scholarly journals Suboptimal Control Strategies for Finite-Time Nonlinear Processes with Input Constraints

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Pablo S. Rivadeneira ◽  
Eduardo J. Adam
Keyword(s):  
Optimal Control ◽  
Finite Time ◽  
Control Strategies ◽  
Batch Reactor ◽  
Infinite Horizon ◽  
Optimization Method ◽  
Suboptimal Control ◽  
Linear Matrix ◽  
Input Constraints ◽  
And Control

Novel techniques for the optimization and control of finite-time processes in real-time are pursued. These are developed in the framework of the Hamiltonian optimal control. Two methods are designed. The first one constructs the reference control trajectory as an approximation of the optimal control via the Riccati equations in an adaptive fashion based on the solutions of a set of partial differential equations called the α and β matrices. These allow calculating the Riccati gain for a range of the duration of the process T and the final penalization S. The second method introduces input constraints to the general optimization formulation. The notions of linear matrix inequalities allow us to recuperate the Riccati gain as in the first method, but using an infinite horizon optimization method. Finally, the performance of the proposed strategies is illustrated through numerical simulations applied to a batch reactor and a penicillin fed-batch reactor.

Strategies to enhance the biodegradation of toxic compounds using discontinuous processes

2001 ◽  
Vol 43 (3) ◽  
pp. 283-290 ◽  
Author(s):  
G. Buitrón ◽  
G. Soto ◽  
G. Vite ◽  
J. Moreno
Keyword(s):  
Optimal Control ◽  
Activated Carbon ◽  
Dissolved Oxygen ◽  
Batch Reactor ◽  
Biological Degradation ◽  
Optimal Control Strategy ◽  
Measured Variable ◽  
Time Optimal ◽  
High Concentrations ◽  
And Control

This study presents two strategies used to enhance the biological degradation of phenolic wastewaters. In the first one the operation of a sequencing batch biofilter added with granular activated carbon (SBB-AC) was studied. The second strategy presents the results of the automation of a sequencing batch reactor in order to optimize the reaction phase. In this case, the dissolved oxygen was employed to monitor and control the reactor. The results of the SBB-AC system, based on the configuration of the reactor, type and size of activated carbon and size of the packing material, are discussed. The system biodegraded efficiently (total phenol removals as high as 97%) high concentrations (600 mg/l) of a mixture of phenol, 4-chlorophenol, 2,4-dichlorophenol and 2,4,6-trichlorophenol. Maximal eliminated loads of 4.33 kg COD/m3-d were achieved. For the second strategy, the applicability of an optimal control for a SBR using the dissolved oxygen as the measured variable was demonstrated. When the reactor was operated under the time-optimal control strategy, the degradation time of 4-chlorophenol was reduced. A very satisfactory operation of the reactor was observed, since the removal efficiencies were around 99%.

scholarly journals SOLUTION OF INFINITE HORIZON NONLINEAR OPTIMAL CONTROL PROBLEMS BY PIECEWISE ADOMIAN DECOMPOSITION METHOD

2013 ◽  
Vol 18 (4) ◽  
pp. 543-560 ◽  
Author(s):  
Hassan Saberi Nik ◽  
Paulo Rebelo ◽  
Moosarreza Shamsyeh Zahedi
Keyword(s):  
Optimal Control ◽  
Decomposition Method ◽  
Optimal Control Problems ◽  
Infinite Horizon ◽  
Adomian Decomposition Method ◽  
Nonlinear Optimal Control ◽  
Suboptimal Control ◽  
Control Problems ◽  
Time Step ◽  
Adomian Decomposition

In this paper, a Piecewise Adomian Decomposition Method (PADM) is used to obtain the analytical approximate solution for a class of infinite horizon nonlinear optimal control problems (OCPs). The method is a new modification of the standard ADM, in which it is treated as an algorithm in a sequence of small intervals (i.e. with small time step) for finding accurate approximate solutions to the corresponding OCPs. Applying the PADM, the nonlinear two-point boundary value problem (TPBVP), derived from the application of Pontryagin's maximum principle (PMP), is transformed into a sequence of linear time-invariant TPBVP's. Through the finite iterations of algorithm, a suboptimal control law is obtained for the nonlinear optimal control problem. Comparing the methodology with some known techniques shows that the present approach is powerful and reliable. It is remarkable accuracy properties are finally demonstrated by two examples.

