Optimal and sub‐optimal control in Dengue epidemics

This work concerns the application of the optimal control theory to Dengue epidemics. The dynamics of this insect‐borne disease is modelled as a set of non‐linear ordinary differential equations including the effect of educational campaigns organized to motivate the population to break the reproduction cycle of the mosquitoes by avoiding the accumulation of still water in open‐air recipients. The cost functional is such that it reflects a compromise between actual financial spending (in insecticides and educational campaigns) and the population health (which can be objectively measured in terms of, for instance, treatment costs and loss of productivity). The optimal control problem is solved numerically using a multiple shooting method. However, the optimal control policy is difficult to implement by the health authorities because it is not practical to adjust the investment rate continuously in time. Therefore, a suboptimal control policy is computed assuming, as the admissible set, only those controls which are piecewise constant. The performance achieved by the optimal control and the sub‐optimal control policies are compared with the cases of control using only insecticides when Breteau Index is greater or equal to 5 and the case of no‐control. The results show that the sub‐optimal policy yields a substantial reduction in the cost, in terms of the proposed functional, and is only slightly inferior to the optimal control policy. Copyright © 2001 John Wiley & Sons, Ltd.     

The impact of changing farm structure on foot‐and‐mouth disease spread and control: A simulation study

Foot‐and‐mouth disease (FMD) is a highly contagious viral disease that affects ruminants and pigs. Countries with large exports of livestock products are highly vulnerable to economic damage following an FMD incursion. The faster disease spread is controlled, the lower the economic damage. During the past decades, the structure of livestock production has dramatically changed. To maintain the relevance of contingency plans, it is important to understand the effects of changes in herd structure on the spread and control of infectious diseases. In this study, we compare the spread and control of FMD based on 2006/2007 and 2018 livestock data. Spread of FMD in Denmark was simulated using the DTU‐DADS model, applying different control measures. The number of cattle, swine and sheep/goat herds reduced from about 50,000 in total in 2006/2007 to about 33,000 in 2018. During this period, the average number of outgoing animal movements and the exports of swine and swine products increased by about 35% and 22%, respectively. This coincided with an overall increase in herd size of 14%. Using the EU and national control measures (Basic: 3 days standstill, depopulation of detected herds followed by cleaning and disinfection and establishment of control zones, where tracing, surveillance and contact restrictions are implemented), we found that the simulated epidemics in 2018 would be about 50% shorter in duration, affect about 50% fewer herds but cause more economic damage, compared to epidemics using 2006/2007 data. When 2006/2007 data were used, Basic + pre‐emptive depopulation (Depop) overall was the optimal control strategy. When 2018 data were used, this was the case only when epidemics were initiated in cattle herds, whereas when epidemics were initiated in sow or sheep/goats herds, basic performed as well as Depop. The results demonstrate that regular assessment of measures to control the spread of infectious diseases is necessary for contingency planning.     

Epidemic Spreading in an Animal Trade Network – Comparison of Distance‐Based and Network‐Based Control Measures

This study considered a simple SIR model for the spread of epidemics amongst holdings of a producer community in Northern Germany, based on the directed network of animal movements. The aim of this study was to evaluate the efficiency of different control measures to reduce the epidemic size substantially. The currently applied control measures based on the distance to an infected holding were compared with the control measures based on the specific network‐based centrality parameters. We found that network‐based measures led to a more efficient control of epidemics with a much smaller number of removed holdings. To assess the impact of different holding types, the analysed control measures were implemented by both including and excluding these holding types. The comparison revealed a crucial role of multipliers in the spread of an epidemic. The network‐based control measures depending on the removal by out‐degree, outgoing infection chain, betweenness centrality and outgoing closeness centrality showed the best results: In the three‐year network, on average, 2.75, 4.15, 3.73 and 3.43 times more holdings had to be removed by the control measures based on the 1, 3, 5 and 10 km radius to reduce the epidemic to the same size compared with the network‐based control measures. In an area with a higher holding density, the improvement of the network‐based control measures may become even more obvious. The removal of holdings based on the above‐mentioned centrality parameters did thus not only rapidly decompose the network into fragments, but also reduced the epidemic size most efficiently.     

