Planning robot trajectory is a complex task that plays a significant role in design and application of robots in task space. The problem is formulated as a trajectory optimization problem which is fundamentally a constrained nonlinear optimization problem. Open-loop optimal control method is proposed as an approach for trajectory optimization of cable parallel manipulator for a given two-end-point task in point-to-point motion. Dynamic equations are organized in a closed form and are formulated in the state space form. A computational technique is developed for obtaining optimal trajectory to maximize dynamic load carrying capacity. By solving the corresponding nonlinear TPBVP, the problem of optimal path and maximum carrying for a 6 DOF spatial cable robot is studied. Finally, dynamic modelling in ADAMS is presented and to validate the optimal control method, optimal trajectory concerned with dynamic motion is compared with the software results.

Flexible manipulators have plentiful applications in Aero-Space fields, due to their less weight and maneuverability. In fact, the ratio of their load carrying capacity to their weight, make them more excellent over their rigid ones. Moreover, these manipulators are known as good candidates in Aero-Space applications because of their less energy consumption, and smaller actuators. In this paper, the dynamic modeling of the flexible manipulators are performed using Finite Element Method (FEM), and optimal control of point-to-point motion of robot is done via optimal control method. To dynamic modeling of flexible manipulator, each link of the robot is divided into sufficient elements, and total displacement of the element is presumed as summation of a rigid displacement and a displacement because of flexibility. By means of Lagrange’s principle, dynamic equations of the flexible robot are derived, and the effect of number of the on dynamic motion of the robot is considered. Also, for the optimal point-to-point motion planning of the elastic manipulator, the nonlinear dynamic equations of the robot is assumed as constraints of optimal control problem, and a proper cost function is defined including torque and speed terms. Then, variation of calculus and Pontryagin’s minimum principle are employed and optimality conditions are resulted in a set of nonlinear differential equations, which is solved numerically. The priority of the optimal control method on the optimal motion planning of the flexible manipulator is discussed, and simulations for a single-link elastic robot illustrate the applicability of the method

In this paper, an optimal robust nonlinear control approach based on the state-dependent Riccati equation (SDRE) is presented for a class of fractional-order nonlinear systems. The SDRE control is a method for the solution of nonlinear systems optimal problems, which has some disadvantages, such as it is not robust against disturbances and uncertainties and has not finite time convergence ability. Sliding mode control (SMC) is also a common method for nonlinear systems control, although it is not an optimal control method, it has great advantages such as robustness which has made it very popular. In the proposed method, a combination of SMC and SDRE methods is used for optimal and robust nonlinear control, which is suitable for a class of fractional-order nonlinear systems. The proposed control method has a robust structure against mismatched disturbances. The closed loop system stability is guaranteed by the Lyapunov theory and simulation examples show the performance improvement of the proposed method.

In this paper¡ a hybrid model-based nonlinear optimal control method is used to compute the optimal power distribution and power management in parallel hybrid electric vehicles. In the power management strategy¡ for optimal power distribution between the internal combustion engine¡ electrical system and the other subsystems¡ nonlinear predictive control is applied. In achieving this goal¡ a hierarchical control structure is utilized. This type of control structure consists of three levels of monitoring¡ coordinating and local level. Nonlinear modeling and performance index in the proposed problem¡ shall be formulated at the regulatory level of the controller. Discrete dynamic mode of operation (motor-generator) in hybrid electric vehicle¡ requires us to use a dual-mode switch model and to define an alternative expression of performance index for the optimal control problem. In the performance index¡ tracking error penalty¡ fuel consumption¡ friction losses and the maintenance of the battery charge has been included. Optimization of performance index is performed by the theory of nonlinear model predictive control using numerical methods.

The effective procedure for activating muscles and improving movements in individuals who have a central nervous system injury is Functional electrical stimulation (FES). To have accurate movements of the limbs, appropriate stimulation patterns should be generated and exerted on the muscles. The challenging problem is the redundancy in the musculoskeletal system that makes it necessary to use optimal control to derive muscle activations. For doing this, the redundant musculoskeletal model of the ankle joint is derived in this paper, then an optimal control method for estimating muscle activation during the gait cycle is designed. The aim of optimal control theory is to minimize the cost function, including muscle activation as the control input and joint angle tracking error as the output of the model. Two optimal control algorithms are implemented in this research. These approaches present direct and indirect control methods to solve the optimization problem of ankle movement achieved by experimental research on two healthy males during the gait cycle. Based on the results, the direct method is smoother for nonlinear systems and estimates desired muscle activation more precisely and the cost function coefficients are chosen with logical and less values in comparison to the indirect method.

