Control Vector Parameterization Approach Research Articles

Optimal Standoff Distance of Subsonic Unpowered Gliding Vehicle

The inverted Y-tail joint standoff weapon is adopted as the Subsonic Unpowered Gliding Vehicle (SUGV) in this article to gain maximum standoff distance. To obtain the optimal standoff distance of SUGV, a direct approach i.e., homogeneous control vector parameterization (CVP), is employed. To achieve the maximum standoff distance, the SUGV requires to spend a maximum amount of time in the air to conduct a gliding flight, resulting in an unspecified final time optimal problem. To deal with this problem, a time scaling approach is adopted in conjunction with homogeneous CVP to achieve the maximum standoff distance. In accordance with the homogeneous CVP technique, the standoff distance of the SUGV is comparatively long in comparison to the maximum step input, and the SUGV reaches a standoff distance of 121 km with an increment of 1.77%. The optimal simulation outcomes indicate that homogeneous CVP delivers a smooth gliding flight as compared to the maximum step input, and this smoother flight results in increased standoff distance. Furthermore, to evaluate the efficiency between the homogeneous CVP approach and maximum step input, the burden on the elevators in the form of integral square value and time scaling parameter is chosen as a criterion for quantitative analysis, and this analysis reveals that the homogeneous CVP approach has less burden on the elevators than the maximum step input.

Trajectory Optimization of a Subsonic Unpowered Gliding Vehicle Using Control Vector Parameterization

In many aero gliding vehicles, achieving the maximum gliding range is a challenging task. A frequent example is the breakdown of an engine during flight or the use of unpowered stand-off weapons. When an unpowered stand-off weapon begins gliding at a given height, it eventually strikes the ground after some distance, and height is considered a stopping constraint in this general condition. To avoid the time-scaling approach for the free time optimal problem, the maximum stoppable time with a stopping constraint is addressed to attain the maximum glide range. This problem can be chosen as an optimal gliding range problem which can be solved by direct or indirect methods. In this paper, the inverted Y-tail joint stand-off weapon is selected as the subsonic unpowered gliding vehicle (SUGV). After being released from dispersion points, the SUGV has to face fluctuating gliding flight because of flight phase transition that causes gliding range reduction. To achieve a damped and steady gliding flight while maximizing the gliding range, we propose a non-uniform control vector parameterization (CVP) approach that uses the notion of exponential spacing for the time vector. When compared with the maximum step input and conventional uniform CVP approach, simulations of the proposed non-uniform CVP approach demonstrate that the SUGV exhibits superior damping and steady gliding flight, with a maximum gliding range of 121.278 km and a maximum horizontal range of 120.856 km.

A Simulation Study on Model-Based Optimization of Intracellular Trehalose Accumulation in Saccharomyces cerevisiae Fed-Batch Cultures

Trehalose is a reserve carbohydrate, which occurs naturally in yeast and acts as a stress protectant for cells. Due to its features, trehalose is used in many industries (food, biopharmaceuticals, cosmetics). Its production/accumulation may be triggered and enhanced by the culture operating conditions, among which the feed flow rate and the start of the starvation period play the most important role. This paper presents a simulation study based on a novel model validated with experimental data, highlighting the interplay between trehalose maximization and biomass maximization. Several single-objective and multi-objective constrained optimization problems are solved using the control vector parameterization approach. It is shown that maximizing either the trehalose concentration or the biomass amount leads to solutions which are not appealing in practice. The best solution is obtained by maximizing trehalose concentration with a lower bound on the biomass amount. A comparison of the optimal solution to experimental data reveals that, although approximately the same amount of biomass can be obtained with different feeding profiles and starvation times, the maximization of trehalose concentration requires feeding most of the culture medium in the first part of the experiment while starting the nitrogen starvation at an early stage.