Epidemiology of the Foot‐and‐Mouth Disease Serotype O Epidemic of November 2010 to April 2011 in the Republic Of Korea

The largest epidemic of foot‐and‐mouth disease (FMD) in Korea since the first record in 1911 occurred between November 2010 and April 2011. The outbreak was confirmed in 153 farms, and more than three million animals were destroyed. This study presents the temporal and spatial distribution patterns, epidemiological investigation and the control measures for the 2010/2011 epidemic in Korea. The index case of this 2010/2011 FMD epidemic was reported in a pig‐farming complex with five piggeries in Andong, GyeongBuk Province, on 28 November 2010, and the outbreak lasted 145 days. The largest number of new detection of the infected farms per day was recorded in mid‐January. Epidemiological investigation revealed that the FMD virus had spread from farm to farm through routine movements associated with animal husbandry operations. In contrast to FMD epidemics in other countries in which movement of the infected animals largely contributed to the spread of the disease, human behaviours were major factors in the spread of the FMD virus in the Korean epidemic. The 2010/2011 epidemic was first confirmed in a local small and medium city where share of smallholder producers is higher than that of other provinces. Although Korea had a well‐developed emergent response system with the experience of controlling infection and re‐obtaining FMD‐free status after the previous epidemics, Korea was prompted to revise their contingency plan by tailoring it to its unique livestock environment. Practical contingency plans tailored to Korea for control of FMD can be fully effective when farmers, livestock‐related agencies, veterinary service providers and the general public work together.     

LQ‐optimal control of positive linear systems

The LQ₊ problem, i.e. the finite‐horizon linear quadratic optimal control problem with nonnegative state constraints, is studied for positive linear systems in continuous time and in discrete time. Necessary and sufficient optimality conditions are obtained by using the maximum principle. These conditions lead to a computational method for the solution of the LQ₊ problem by means of a corresponding Hamiltonian system. In addition, the necessary and sufficient conditions are proved for the LQ₊‐optimal control to be given by the standard LQ‐optimal state feedback law. Then sufficient conditions are established for the positivity of the LQ‐optimal closed‐loop system. In particular, such conditions are obtained for the problem of minimal energy control with penalization of the final state. Moreover, a positivity criterion for the LQ‐optimal closed‐loop system is derived for positive discrete‐time systems with a positively invertible (dynamics) generator. The main results are illustrated by numerical examples. Copyright © 2010 John Wiley & Sons, Ltd.     

A direct search approach to optimization for nonlinear model predictive control

Nonlinear model predictive control (NMPC) depends on performing a constrained nonlinear optimization, based on predictions of future system behavior, during a sampling interval to determine the control action to be applied to the system during the next time step. The difficulty in designing an optimization procedure to solve a constrained NMPC problem is due to the finite time horizon to which the predictive model is evaluated, the state and control actuator constraints, and sampling interval length. The resulting objective function, which is to be optimized is typically not differentiable. Although there are many commercial, shareware, and open‐source optimization packages available that can perform a nonlinear constrained optimization for most cases, there are NMPC implementations requiring embedded code or that must meet stringent timing requirements that preclude the use of off‐the‐shelf packages. In cases where the predictive model is known, such as aerodynamic or hydrodynamic systems, a direct‐search optimization algorithm can perform well enough in a real‐time environment. Direct search algorithms are simple to implement and can be made more efficient by applying differential geometric techniques to the search methodology. The typical smoothness of the equations of motion for vehicular systems allows the objective function's stationarities to be handled in a straight‐forward way. Copyright © 2013 John Wiley & Sons, Ltd.     

Optimal multi‐interval control of a cantilever beam by a recursive control algorithm

The optimal‐distributed control of a transversely vibrating cantilever beam is studied with the objective of minimizing the deflection and velocity in a given period of time with the minimum possible expenditure of force. The beam undergoes transient vibrations and is subject to given displacement and velocity initial conditions. The control is exercised by means of a transversely distributed force referred to as the control force. In the present study, a multi‐interval optimal control method is developed with the application of a maximum principle. The method consists of dividing the control duration into several intervals and using the maximum principle to obtain the optimality conditions at each interval. The explicit solutions for a cantilever beam are obtained by a recursive algorithm that takes the final conditions of the last interval as the initial conditions of the next interval. The formulation and the method of solution are suitable and convenient for digital computation. Numerical results are given, which compare the deflections, velocities and the control force under the optimal multi‐interval control with those under the optimal single‐interval control. Copyright © 2008 John Wiley & Sons, Ltd.     

