State-dependent differential Riccati equation to track control of time-varying systems with state and control nonlinearities

Korayem, M. H.; Nekoo, Saeed Rafee

doi:10.1016/j.isatra.2015.02.008

Cited by 57 publications

(45 citation statements)

References 31 publications

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“…A(e(t), t) T P + PA(e(t), t) − PBR −1 B T P + Q � 0. (20) Although the solution of equation (20) provides an optimal control solution, in the SDRE control, this solution is presented as suboptimal because each interaction recalculates the local optimal value for the control, based on the error state arrays A(e(t), t) and B.…”

Section: Discrete Time Sdre Controller Designmentioning

confidence: 99%

“…e SDRE control is being applied in many nonlinear systems due to its easy application and advantage of considering the influence of nonlinearities of the system, i.e., there is no need to linearize the system to be applied [10][11][12][13][14]. Such control has been widely used in rigid and flexible robotic manipulators as the works of authors [8,[14][15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On Positioning and Vibration Control Application to Robotic Manipulators with a Nonideal Load Carrying

Lima

Balthazar

Rocha

et al. 2019

Shock and Vibration

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In recent years, the evolution of artificial intelligence techniques has widely grown such that it gives new ways to improve human life, not only at work but also living. Nowadays, to the human being, physical human-robot interactions (PHRIs) have been presented very important and present itself as a major challenge for the current engineering. Therefore, this work designs and analyses a two-degree-of-freedom robotic arm with flexible joints driven by a DC motor. Due to the interaction between the robot links and flexible joints, the arm may present overshoots when it is moved such that it becomes difficult to manipulate the arm. Therefore, Magnetorheological dampers (MR damper or MR brake) are attached to the links of the arm in order to control such overshoot and provide a way to adjust the mechanical limitations of the arm. The dynamics of the system will be investigated, showing the appearance of chaotic behavior due to the coupling of the manipulator to the motors. After that, the feedback control is obtained through the state-dependent Riccati equation (SDRE) aiming the control of the positioning of the manipulator and the torque applied on the MR damper. Numerical results showed that the proposed control using hybrid actuators, DC motor, and MR brake was effective to control the position and behavior of the flexible joints of the manipulators.

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Section: Discrete Time Sdre Controller Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Positioning and Vibration Control Application to Robotic Manipulators with a Nonideal Load Carrying

Lima

Balthazar

Rocha

et al. 2019

Shock and Vibration

View full text Add to dashboard Cite

show abstract

“…The dynamics of the robot is attainable using a general program in section 4‐1 of the work of Korayem and Nekoo with n = 2 in derivation; moreover, the estimator design of Section 2.2 must be added to the system. This rigid dynamics then should be placed in the FJR structure of the work of Korayem and Nekoo .…”

Section: Illustrative Example: Planar Robotmentioning

confidence: 99%

“…Korayem et al implemented the SDRE controller for flexible‐joint manipulators based on the assumption that full state feedback is available and, as such, the essence of an observer is necessary. (–)…”

Section: Introductionmentioning

confidence: 99%

“…17 Korayem et al implemented the SDRE controller for flexible-joint manipulators based on the assumption that full state feedback is available and, as such, the essence of an observer is necessary. [20][21][22] Section 2 presents the formulation of the SDRE controller and estimator in a closed-loop control design. In Section 3, simulations and analysis of an illustrative example are summarized in different situations.…”

Section: Introductionmentioning

confidence: 99%

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Application of the state‐dependent Riccati equation for flexible‐joint arms: Controller and estimator design

Korayem

Lademakhi

Nekoo

2017

Optim Control Appl Methods

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Summary Full feedback data is mostly essential in control design. Measuring the links' variation of a flexible‐joint robot (FJR) is easy but not for its actuators. The measurement of states and workspace are also affected by noise and disturbance, respectively; hence, a state observer or a nonlinear estimator is very helpful to improve the control performance of a dynamic system. The state‐dependent Riccati equation (SDRE) is one of the most promising methods in the field of nonlinear optimal observers for estimating variables of multiple‐input–multiple‐output systems. Systematic procedure, simple structure, and incorporation of a wide range of systems (under an observability condition) are some of the advantages of the method. Therefore, the aim of this study is to compose the SDRE controller and estimator simultaneously to reduce the state error of the system in the presence of external disturbance and noise. The application of this method is shown for FJRs in the estimation of changes in motion behind the connection of the motor and link where there is no easy way to measure. The proposed composition of the SDRE controller and estimator was implemented on a 6R robot to examine the various aspects of FJR systems.

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A PDE breach to the SDRE

Nekoo¹

2018

Asian Journal of Control

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The state‐dependent Riccati equation (SDRE) is a nonlinear optimal controller derived from applying optimality conditions on a Hamiltonian equation. A co‐state vector is involved in the derivation process. This has been commonly considered a function of time only, despite the existence of states in the co‐state vector. This has resulted in a series of nonlinear coupled ordinary differential equations (ODEs) with a final boundary condition, known as the SDRE. In this work, for the first time, the co‐state vector is regarded as a function of time and states that results in a partial differential equation (PDE) instead of an ODE. The new governing equation is named partial differential state‐dependent Riccati equation (PDSDRE), and the PDE provides a tensor for gain over domains of time and states. Since the generated PDE is highly nonlinear, the solution to the PDSDRE is proposed based on the method of lines (MOL), which is an extension to the finite difference method (FDM). The proposed approach is implemented on both scalar and second order systems and is compared with an SDRE technique to validate the results and show the advantages of proposed structure.

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State-dependent differential Riccati equation to track control of time-varying systems with state and control nonlinearities

Cited by 57 publications

References 31 publications

On Positioning and Vibration Control Application to Robotic Manipulators with a Nonideal Load Carrying

On Positioning and Vibration Control Application to Robotic Manipulators with a Nonideal Load Carrying

Application of the state‐dependent Riccati equation for flexible‐joint arms: Controller and estimator design

A PDE breach to the SDRE

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