Evaluation and control estimation strategy for three acting play diseases with six control variables

The deterioration of a linear optimal stochastic control scheme, designed under the assumptions of the certainty-equivalence principle (the optimal filter and controller, determined independently, combine to give a totally optimal system), is investigated when the parameters of the actual system do not coincide with the design values. This linear suboptimal stochastic system is described by a covariance matrix composed of covariances of the estimates of the state variables, the errors in the estimates of the state variables, and the correlation between these errors and the estimates. In particular, this paper is concerned with the covariance matrix resulting from a single state dynamical system and a scalar linear measurement function of both the state variable and the control variable (e.g., accelerometer measurements). A modeling error in the control variable coefficient of the measurement function may induce instability in the stochastic system with either unstable or stable dynamics. Furthermore, the absolute magnitude of the error in the control variable coefficient directly influences system stability, not the relative error. Thus, relatively small errors compared to the design value of this coefficient may be quite important. 4 LTHOUGH there are many studies on divergence of op-£^- tirnal filters, little attention has been given to the effect of modeling inaccuracies on optimal linear stochastic control systems. Here we extend Fitzgerald's1 investigation of Kalman filter divergence to optimal linear stochastic control systems. These systems are designed under the certainty equivalence principle2 which states that if the expected value of a quadratic function of the state and the control variables is to be minimized subject to linear dynamics, the optimal system is composed of an optimal filter in cascade with an optimal controller. This separation is possible because the estimate in the state is uncorrelated with the error in this estimate. If the parameters in the assumed model of the dynamics or the measurement device deviate from the parameters of the actual system, the estimate and the error in the estimate become correlated. The behavior of the system because of the gains based on an inaccurate model is studied by considering the coupled matrix covariance equation composed of the Covariances of the error in the estimate, the estimate, and the estimate with its error. Some of the characteristics of this linear matrix equation are studied through a scalar linear dynamic equation. The errors in system parameters enter into the 2X2 covariance equation in a dimensionless form allowing the following general results to be obtained: 1) The stochastic control system may be unstable when the nonoptimal filter and deterministic control systems individually are stable. 2) Instability occurs only when the error in the parameter exceeds a finite threshold value. 3) If the measurement is a linear function of the control variable as well as the state (e.g., accelerometer measurements) and there are errors in the coefficient of the control, then instability of the total system may occur for both stable and unstable dynamical systems. 4) The filter or control gains are not functions of the coefficient of the control variable in the measurement function. Consequently, Presented as Paper 70-36 at the AIAA 8th Aerospace Sciences

The deterioration of a linear optimal stochastic control scheme, designed under the assumptions of the certainty-equivalence principle (the optimal filter and controller, determined independently, combine to give a totally optimal system), is investigated when the parameters of the actual system do not coincide with the design values. This linear suboptimal stochastic system is described by a covariance matrix composed of covariances of the estimates of the state variables, the errors in the estimates of the state variables, and the correlation between these errors and the estimates. In particular, this paper is concerned with the covariance matrix resulting from a single state dynamical system and a scalar linear measurement function of both the state variable and the control variable (e.g., accelerometer measurements). A modeling error in the control variable coefficient of the measurement function may induce instability in the stochastic system with either unstable or stable dynamics. Furthermore, the absolute magnitude of the error in the control variable coefficient directly influences system stability, not the relative error. Thus, relatively small errors compared to the design value of this coefficient may be quite important. 4 LTHOUGH there are many studies on divergence of op-£^- tirnal filters, little attention has been given to the effect of modeling inaccuracies on optimal linear stochastic control systems. Here we extend Fitzgerald's1 investigation of Kalman filter divergence to optimal linear stochastic control systems. These systems are designed under the certainty equivalence principle2 which states that if the expected value of a quadratic function of the state and the control variables is to be minimized subject to linear dynamics, the optimal system is composed of an optimal filter in cascade with an optimal controller. This separation is possible because the estimate in the state is uncorrelated with the error in this estimate. If the parameters in the assumed model of the dynamics or the measurement device deviate from the parameters of the actual system, the estimate and the error in the estimate become correlated. The behavior of the system because of the gains based on an inaccurate model is studied by considering the coupled matrix covariance equation composed of the Covariances of the error in the estimate, the estimate, and the estimate with its error. Some of the characteristics of this linear matrix equation are studied through a scalar linear dynamic equation. The errors in system parameters enter into the 2X2 covariance equation in a dimensionless form allowing the following general results to be obtained: 1) The stochastic control system may be unstable when the nonoptimal filter and deterministic control systems individually are stable. 2) Instability occurs only when the error in the parameter exceeds a finite threshold value. 3) If the measurement is a linear function of the control variable as well as the state (e.g., accelerometer measurements) and there are errors in the coefficient of the control, then instability of the total system may occur for both stable and unstable dynamical systems. 4) The filter or control gains are not functions of the coefficient of the control variable in the measurement function. Consequently, Presented as Paper 70-36 at the AIAA 8th Aerospace Sciences