Nonlinear model predictive control strategy for low thrust spacecraft missions

In this paper, two nonlinear model predictive control (MPC) strategies are applied to solve a low thrust interplanetary rendezvous problem. Each employs a unique, nonclassical parameterization of the control to adapt the nonlinear MPC approach to interplanetary orbital dynamics with low control authority. The approach is demonstrated numerically for a minimum‐fuel Earth‐to‐Mars rendezvous maneuver, cast as a simplified coplanar circular orbit heliocentric transfer problem. The interplanetary transfer is accomplished by repeated solution of an optimal control problem over (i) a receding horizon with fixed number of control subintervals and (ii) a receding horizon with shrinking number of control subintervals, with a doubling strategy to maintain controllability. In both cases, the end time is left unconstrained. The performances of the nonlinear MPC strategies in terms of computation time, fuel consumption, and transfer time are compared for a constant thrust nuclear‐electric propulsion system. For this example, the ability to withstand unmodeled effects and control allocation errors is verified. The second strategy, with shrinking number of control subintervals, is also shown to easily handle the more complicated bounded thrust nuclear‐electric case, as well as a state‐control‐constrained solar‐electric case. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust reliable control for discrete‐time‐delay systems with stochastic nonlinearities and multiplicative noises

This paper is concerned with the reliable control problem against actuator failures for a class of uncertain discrete‐time stochastic nonlinear time‐delay systems. The failures of actuators are quantified by a variable varying in a given interval. The stochastic nonlinearities described by statistical means cover several well‐studied nonlinear functions as special cases. The time‐varying delay is unknown with given lower and upper bounds. The multiplicative stochastic disturbances are in the form of a scalar Gaussian white noise with unit variance. Attention is focused on the analysis and design of a stable controller such that, for all possible actuator failures, stochastic nonlinearities and disturbances, time delays and admissible parameter uncertainties, the closed‐loop system is exponentially mean‐square stable. A linear matrix inequality approach is developed to solve the addressed problem. A numerical example is given to demonstrate the effectiveness of the proposed design approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Finite‐time convergence results in robust model predictive control

Robust asymptotic stability (asymptotic attractivity and ?‐δ stability) of equilibrium regions under robust model predictive control (MPC) strategies was extensively studied in the last decades making use of Lyapunov theory in most cases. However, in spite of its potential application benefits, the problem of finite‐time convergence under fixed prediction horizon has not received, with some few exceptions, much attention in the literature. Considering the importance in several applications of having finite‐time convergence results in the context of fixed horizon MPC controllers and the lack of studies on this matter, this work presents a new set‐based robust MPC (RMPC) for which, in addition to traditional stability guarantees, finite‐time convergence to a target set is proved, and moreover, an upper bound on the time necessary to reach that set is provided. It is remarkable that the results apply to general nonlinear systems and only require some weak assumptions on the model, cost function, and target set.     

Energy‐optimal trajectory planning for the Pendubot and the Acrobot

In this paper, we study the trajectory‐planning problem for planar underactuated robot manipulators with two revolute joints in the presence of gravity. This problem is studied as an optimal control problem. We consider both possible models of planar underactuated robot manipulators, namely with the elbow joint not actuated, called Pendubot, and with the shoulder joint not actuated, called Acrobot. Our method consists of a numerical resolution of a reformulation of the optimal control problem, as an unconstrained calculus of variations problem, in which the dynamic equations of the mechanical system are regarded as constraints and treated by means of special derivative multipliers. We solve the resulting calculus of variations problem by using a numerical approach based on the Euler–Lagrange necessary condition in integral form. In which, time is discretized, and admissible variations for each variable are approximated using a linear combination of the piecewise continuous basis functions of time. In this way, a general method for the solution of optimal control problems with constraints is obtained, which, in particular, can deal with nonintegrable differential constraints arising from the dynamic models of underactuated planar robot manipulators with two revolute joints in the presence of gravity. Copyright © 2012 John Wiley & Sons, Ltd.     

