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We study a system of ordinary differential equations which describes the metapopulation SIR model. The main target is to control the epidemic spreading using the structure of connections between cities. For this purpose, we formulate optimal control strategy that the control represents a drug treatment and Prevention strategies . Some methods are given in numerical example section such as control through spectral radius of movement matrix or optimal control through travelling between cities. Existence results for the optimal control are studied  

Due to inherent potential of General Regression Neural Network(GRNN) to approximate nonlinear functions, it can be implemented as a nonlinear state-feedback controller. In this paper the methodology of direct collocation and nonlinear programming is utilized in combination with GRNN to determine the optimal control of dynamical systems. Application of this method to the design of an optimal controller for a chaotic flexible beam as a non-autonomous, nonlinear system is investigated. © 2002 The American Institute Aeronautics and Astronautics Inc. All rights reserved  

In this paper, a new control strategy for optimal attitude tracking control of a multivariable satellite system has been presented. The approach is based on Radial Basis Function Neural Network (RBFNN) and classical PD Controller for its initial stabilization. It is shown how the network can be employed as a multivariable self- organizing and self learning controller in conjunction with a PD controller for attitude control of a satellite. By using four reaction wheels and quaternion for kinematics representation, the attitude dynamics of the satellite has been presented. In contrast to the previous classical approaches, it is shown how this controller can be carried out in an on-line manner... 

Optimal trajectory and muscle forces of a human-like musculoskeletal arm are predicted for planar point-to-point movements using optimal control theory. The central nervous system (CNS) is modeled as an optimal controller that performs a reaching motion to final states via minimization of an objective function. For the CNS strategy, a cubic function of muscles stresses is considered as an appropriate objective function that minimizes muscles fatigue. A two-DOF nonlinear musculoskeletal planar arm model with four states and six muscle actuators is used for the evaluation of the proposed optimal strategy. The nonlinear variational formulation of the corresponding optimal control problem is... 

In this paper, an optimal control framework is formed to control rotor-Active Magnetic Bearing (AMB) systems. The multi-input-multi-output non-affine model of AMBs is well established in the literature and represents a challenging problem for control design, where the design requirement is to keep the rotor at the bearing centre in the presence of external disturbances. To satisfy the constraints on the states and the control inputs of the AMB nonlinear dynamics, a nonlinear optimal controller is formed to minimize tracking error between the current and desired position of the rotor. To solve the resulted nonlinear constrained optimal control problem, the Gauss Pseudospectral Collocation... 

During the milling process, self-excited vibration or chatter adversely affects tool life, surface quality and productivity rate. In this paper, nonlinear cutting forces of milling process are considered as a function of chip thickness with a complete third order polynomial (instead of the common linear dependency). An optimal control strategy is developed for chatter suppression of the system described through nonlinear delay differential equations. Counterbalance forces exerted by actuators in x and y directions are the control inputs. For optimal control problem, an appropriate performance index is defined such that the regenerative chatter is suppressed while control efforts are... 

Properly adjusting the trim angle during the craft speed up, plays an important role in easily passing through the resistance hump and to reach final speed in minimum possible time. Present study tries to reply to this question that how the angles applied to a trimmable drive system and trim tab of the planing craft should be changed during speed up from rest, to craft reach a final speed in minimum time. This is a time-optimal control problem with the drive and trim tab angles as its control variables. To solve this problem a 3-DOF dynamic model is developed here rely on empirical data and relations. For the propulsion system operation of propeller, drive and engine altogether are taken... 

Based on the optimal control theory, the present study proposes a novel approach to derive a cooperative guidance law for two pursuers with an arbitrary-order linear dynamics against one zero-lag evader with random step maneuver. This approach is intended to minimize the mean value of the resultant control effort taken over a set of possible evader maneuvers which is modeled as a step function, the parameters of which are unknown. Since the resultant control effort is the minimum effort among the pursuers, we encounter the nonlinear "min" function in the performance index. By introducing binary parameters, it is changed to a linear function including binary parameters and continuous... 

This paper presents an optimal control strategy for optimal trajectory planning of mobile robots by considering nonlinear dynamic model and nonholonomic constraints of the system. The nonholonomic constraints of the system are introduced by a nonintegrable set of differential equations which represent kinematic restriction on the motion. The Lagrange's principle is employed to derive the nonlinear equations of the system. Then, the optimal path planning of the mobile robot is formulated as an optimal control problem. To set up the problem, the nonlinear equations of the system are assumed as constraints, and a minimum energy objective function is defined. To solve the problem, an indirect... 

In this paper, control of a non-isothermal continuous stirred tank reactor in which two parallel autocatalytic reactions take place has been addressed. The reactor shows chaotic behavior for a certain set of reactor parameters. In order to control the product concentration, an optimal state feedback controller has been designed. Since concentrations of reactor species are not measured, an observer has been designed for implementation of the proposed control scheme. The local asymptotic stability of the closed-loop system including observer dynamics has been shown via the Lyapunov stability theorem. effectiveness of the proposed controller in load rejection and set point tracking has been... 