Dynamic Multi-Objective Optimization of Autocatalytic Esterification in Semi Batch by Using Control Vector Parameterization (CVP) and Non-Dominated Sorting Genetic Algorithm (NSGA-II)

Catalyzed Esterification of sec-butyl propionate in semi batch reactor prefers to be solved by dynamic-nonlinear programming (NLP) based optimization for determining optimal temperature and feed flowrate trajectories. In this autocatalytic esterification process, there are contrary objective functions, i.e. maximum productivity and minimum process time. Simultaneous optimization of these objectives yields in a dynamic multi-objective optimization (DMOO) problem, which is characterized by a set of multiple solutions, known as non-dominated or Pareto solutions. In this work, a control vector parameterization (CVP) and non-dominated sorting genetic algorithm (NSGA-II) approach were used to generate the Pareto solutions for two objectives: maximize conversion and minimize process time. Each point of Pareto solutions consists of different optimal temperature reactor and feed rate profiles, which lead to a variation combination of conversion and process time. These solutions give multiple alternatives in evaluating the trade-offs and selecting the most suitable operating policy.

Integrated mathematical models for drinking water reservoirs and constructed wetlands as a tool for restoration planning

In this work, we propose the integration of mechanistic models for eutrophic reservoirs and constructed wetland within a dynamic optimization framework for the optimal design of wetlands for water quality restoration purposes. A partial differential equation system results from dynamic mass balances for the main biogeochemical variables in both reservoir and wetland. The integrated model is formulated as an optimal control problem within a control vector parameterization approach. The optimization model includes wetland areas as design variables and the fractions of tributaries that are diverted through the wetlands as control variables. The objective function is the minimization of the sum of the integral of the quadratic difference between total phosphorus concentration and a desired value below eutrophication limits and the integral of the quadratic difference between total nitrogen concentration and a desired value below eutrophication limits, along a twelve-year time horizon. The case of study is the eutrophic Paso de las Piedras Reservoir which supplies drinking water to two cities in Argentina, and it has two tributaries which run through an important agricultural area in the region. Numerical results provide: a) the optimal areas for constructed wetlands next to tributaries, b) optimal temporal profiles for diverted fraction of tributaries through wetlands, and c) temporal profiles of the main biogeochemical variables within the lake and the wetlands. The integrated model, which constitutes a useful management tool for a more rational planning of water quality restoration.

Optimal grade transition of a non-isothermal continuous reactor with multi-objective dynamic optimization approach

Dynamic optimization (DO) is a useful tool for carrying out grade transitions in polymer industry. Most open literature studies on DO emphasize such grade transitions using single objective optimization. However, there are multiple criteria which must be met simultaneously for economic benefits. In this work, we solve a multi-objective DO problem for free-radical polymerization of methyl methacrylate in a non-isothermal continuous stirred tank reactor. The process objectives considered in the DO activity include minimization of off-spec, minimization of grade transition time, and minimization of the averaged feed flowrate. The manipulated variables considered for this problem are the initiator and coolant flowrates. The DO problem is solved using control vector parameterization (CVP) approach with first order interpolation. The solution of the aforementioned multi-objective DO problem is obtained in terms of a trade-off curve, pareto curve, using non-dominated sorting genetic algorithm (NSGA II). The three-dimensional pareto front is then projected to each of the three pairs of the objectives for better visualization and analysis. Furthermore, three representative pareto solution points, namely the two end points and a utopia point are further analysed for of each of the bi-objective pareto solution curves.

Optimality and identification of dynamic models in systems biology: an inverse optimal control framework.

Optimality principles have been used to explain many biological processes and systems. However, the functions being optimized are in general unknown a priori. Here we present an inverse optimal control framework for modeling dynamics in systems biology. The objective is to identify the underlying optimality principle from observed time-series data and simultaneously estimate unmeasured time-dependent inputs and time-invariant model parameters. As a special case, we also consider the problem of optimal simultaneous estimation of inputs and parameters from noisy data. After presenting a general statement of the inverse optimal control problem, and discussing special cases of interest, we outline numerical strategies which are scalable and robust. We discuss the existence, relevance and implications of identifiability issues in the above problems. We present a robust computational approach based on regularized cost functions and the use of suitable direct numerical methods based on the control-vector parameterization approach. To avoid convergence to local solutions, we make use of hybrid global-local methods. We illustrate the performance and capabilities of this approach with several challenging case studies, including simulated and real data. We pay particular attention to the computational scalability of our approach (with the objective of considering large numbers of inputs and states). We provide a software implementation of both the methods and the case studies. The code used to obtain the results reported here is available at https://zenodo.org/record/1009541. Supplementary data are available at Bioinformatics online.