A suboptimal learning control scheme for non‐linear systems with time‐varying parametric uncertainties

In this paper, learning control is integrated with non‐linear optimal control to enhance control performance of a class of non‐linear systems with time‐varying parametric uncertainties. A suboptimal control strategy based on a control Lyapunov function (CLF) and Sontag's formula provides suboptimal performance as well as stability along the time horizon for the nominal part of the non‐linear dynamic system. The proposed learning mechanism learns the unknown time‐varying parametric uncertainties so as to eliminate uncertain effects. System information both in time horizon and learning repetition horizon are incorporated in a composite energy function (CEF). The proposed control scheme achieves asymptotic convergence along the learning repetition horizon and boundedness and pointwise convergence of the tracking error (perfect tracking performance) along the time horizon. Copyright © 2001 John Wiley & Sons, Ltd.     

Robust H∞ control of linear time‐varying systems with mixed delays in the Hilbert space

In this paper, a class of linear infinite‐dimensional systems with discrete and distributed time‐varying delays is studied. New sufficient conditions for the robust H_∞ control of linear time‐varying control systems with mixed time‐varying delays in Hilbert spaces have been established. The conditions are given in terms of the solution of a Riccati differential equation. Furthermore, it is proved for the first time that the solution to the robust H_∞ control problem can be solved by the global controllability of an appropriate linear control delay‐like system. Copyright © 2010 John Wiley & Sons, Ltd.     

Analytical design of stable delta‐domain generalized predictive control

This paper addresses certain fundamental issues related to the discrete‐time design problem of the delta‐domain generalized predictive control (δ‐GPC) for both minimum phase and non‐minimum phase linear SISO plants including nominal stability and nominal performance of the closed‐loop system. The approach being presented is completely analytical, and the nominal performance of the control system is directly achieved by a prototype design of the closed‐loop system characteristics resulting in definite time‐domain specifications. Two design methods are offered in which a model‐based prediction paradigm is applied to achieve the future output and the future filtered output trajectory of the plant. Prediction of the first type is based on suitable emulations of the output δ‐derivatives and is used in the GPC controller design for minimum‐phase models of the plant. Prediction of the second type utilizes emulation of derivatives of the output filtered by the numerator polynomial of the transfer function of the controlled part of the plant. It can be employed both for minimum phase and non‐minimum phase plants. A numerical example is given that illustrates the δ‐GPC method for controller design. Copyright © 2002 John Wiley & Sons, Ltd.     

Decentralized control strategies for dynamic routing

The routing problem in multi‐destination data communication networks is considered. A dynamic model, which can incorporate arbitrary, different, time‐varying processing delays at different nodes, is developed to describe the network dynamics. Based on this model, controllers for routing control are proposed. The structures of the proposed controllers are motivated by an optimal control problem. These proposed controllers are completely decentralized in the sense that all necessary on‐line computations are done locally at each node. Furthermore, the information needed for these computations is related only to the queue lengths at the present node and the adjacent downstream nodes. Both cases when the controls can be continuously changed and when the controls are updated at discrete time instants are considered. In the latter case the controls at different nodes may be updated at different time instants (i.e. the network is not necessarily synchronous). It is shown that the controllers enjoy many desirable properties; in particular, they clear all the queues of the network in the absence of external message arrivals, in finite time. Furthermore, the controllers do not direct messages around a loop. They also have certain robustness properties. Some simulation results relating to a number of realistic problems are presented to illustrate various features of the controllers. Copyright © 2002 John Wiley & Sons, Ltd.     