A central problem in motor control is to understand how the many biomechanical degrees of freedom are coordinated to achieve a goal. A common assumption is that Central Nervous System (CNS) will plan tasks based on open-loop optimal control theory which simultaneously predicts state variables and motor commands based on a compound objective function. A 3D computational method incorporated with 18 anatomically oriented muscles is used to simulate human trunk system. Direct collocation method allows us to convert a constrained optimal control problem to a common nonlinear programming problem to assume the spinal stability condition. Trunk movement from the upright standing to 60 degrees of... 

In this paper, the optimal performance of a planar humanlike musculoskeletal arm is investigated during reaching movements employing an optimal control policy. The initial and final states (position and velocity) are the only known data of the response trajectory. Two biomechanical objective functions are taken into account to be minimized as the central nervous system (CNS) strategy: (1) a quadratic function of muscle stresses (or forces), (2) total time of movement plus a quadratic function of muscle stresses. A two-degress of freedom (DOF) nonlinear musculoskeletal arm model (for planar movements) with six muscle actuators and four state variables is used in order to evaluate the proposed... 

This paper concerns a study on the optimal control for nonlinear systems. An appropriate alternative in order to alleviate the nonlinearity of a system is the exact linearization approach. In this fashion, the nonlinear system has been linearized using input-output feedback linearization (IOFL). Then, by utilizing the well developed optimal control theory of linear systems, the compensated nonlinear system has been controlled. Thus, the structure of the objective function will be converted into a quadratic form which is qualitativly comparable with usual cost functions, and from operating viewpoint is more favorable. To qualify such a procedure, it has been applied to two minimum and... 

A new optimal control law for direct yaw moment control, to improve the vehicle handling, is developed. Although, this can be considered as part of a multi-layer system, for the traction control of a motorized wheels electric vehicle, but the results of this study are quite general and can be applied to other types of vehicles. The dynamic model of the vehicle system is initially developed and, using the well-known optimal control theory, an optimal controller is designed. Two different versions of control laws are considered here and the performance of each version of the control law is compared with the other one. The numerical simulation of the vehicle handling with and without the use of... 

An optimal preview control of a vehicle suspension system traveling on a rough road is studied. A three-dimensional seven degree-of-freedom car-riding model and several descriptions of the road surface roughness heights, including haversine (hole/bump) and stochastic filtered white noise models, are used in the analysis. It is assumed that contact-less sensors affixed to the vehicle front bumper measure the road surface height at some distances in the front of the car. The suspension systems are optimized with respect to ride comfort and road holding preferences including accelerations of the sprung mass, tire deflection, suspension rattle space and control force. The performance and power... 

In this paper, which consists of two parts, a new two-level computational algorithm is used for nonlinear optimal control of large-scale systems. The two-level optimizer uses a new coordination strategy which is based on the gradient of interaction errors instead of the gradient of overall performance function. The advantages of the new method can be categorized into two parts: First, the new formulation is applicable to a large class of problems whilst the classical model coordination method is not. Second, it extremely reduces the number of iterations required for obtaining the overall optimal solution. Although the computational burden of the algorithm in the first level increases... 

In this paper, we have developed a production planning and marketing model in unreliable flexible manufacturing systems with inconstant demand rate that its rate depends on the level of advertisement on that product. The proposed model is more realistic and useful from a practical point of view. The flexible manufacturing system is composed of two machines that produce a single product. Markovian models frequently have been used in modeling a wide variety of real-world systems under uncertainties. Therefore, in this paper, the inventory balance equation is represented by a continuous-time model with Markov jump process to take into account machines breakdown. The objective is to minimize the... 

In this paper, optimal approaches for controlling chaos is studied. The unstable periodic orbits (UPOs) of chaotic system are selected as desired trajectories, which the optimal control strategy should keep the system states on it. Classical gradient-based optimal control methods as well as modern optimization algorithm Particle Swarm Optimization (PSO) are utilized to force the chaotic system to follow the desired UPOs. For better performance, gradient-based is applied in multi-intervals and the results are promising. The Duffing system is selected for examining the proposed approaches. Multi-interval gradient-based approach can put the states on UPOs very fast and keep tracking UPOs with... 

In this paper, we propose an optimal control technique for a class of continuous-time nonlinear systems. The key idea of the proposed approach is to parametrize continuous stale trajectories by sequences of a finite number of intermediate target states; namely, waypoint sequences. It is shown that the optimal control problem for transferring the state from one waypoint to the next is given an explicit-form suboptimal solution, by means of linear approximation. Thus the original continuous-time nonlinear control problem reduces to a finite-dimensional optimization problem of waypoint sequences. Any efficient numerical optimization method, such as the interior-reflection Newton method, can be... 

In this paper, optimal control strategy is applied to parallel three-phase inverters using SVPWM technique. The three-phase system is transformed to a synchronous-stationary frame, suitable cost functions are defined, and the switching schemes are determined for the inverters. The control strategy minimizes the circulating current between the inverters, therefore, proper load sharing scheme is achieved. Simulations are performed for steady state and load change operation, and the results which show the suitability of the controller are provided. ©2009 IEEE