Multi Objective Dynamic Optimization Study of Butylated Urea Formaldehyde Resin Process in a Batch Reactor

Butylated urea formaldehyde (BUF) is a key intermediate for manufacturing paint and coating. The quality of BUF resins can be measured in terms of the concentration of free formaldehyde in the BUF resins and the extent of butylation. We in this work present an optimal control study to obtain minimum free formaldehyde concentration and minimum butanol concentration at the end of the batch operation. Reactor temperature is used as the manipulated variable and optimum temporal reactor temperature profiles are obtained using control vector parameterization approach. The two aforementioned criteria are observed to be mutually conflicting and hence the multi-objective optimal control problem is solved in this work yielding the pareto optimal curve showing the trade-off solutions of the MOO problem. Such pareto optimal curve helps the operator to choose an operating condition for a desired operation.

A novel non-uniform control vector parameterization approach with time grid refinement for flight level tracking optimal control problems

High quality control method is essential for the implementation of aircraft autopilot system. An optimal control problem model considering the safe aerodynamic envelop is therefore established to improve the control quality of aircraft flight level tracking. A novel non-uniform control vector parameterization (CVP) method with time grid refinement is then proposed for solving the optimal control problem. By introducing the Hilbert-Huang transform (HHT) analysis, an efficient time grid refinement approach is presented and an adaptive time grid is automatically obtained. With this refinement, the proposed method needs fewer optimization parameters to achieve better control quality when compared with uniform refinement CVP method, whereas the computational cost is lower. Two well-known flight level altitude tracking problems and one minimum time cost problem are tested as illustrations and the uniform refinement control vector parameterization method is adopted as the comparative base. Numerical results show that the proposed method achieves better performances in terms of optimization accuracy and computation cost; meanwhile, the control quality is efficiently improved.

Optimal Reconfiguration of Formation Flying Using A Direct Sequential Method

Formation flying of multiple Unmanned Aerial Vehicles (UAVs) or satellites enables cooperation among agents, and thus constitutes a system of greater performance than the simple sum of its parts by taking advantage of that cooperation. As a prerequisite, how to reconfigure, energy-optimally or time-optimally, from the current formation to the desired one shall be planned beforehand. This paper addresses such a planning problem from the perspective of optimal control that exploits a direct sequential method. In our study, during the reconfiguration agents subject to nonlinear dynamics, and final formation constraints are imposed where there exist unknown parameters to be determined optimally. In the developed direct method the original problem is transcribed into a sequence of convex optimization problems via the control vector parameterization approach using piecewise-constant approximation. In the end, each instance in the sequence is essentially a programming problem (quadratic or linear) subject to linear constraints that can be solved very efficiently. In this paper, the proposed method has been applied to two scenarios: the energy-optimal reconfiguration of five UAVs and the time-optimal formation reconfiguration of four satellites. In our implementation the free open source solver CVX is used. By comparison with the global optimization technique provided in MATLAB, the solutions converge very fast to the global minimum.

A new sensitivity-based adaptive control vector parameterization approach for dynamic optimization of bioprocesses.

Dynamic optimization is a very effective way to increase the profitability or productivity of bioprocesses. As an important method of dynamic optimization, the control vector parameterization (CVP) approach needs to select an optimal discretization level to balance the computational cost with the desired solution quality. A new sensitivity-based adaptive refinement method is therefore proposed, by which new time grid points are only inserted where necessary and unnecessary points are eliminated so as to obtain economic and effective discretization grids. Moreover, considering that traditional refinement methods may cost a lot to get the high-quality solutions of some bioprocess problems, whose performance indices are sensitive to some significant time points, an optimization technique is further proposed and embedded into the new sensitivity-based CVP approach to efficiently solve these problems. The proposed methods are applied to two well-known bioprocess optimization problems and the results illustrate their effectiveness.