Optimal control of sugarscape agent‐based model via a PDE approximation model

There is no standard framework for solving optimization problems for systems described by agent‐based models (ABMs). We present a method for constructing individual‐level controls that steer the population‐level dynamics of an ABM towards a desired state. Our method uses a system of partial differential equations (PDEs) with control functions to approximate the dynamics of the ABM with control. An optimal control problem is formulated in terms of the PDE model to mimic the optimization goal of the ABM. Mathematical theory is used to derive optimal controls for the PDE model, which are numerically approximated and transformed for use in the ABM. We use the Sugarscape ABM, a prototype ABM that includes agent and environmental heterogeneity and accumulation of agent resources over time. We present a PDE model that approximates well the spatial, temporal, and resource dynamics of the Sugarscape ABM. In both models, control represents taxation of agent wealth with the goal to maximize total taxes collected while minimizing the impact of taxation on the population over a finite time. Solutions to the optimal control problem yield taxation rates specific to an agent's location and current wealth. The use of optimal controls (generated by the PDE model) within the ABM performed better than other controls we evaluated, even though some error was introduced between the ABM and PDE models. Our results demonstrate the feasibility of using a PDE to approximate an ABM for control purposes and illustrate challenges that can arise in applying this technique to sophisticated ABMs. Copyright © 2016 John Wiley & Sons, Ltd.     

H∞ output tracking control over networked control systems with Markovian jumping parameters

The problem of H_∞ output tracking control over networked control systems (NCSs) with communication limits and environmental disturbances is studied in this paper. A wide range of time‐varying stochastic problem arising in networked tracking control system is reduced to a standard convex optimization problem involving linear matrix inequalities (LMIs). The closed‐loop hybrid NCS is modeled as a Markov jump linear system in which random time delays and packet dropouts are described as two stochastic Markov chains. Gridding approach is introduced to guarantee the finite value of the sequences of transmission delays from sensor to actuator. Sufficient conditions for the stochastic stabilization of the hybrid NCS tracking system are derived by the LMI‐based approach through the computation of the optimal H_∞ performance. The mode‐dependent robust H_∞ output tracking controller is obtained by the optimal iteration method. Numerical examples are given to demonstrate the effectiveness of the proposed robust output tracking controller for NCS. Copyright © 2016 John Wiley & Sons, Ltd.     

Design and performance analysis of elephant herding optimization based controller for load frequency control in thermal interconnected power system

In this present contribution, an attempt has been taken to design and analyze the performance of elephant herding optimization (EHO) based controller for load frequency control (LFC) applications of interconnected power system. The studied system is a two‐area nonreheat thermal interconnected system which is widely used in literature. A proportional‐integral‐differential controller is utilized for LFC of the studied system. EHO technique is applied to obtain the tuned set of controller parameters. The objectives considered for design of the controller are the minimization of settling times and integral‐time‐multiplied‐absolute‐error of frequency deviations (FDs) and tie‐line power deviation (TPD). The design objectives are integrated together to form a function with single objective by assigning equal weights after normalization. Several test cases of diverse set of disturbances are taken into account to test the performance of the proposed controller and the obtained results are compared with other controllers designed with differential evolution, gray wolf optimization, particle swarm optimization, teacher‐learner‐based optimization, and whale optimization algorithm. Furthermore, the time‐domain simulations of FDs and TPD are illustrated to support the tabulated results. In addition, comparative statistical analysis is presented to validate the robust behavior of the proposed controller.     

Outbreaks of Foot‐and‐Mouth Disease in Libya and Saudi Arabia During 2013 Due to an Exotic O/ME‐SA/Ind‐2001 Lineage Virus

Foot‐and‐mouth disease viruses are often restricted to specific geographical regions and spread to new areas may lead to significant epidemics. Phylogenetic analysis of sequences of the VP1 genome region of recent outbreak viruses from Libya and Saudi Arabia has revealed a lineage, O‐Ind‐2001, normally found in the Indian subcontinent. This paper describes the characterization of field viruses collected from these cases and provides information about a new real‐time RT‐PCR assay that can be used to detect viruses from this lineage and discriminate them from other endemic FMD viruses that are co‐circulating in North Africa and western Eurasia.     

Two‐stage construction of aircraft thrust models for optimal control computations

A two‐stage method for building analytic models based on experimental data is proposed. It is applied to thrust modeling for the F‐15 aircraft. A minimum‐time problem is solved to show efficacy of the models in indirect optimal control computations. Copyright © 2008 John Wiley & Sons, Ltd.