Practical Methods for Optimal Control using Nonlinear Programming

Optimal control problems of hereditary systems have been given a great deal of attention in recent years. In this paper a class of non-linear systems with finite heredity in both the state and the control variables is considered. Using Pontryagin's geometric approach necessary conditions not only for the optimal control but also for the optimal initial control are derived. In the linear time-optimal case theorems for the form and uniqueness of the optimal control and optimal initial control are given. An example of a Fixed-time energy-optimal problem demonstrates the effect of the optimization of the initial control.

Robust multi-objective optimal switching control arising in 1,3-propanediol microbial fed-batch process

The tidal flow through a channel connecting two basins with different tidal regimes can be optimally controlled by means of a turbine fence or array to maximise the extracted mechanical power. The paper gives the optimal control strategy as a function of the blockage ratio $\sigma$ , i.e. the ratio of the turbine cross-section to the cross-section of the local passage of a turbine. The results presented are a physically consistent generalisation of the results of Garrett & Cummins (Proc. R. Soc. Lond. A, vol. 461, 2060, pp, 2563–2572), valid only for $\sigma =1$ and turbine efficiency of one, now for arbitrary blockage ratio $0 < \sigma \leqslant 1$ . Published research over the past decade on the same topic has taken the momentum equation and the turbine drag force as a starting point. The new approach presented here, in contrast, takes the energy equation as the starting point and uses the relative volume flow as the control variable. As the work shows, this new approach has three advantages. First, starting with the energy equation allows us to derive an optimal flow control problem resulting in an Euler–Lagrange equation using the physically consistent and experimentally validated actuator disk model for the free surface flow of Pelz et al. (J. Fluid Mech., vol. 889, 2020) in a direct and formal way. The optimal control problem is solved (a) numerically and (b) analytically. In the latter case, the turbine characteristics are approximated by a rational function in the relevant design and operating range. The analytical solution (b) validated against the numerical solution (a) is surprisingly concise and easy to apply in practice, as shown by use cases. Second, instead of the induction factor, we use the volume flow that is the same for all turbines in a cascade, i.e. a row of turbines in the direction of flow, which significantly reduces the complexity of the optimal control task of turbine arrays. Third, we obtain a well-founded energy estimate, whereas previous methods overestimate the energy yield due to inconsistent turbine disc models (for the consistency and valid parameter ranges of different models, also in comparison with experiments, see Pelz et al., J. Fluid Mech., vol. 889, 2020). The results can be used for the conceptual design of turbine arrays, but also for a sound physically realistic and consistent resource assessment of tidal power for a system consisting of two basins, a channel and a turbine fence with $0<\sigma \leqslant 1$ and operated in a complete tidal cycle.