A Control Parameterization Approach with Variable Time Nodes for Optimal Control Problems

AbstractThis paper presents a novel computational approach to deal with optimal multivariable control problems using a control vector parameterization approach with multiple time grids, where each of the control variables has its own time grid of parametrization. Both the control parameters and time nodes in the grid partition are treated directly as variables to be optimized. Based on the derived relationship between the gradients of time nodes and the ones of interval lengths, the gradient formulae for parameters are presented. Compared with the existing approaches, for which all the control variables are parameterized on the same time grid, the proposed method is more general and flexible. To illustrate, two numerical cases are tested, and the results demonstrate that fewer parameters are needed to achieve the same level of optimization.

Optimal drug infusion profiles using a Particle Swarm Optimization algorithm

The dynamic optimization of the administration of therapeutic drugs in simulated patients is proposed. The approach is based on a non-linear discontinuous cardiorespiratory model, which has been conceived to simulate the effect of inotropic and vasoactive drugs as well as anesthetic agents. A stochastic technique (Particle Swarm Optimization), within the context of the control vector parameterization approach, is adopted to identify the infusion profiles of various drugs in order to track, as close as possible, the set-points on several variables of medical interest. Two different medical procedures are investigated in order to test the efficiency and robustness of the algorithm: a congestive heart failure and the unclamping of an aortic vessel. Due to the conflicting nature of the different objectives, compromise solutions are obtained in all cases.

A Novel Penalty Approach for Nonlinear Dynamic Optimization Problems With Inequality Path Constraints

The control vector parameterization (CVP) approach is popular to solve nonlinear dynamic optimization problems, but handling inequality path constraints within its framework is a challenge. This study deals with inequality path constraints by using the l 1 penalty function and a novel smoothing technique. After clarifying some theories of the proposed approach, a concomitant algorithm is also put forward and verified.

Off-line optimization of baker׳s yeast production process

A macroscopic model describing the influence of nitrogen on a fed-batch baker׳s yeast production process was used for the determination of optimal operating conditions in the sense of a production criterion. To this end, two different approaches were used: a control vector parameterization approach with mesh refinement and an approach based on the mathematical analysis of optimal operating policy (semi-analytical approach). The results of the two approaches lead to the determination of similar optimal operation conditions, which have been implemented for a new experimental phase. Moreover, these optimal conditions are in agreement with the profiles obtained by industrial manufacturers through an empirical optimization of the process (trial and error method). The model predictions are in good accordance with experimental data. This conclusion was supported by an uncertainty analysis on the model outputs with respect to the parameter estimation errors.

Optimization of lipid production by oleaginous yeast in continuous culture

Oleaginous yeasts are microbial factories capable of converting carbohydrates and fat substrates into lipids. The transesterification of these lipids results in the production of biodiesel, a renewable energy source that has emerged as a promising and sustainable alternative to overcome the eminent depletion of fossil fuels and to reduce the environmental impacts of petroleum exploitation. To bring biodiesel production as a realistic technology to respond to the worldwide energy demand, process optimization is to be pursued. In this paper, we performed a model-based optimization of lipid productivity in continuous mode operation. It is considered that two input flow rates at different carbon/nitrogen ratio are available as manipulated variables. The optimal control problem was solved numerically by using the control vector parameterization approach. A simple parameterization with piecewise linear functions was found to be suitable for providing optimal performances. We showed that by driving the carbon/nitrogen ratio along the process adequately, optimal performances are attained. The control strategy here developed excels substantially an operation with a single input flow rate with fixed C/N ratio. This work sets up useful guidelines towards optimal bioprocesses for microbial lipid production.

