show that the backstepping design (in its standard form) has an inherent ability to make the regions of feasibility and attraction coincide, thus maximizing the latter. The key observation that this paper provides is that a standard backstepping-style control Lyapunov function, which grows unbounded on the set where the control law becomes unbounded, has level sets that always remain in the feasibility region, which makes the feasibility region positively invariant. A simulation comparison with a feedback linearization design shows a dramatic improvement of the region of attraction with backstepping. Since our theorem imposes a strong assumption that the feasibility region for the first subsystem in the backstepping problem is positively invariant, we present examples (ranging from simple to fairly difficult) which demonstrate how this condition can be satisfied.

Tensile failure load and fiber diameter as stochastic variables in the determination of fiber strength statistics

The combined effect of treating failure load and fiber diameter as stochastic variables, on reliability is examined. The approach assumes specific distributions for diameter and failure load to determine the reliability of the system, through a joint probability distribution function defined over a two-dimensional region of feasibility. It is shown that neglecting diameter variations results in a lower probability of failure making the prediction for the system potentially unsafe. This effect is significant for high Weibull modulus materials.

Feasible images and practical stopping rules for iterative algorithms in emission tomography

The discussion of the causes of image deterioration in the maximum-likelihood estimator (MLE) method of tomographic image reconstruction, initiated with the publication of a stopping rule for that iterative process (E. Veklerov and J. Llacer, 1987) is continued. The concept of a feasible image is introduced, which is a result of a reconstruction that, if it were a radiation field, could have generated the initial projection data by the Poisson process that governs radioactive decay. From the premise that the result of a reconstruction should be feasible, the shape and characteristics of the region of feasibility in projection space are examined. With a new rule, reconstructions from real data can be tested for feasibility. Results of the tests and reconstructed images for the Hoffman brain phantom are shown. A comparative examination of the current methods of dealing with MLE image deterioration is included.