This study focuses on a nonlinear deterministic mathematical model for coffee berry borer (Hypothenemus hampei) with temperature and rainfall variability. In the model analysis, CBB free and coexistence equilibria are computed. The basic reproduction numbers at a minimum and maximum temperature and rainfall are derived. The qualitative analysis of the model revealed the scenario for equilibria together with basic reproduction numbers. The local stability of equilibria is established through the Jacobian matrix and the Routh–Hurwitz criteria, while the global stability of equilibria is demonstrated using an appropriate Lyapunov function. The normalized sensitivity analysis has also been performed to observe the impact of different parameters on basic reproduction numbers. The proposed model is extended into an optimal control problem by incorporating two control variables, namely, the preventive measure variable based on the separation of susceptible coffee berries from contacting the pests based on biological control and an increase in the death rate of colonizing females of CBB based on chemical control. Optimal disease control analysis is examined using Pontryagin’s minimum principle. Finally, the numerical simulations are performed based on analytical results and are discussed quantitatively. Furthermore, the cost-effectiveness of control strategies to determine the best approach to minimize the CBB burden was studied. The study is significant in providing reliable information on how one can use mathematical modeling to improve the roles of control strategies and prevention in CBB transmission in a coffee farm. The outcome of the study may guide public agriculture policymakers on optimal control strategies to control the pests. In particular, using chemical pesticides is very effective to combat pests with minimum costs.

Optimal field development and control aim to maximize the economic profit of oil and gas production. This, however, results in a complex optimization problem with a large number of correlated control variables at different levels (e.g. well locations, completions and controls) and a computationally expensive objective function (i.e. a simulated reservoir model). The typical limitations of the existing optimization frameworks are: (1) single-level optimization at a time (i.e. ignoring correlations among control variables at different levels); and (2) providing a single solution only whereas operational problems often add unexpected constraints likely to reduce the ‘optimal’, inflexible solution to a sub-optimal scenario. The developed framework in this paper is based on sequential iterative optimization of control variables at different levels. An ensemble of close-to-optimum solutions is selected from each level (e.g. for well location) and transferred to the next level of optimization (e.g. to control settings), and this loop continues until no significant improvement is observed in the objective value. Fit-for-purpose clustering techniques are developed to systematically select an ensemble of solutions, with maximum differences in control variables but close-to-optimum objective values, at each level of optimization. The framework also considers pre-defined constraints such as the minimum well spacing, irregular reservoir boundaries, and production/injection rate limits. The proposed framework has been tested on a benchmark case study, known as the Brugge field, to find the optimal well placement and control in two development scenarios: with conventional (surface control only) and intelligent wells (with additional zonal control using Interval Control Valves). Multiple solutions are obtained in both development scenarios, with different well locations and control settings but close-to-optimum objective values. We also show that suboptimal solutions from an early optimization level can approach and even outdo the optimal one at the higher-level optimization, highlighting the value of the here-developed multi-solution framework in exploring the search space as compared to the traditional single-solution approaches. The development scenario with intelligent completion installed at the optimal well location and optimally controlled during the production period achieved the maximum added value. Our results demonstrate the advantage of the developed multi-solution optimization framework in providing the much-needed operational flexibility to field operators.

Features Discusses economic optimization of greenhouse control through mathematical modeling Examines 30 years of scientific research to present a unified framework for efficient decision-making Presents modern methods of control and optimization including classical rule-based and multivariable feedback controllers Utilizes real and experimental examples and novel case discussions such as solar greenhouses Concludes with a discussion of open issues to stimulate new areas of research and development Summary Greenhouse control system manufacturers produce equipment and software with hundreds of settings and, while they hold training courses on how to adjust these settings, there is as yet no integrated instruction on when or why. Despite rapid growth in the greenhouse industry, growers are still faced with a multitude of variables and no unifying framework from which to choose the best option. Consolidating 30 years of research in greenhouse climate control, Optimal Control of Greenhouse Cultivation utilizes mathmatical models to incorporate the wealth of scientific knowledge into a feasible optimal control methodology for greenhouse crop cultivation. Discussing several different paradigms on greenhouse climate control, it integrates the current research into physical modeling of the greenhouse climate in response to heating, ventilation, and other control variables with the biological modeling of variables such as plant evapo-transpiration and growth. Key topics include state-space greenhouse and crop modeling needed for the design of integrated optimal controllers that exploit rather than mitigate outside weather conditions, especially sunlight, given widely different time scales. The book reviews classical rule-based and multivariable feedback controllers in comparison with the optimal hierarchical control paradigm. It considers real and hypothetical examples including lettuce, tomato, and solar greenhouses and examines experimental results of greenhouse climate control using optimal control software. The book concludes with a discussion of open issues as well as future perspectives and challenges. Providing a tool to automatically determine the most economical controls and settings for their operation, this much-needed book relieves growers of unnecessary control tasks, and allows them to achieve the best possible trade-off between short term savings and optimal harvest yield.