Advances in Near-Optimal Control of Passive Building Thermal Storage

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Gregor P. Henze ◽  
Anthony R. Florita ◽  
Michael J. Brandemuehl ◽  
Clemens Felsmann ◽  
Hwakong Cheng
Keyword(s):  
Optimal Control ◽  
Control Strategies ◽  
Thermal Storage ◽  
Thermal Mass ◽  
Commercial Building ◽  
Simulation And Optimization ◽  
Rate Structure ◽  
Starting Point ◽  
Utility Rate ◽  
And Control

Using a simulation and optimization environment, this paper presents advances toward near-optimal building thermal mass control derived from full factorial analyses of the important parameters influencing the passive thermal storage process for a range of buildings and climate/utility rate structure combinations. Guidelines for the application of, and expected savings from, building thermal mass control strategies that can be easily implemented and result in a significant reduction in building operating costs and peak electrical demand are sought. In response to the actual utility rates imposed in the investigated cities, fundamental insights and control simplifications are derived from those buildings deemed suitable candidates. The near-optimal strategies are derived from the optimal control trajectory, consisting of four variables, and then tested for effectiveness and validated with respect to uncertainty regarding building parameters and climate variations. Due to the overriding impact of the utility rate structure on both savings and control strategy, combined with the overwhelming diversity of utility rates offered to commercial building customers, this study cannot offer universally valid control guidelines. Nevertheless, a significant number of cases, i.e., combinations of buildings, weather, and utility rate structure, have been investigated, which offer both insights and recommendations for simplified control strategies. These guidelines represent a good starting point for experimentation with building thermal mass control for a substantial range of building types, equipments, climates, and utility rates.

scholarly journals An Optimal Control Framework for Resources Management in Agriculture

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Fernando Lobo Pereira ◽  
Fernando Arménio Fontes ◽  
Maria Margarida Ferreira ◽  
Maria do Rosário Pinho ◽  
Vilma Alves Oliveira ◽  
...  
Keyword(s):  
Optimal Control ◽  
Infinite Horizon ◽  
Past Research ◽  
Resources Management ◽  
Optimization Framework ◽  
Control Framework ◽  
Control Scheme ◽  
Wide Range ◽  
And Control ◽  
The Pontryagin Maximum Principle

An optimal control framework to support the management and control of resources in a wide range of problems arising in agriculture is discussed. Lessons extracted from past research on the weed control problem and a survey of a vast body of pertinent literature led to the specification of key requirements to be met by a suitable optimization framework. The proposed layered control structure—including planning, coordination, and execution layers—relies on a set of nested optimization processes of which an “infinite horizon” Model Predictive Control scheme plays a key role in planning and coordination. Some challenges and recent results on the Pontryagin Maximum Principle for infinite horizon optimal control are also discussed.

scholarly journals Effect of an antiviral drug control in host COVID-19 kinetics

2020 ◽  
Author(s):  
AMAR NATH CHATTERJEE ◽  
JAYANTA MONDAL ◽  
PIU SAMUI
Keyword(s):  
Optimal Control ◽  
Control Strategies ◽  
Low Cost ◽  
Antiviral Drug ◽  
Infection Process ◽  
Control Mechanisms ◽  
Effective Strategies ◽  
Effectiveness Analysis ◽  
Human Lungs ◽  
And Control

Abstract The article proposes and analyzes a system of differential equations modeling the interaction of the SARS-CoV-2 virus and the epithelial cells of the human lungs. Optimal control strategies representing antiviral drug treatment effects of this model are explored here. The Pontryagin’s max-imum principle is used to clarify the optimal control strategies. The exis-tence of optimal control is proved and effective strategies are illustrated. Numerical simulations, efficiency analysis, and cost-effectiveness analysis reveal that time-dependent antiviral drug with other control mechanisms, would reduce the viral load and control the infection process at low cost.