Parameter estimation in kinetic models for large scale biotechnological systems with advanced mathematical programming techniques

In the present work, we formulate parameter estimation problems for kinetic models of large-scale dynamic biotechnological systems. We propose dynamic models of increasing complexity for metabolic networks and continuous bioreactors. The differential algebraic equations (DAE) system for the metabolic network represent the glycolysis, the phosphotransferase system and the pentose-phosphate pathway of Escherichia coli, with modifications proposed for several enzyme kinetics. The most sensitive parameters have been ranked by performing global sensitivity analysis on the dynamic metabolic network. Since the kinetic parameters for the enzymes have been obtained from in vitro experiments, the formulation of a detailed kinetic model for the metabolic network allows parameter adjustment for in vivo conditions. We formulate an unstructured non-segregated model for a chemostat to study the dynamic response to a glucose pulse in a continuous culture of E. coli. Moreover, we perform parameter estimation by formulating a maximum likelihood problem, subject to the DAE systems, within a control vector parameterization approach. Nine kinetic parameters in the metabolic network model have been estimated with good agreement with published experimental data. For the bioreactor model, seven parameters have been tuned based on experimental data obtained in this work. Numerical results show a good agreement between the observed data and the predicted profiles.

Dynamic Optimization Based Reactive Power Planning to Mitigate Slow Voltage Recovery and Short Term Voltage Instability

Short term voltage stability poses a significant threat to system stability and reliability. This paper applies dynamic VAr injection to ensure short term voltage stability following a large disturbance in a power system with high concentration of induction motor loads. Decelerating and stalling of induction motor loads is considered to be the major cause of fault induced delayed voltage recovery (FIDVR) and short term voltage stability. If system dynamics are not taken into account properly, the proposed control solution may be an expensive over design or an under design that is not capable of eliminating FIDVR problems completely. In this work, the optimal amount and locations for installing dynamic reactive resources are found by control vector parameterization (CVP), a dynamic optimization approach. The efficiency and effectiveness of this approach is improved by utilizing results from trajectory sensitivity analysis, singular value decomposition and linear programming optimization. Dynamic optimization based on CVP approach is tested in an IEEE 162-bus system and a realistic large scale utility power system.

Optimization method for solving bang-bang and singular control problems

In this paper we study optimal control problems with the control variable appearing linearly. A novel method for optimization with respect to the switching times of controls containing both bang-bang and singular arcs is presented. This method transforms the control problem into a finite-dimensional optimization problem by reformulating the control problem as a multi-stage optimization problem. The optimal control problem is partitioned as several stages, with each stage corresponding to a particular control arc. A control vector parameterization approach is applied to convert the control problem to a static nonlinear programming (NLP) problem. The control profiles and stage lengths act as decision variables. Based on the Pontryagin maximal principle, a multi-stage adjoint system is constructed to calculate the gradients required by the NLP solvers. Two examples are studied to demonstrate the effectiveness of this strategy.

Dynamic optimization of distributed biological systems using robust and efficient numerical techniques

BackgroundSystems biology allows the analysis of biological systems behavior under different conditions through in silico experimentation. The possibility of perturbing biological systems in different manners calls for the design of perturbations to achieve particular goals. Examples would include, the design of a chemical stimulation to maximize the amplitude of a given cellular signal or to achieve a desired pattern in pattern formation systems, etc. Such design problems can be mathematically formulated as dynamic optimization problems which are particularly challenging when the system is described by partial differential equations.This work addresses the numerical solution of such dynamic optimization problems for spatially distributed biological systems. The usual nonlinear and large scale nature of the mathematical models related to this class of systems and the presence of constraints on the optimization problems, impose a number of difficulties, such as the presence of suboptimal solutions, which call for robust and efficient numerical techniques.ResultsHere, the use of a control vector parameterization approach combined with efficient and robust hybrid global optimization methods and a reduced order model methodology is proposed. The capabilities of this strategy are illustrated considering the solution of a two challenging problems: bacterial chemotaxis and the FitzHugh-Nagumo model.ConclusionsIn the process of chemotaxis the objective was to efficiently compute the time-varying optimal concentration of chemotractant in one of the spatial boundaries in order to achieve predefined cell distribution profiles. Results are in agreement with those previously published in the literature. The FitzHugh-Nagumo problem is also efficiently solved and it illustrates very well how dynamic optimization may be used to force a system to evolve from an undesired to a desired pattern with a reduced number of actuators. The presented methodology can be used for the efficient dynamic optimization of generic distributed biological systems.