A class of optimal state-delay control problems

Cellulose hydrolysis is a key step in lignocellulosic ethanol production. At present, commercial production of lignocellulosic ethanol is limited due to the long hydrolysis times and requirement of large quantity of expensive enzymes. Therefore, reduction of the enzyme consumption as well as hydrolysis time is crucial and model based optimisation methods can be used for the same. A semi-mechanistic model with cellobiose, glucose, and xylose inhibition with Arrhenius based relationship between temperature and kinetic parameters and thermal deactivation of enzymes was used for the present study. Optimal control problem with temperature as control variable was formulated after considering two different objective functions. For the objective of glucose concentration maximisation at final batch time, the benefit of implementing optimal control increased with reducing batch times. For the batch time of 24 hours, the final glucose concentration increased by 3.2%. For the objective of batch time minimisation, the reduction of batch time was 5.8% and it was observed for a target glucose concentration of 45 g/kg of cellulose. The use of optimal control can reduce the enzyme requirement up to 77.8% of endoglucanase and exoglucanase for glucose maximisation and 22.2% for batch time minimisation. The above results show the usefulness of optimal temperature control in increasing the glucose concentration, and reducing the batch time without increasing the enzyme used.

Synthesis of optimal controllers for a class of maximization problems

Combination of topology optimization and optimal control method

In many applied problems, we find constraints on control and state variables. In Sect. 3.1, a Lagrangian form of the maximum principle is discussed for models in which there are mixed constraints involving both state and control variables in addition to constraints only on control variables. In Sect. 3.2, we state conditions under which the Lagrangian maximum principle is also sufficient for optimality. Economists frequently analyze optimal control problems involving a discount rate. In that case, it is convenient to use the current-value formulation of the maximum principle as described in Sect. 3.3. It is often the case infinite horizon problems that some restrictions are imposed on the state variables at the end of the horizon. In Sect. 3.4, we discuss the transversality conditions to be satisfied by the adjoint variable in special cases of interest. Section 3.5 is devoted to the study of free terminal time problems where the terminal time itself is a decision variable to be determined. Models with infinite horizons and their stationary equilibrium solutions are covered in Sect. 3.6. Section 3.7 presents a classification of a number of the most important and commonly used kinds of optimal control models, together with a brief description of the forms of their optimal solutions. Several examples are solved throughout the chapter to illustrate the theory. There are many exercises at the end of the chapter.

Optimizing the operating conditions and control set points of the heating, ventilation, and air-conditioning (HVAC) system in a building is one of the most effective ways to save energy and improve the building’s energy performance. Here, we optimized different control variables using a genetic algorithm. We constructed and evaluated three optimal control scenarios (cases) to compare the energy savings of each by varying the setting and number and type of the optimized control variables. Case 1 used only air-side control variables and achieved an energy savings rate of about 5.72%; case 2 used only water-side control variables and achieved an energy savings rate of 16.98%; and case 3, which combined all the control variables, achieved 25.14% energy savings. The energy savings percentages differed depending on the setting and type of the control variables. The results show that, when multiple control set points are optimized simultaneously in an HVAC system, the energy savings efficiency becomes more effective. It was also confirmed that the control characteristics and energy saving rate change depending on the location and number of control variables when optimizing using the same algorithm.