Advances in Near-Optimal Control of Passive Building Thermal Storage

2009 ◽  
Author(s):  
Gregor P. Henze ◽  
Anthony R. Florita ◽  
Michael J. Brandemuehl ◽  
Clemens Felsmann ◽  
Hwakong Cheng
Keyword(s):  
Optimal Control ◽  
Control Strategies ◽  
Thermal Storage ◽  
Thermal Mass ◽  
Commercial Building ◽  
Simulation And Optimization ◽  
Rate Structure ◽  
Starting Point ◽  
Utility Rate ◽  
And Control

Using a simulation and optimization environment, this paper presents advances towards near-optimal building thermal mass control derived from full factorial analyses of the important parameters influencing the passive thermal storage process for a range of buildings and climate/utility rate structure combinations. Guidelines for the application of, and expected savings from, building thermal mass control strategies that can be easily implemented and result in a significant reduction in building operating costs and peak electrical demand are sought. In response to the actual utility rates imposed in the investigated cities, fundamental insights and control simplifications are derived from those buildings deemed suitable candidates. The near-optimal strategies are derived from the optimal control trajectory, consisting of four variables, and then tested for effectiveness and validated with respect to uncertainty regarding building parameters and climate variations. Due to the overriding impact of the utility rate structure on both savings and control strategy, combined with the overwhelming diversity of utility rates offered to commercial building customers, the study cannot offer universally valid control guidelines. Nevertheless, a significant number of cases, i.e. combinations of buildings, weather, and utility rate structure, have been investigated, which offer both insight and recommendations for simplified control strategies. These guidelines represent a good starting point for experimentation with building thermal mass control for a substantial range of building types, equipment, climates, and utility rates.

Dynamics and optimal control in transmission of tungiasis diseases

2021 ◽  
pp. 2150076
Author(s):  
Wei Lv ◽  
Lu Liu ◽  
Shi-Jia Zhuang
Keyword(s):  
Optimal Control ◽  
Control Strategies ◽  
Development Stage ◽  
Latent Stage ◽  
Flea Control ◽  
Control Schemes ◽  
Lyapunov Function Method ◽  
Individual Protection ◽  
And Control ◽  
The Impact

This paper aims to model the transmission of tungiasis disease and assess the optimal control schemes to stop its occurrence. Based on the development stage of fleas and propagation process of diseases, we propose a human-flea model without control, in which the susceptible-infected in latent stage-infectious populations and the egg-larva-pupa-adult stage of fleas are all in involved. In the light of the Lyapunov function method, we prove global stability of equilibria. The model is extended by reformulating it as an optimal control problem, with the use of four time-dependent controls, to assess the impact of individual protection, treatment and two flea control strategies (killing adult fleas and reduction of eggs and larvae). By using Pontryagin’s maximum principle, we characterize the optimal control. Using the data of human and flea in Brazil and Nigeri, numerical simulations are performed. The numerical results show that enhancing the protection and treatment of people and increasing the killing efficacy of flea adults would contribute to prevent and control the spread of the disease appreciably.

Stochastic Finite-Time Stabilization for a Class of Nonlinear Markovian Jump Stochastic Systems With Impulsive Effects

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Wu-Hua Chen ◽  
Chenghai Wei ◽  
Xiaomei Lu
Keyword(s):  
Finite Time ◽  
Stochastic Systems ◽  
Impulsive Effects ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Feedback Controllers ◽  
Finite Time Stability ◽  
And Control ◽  
Stochastic Lyapunov Function

This paper is dedicated to the study of stochastic finite-time stability (SFTS) and control synthesis for a class of nonlinear Markovian jump stochastic systems with impulsive effects. By introducing a time-varying stochastic Lyapunov function with discontinuities at impulse times, an improved criterion for SFTS is derived in terms of linear matrix inequalities (LMIs). Based on the new SFTS criterion, four kinds of finite-time hybrid/continuous-time state feedback controllers are constructed by using the solutions to certain sets of LMIs. The effectiveness of the proposed method is validated through one numerical example.

Sign in / Sign up

Export Citation Format

Share Document