The present paper addresses an effective cyber defense model by applying information fusion based game theoretical approaches‎. ‎In the present paper, we are trying to improve previous models by applying stochastic optimal control and robust optimization techniques‎. ‎Jump processes are applied to model different and complex situations in cyber games‎. ‎Applying jump processes we propose some models for cyber battle spaces‎. ‎The resulted stochastic models are solved by applying stochastic optimal control methods‎. ‎A robust optimization technique is proposed to obtain robust estimations in the case of lack of complete data‎. ‎We address reinforcement learning throughout the by stochastic optimal control formulation‎. ‎Previous models are improved by applying optimal control approaches to overcome the issue of time steps in game theory based approaches in which times steps cause limitations by considering the cases that may take longer times‎. ‎Two adaptation methods are proposed in incomplete information cases.

In this paper, a control system with two layers is analytically designed using prediction-based optimal control method for nonlinear vehicle dynamics. In the first layer, an optimal external yaw moment for stabilizing the vehicle lateral dynamics is designed. After transforming this external yaw moment to differential forces between the four wheels and by using the inverse tire model for extraction of desired longitudinal slips, the desired values are sent to the second layer. In the second layer, each wheel motor regulates the control torque to track the desired slip. Since the energy consumption of battery is important in electric vehicles, considering the optimal control idea for designing the torque vectoring system reduces the battery consumption.Therefore, by examining suitable weighting factors, the electric motors are forced to operate within the admissible range and also the minimum usage of batteries are provided. The simulation results demonstrate that the designed control system has a suitable performance to cope with nonlinearities and consequently stabilizes the vehicle.

This paper presents optimal control method to path planning of mobile robotswith flexible joints. Dynamic equations are derived and additional kinematic constraintsare used to solve the extra Dofs arose from base mobility. Then with modeling theelasticity at each joint as a linear torsinal spring, the set of equations are formed. TheHamiltonian function is formed and the necessary conditions for optimality are derivedfrom the Pontryagin''s minimum principle. The obtained equations established a two pointboundary value problem solved by numerical techniques. This problem is known to becomplex in particular when combined motion of the base and manipulator, non-holonomicconstraint of base and non-linear and complicated dynamic equations as a result of flexiblenature of joints are taken into account. The study emphasizes on modeling of the complete optimal control problem by remaining all nonlinear state and costate variables as well as control constraints to establish accompanying boundary value problem. Another advantage of this method is obtaining various optimal trajectories with different characteristics by changing the penalty matrices values which enables the designer to choose the best trajectory. A mobile flexible joint manipulator is studied to verify the feasibility of the proposed approach.

In this paper a time varying optimal control algorithm (β-Method) is proposed to control building responses, against environmental earthquake excitations. The proposed method is presented through defining a rational relation between the state variables of a structure with active and passive control systems with identical mechanisms. This procedure results in a time varying gain matrix with adaptable ability to external excitation in order to decrease the extra need for maximum and/or total control force. Performance of the proposed method is examined by applying it to an eight-story shear type building subjected to various ground accelerations. Numerical results indicate that the proposed algorithm in some cases reduces the power consumption demand significantly without any reduction in control system performances in comparison with the classical closed loop optimal control method and acts similar in the worst case.

The purpose of this study is to determine the preferences of the central bank of Iran and the optimal monetary policy rule using the optimal control method. so, we assumed that monetary authorities solving an optimization problem in backward looking expectation framework with regard to the constraints of the economic structure, which includes four equations of aggregate supply, aggregate demand, money demand and government expenditures. using Ordinary Least Squares (OLS) and Seemingly Unrelated Regression Method (SUR), for the period of 1979-1397, the preferences of the monetary authorities that minimize the amount of Social welfare losses, were selected. The results indicate that the central bank should consider the deviation of monetary growth rate and then the output gap. Also, the optimal rule of monetary policy derived from the optimal preferences indicates that the central bank must react simultaneously to the changes in inflation, output gap, real exchange rates, government expenditure growth, oil and tax revenues growth.