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Table Of Integrals Series And Products

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Guidance And Control Of Ocean Vehicles

In this paper, we investigate the trajectory tracking problem for a fully actuated autonomous underwater vehicle (AUV) that moves in the horizontal plane. External disturbances, control input nonlinearities and model uncertainties are considered in our control design. Based on the dynamics model derived in the discrete-time domain, two neural networks (NNs), including a critic and an action NN, are integrated into our adaptive control design. The critic NN is introduced to evaluate the long-time performance of the designed control in the current time step, and the action NN is used to compensate for the unknown dynamics. To eliminate the AUV’s control input nonlinearities, a compensation item is also designed in the adaptive control. Rigorous theoretical analysis is performed to prove the stability and performance of the proposed control law. Moreover, the robustness and effectiveness of the proposed control method are tested and validated through extensive numerical simulation results.

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Adaptive Neural Network Control of AUVs With Control Input Nonlinearities Using Reinforcement Learning

Adaptive sliding-mode attitude control for autonomous underwater vehicles with input nonlinearities

Terminal sliding mode control for the trajectory tracking of underactuated Autonomous Underwater Vehicles

This article investigates finite-time optimal and suboptimal controls for time-varying systems with state and control nonlinearities. The state-dependent Riccati equation (SDRE) controller was the main framework. A finite-time constraint imposed on the equation changes it to a differential equation, known as the state-dependent differential Riccati equation (SDDRE) and this equation was applied to the problem reported in this study that provides general formulation and stability analysis. The following four solution methods were developed for solving the SDDRE; backward integration, state transition matrix (STM) and the Lyapunov based method. In the Lyapunov approach, both positive and negative definite solutions to related SDRE were used to provide suboptimal gain for the SDDRE. Finite-time suboptimal control is applied for robotic manipulator, as finite-time constraint strongly decreases state error and operation time. General state-dependent coefficient (SDC) parameterizations for rigid and flexible joint arms (prismatic or revolute joints) are introduced. By including nonlinear control inputs in the formulation, the actuator׳s limits can be inserted directly to the state-space equation of a manipulator. A finite-time SDRE was implemented on a 6R manipulator both in theory and experimentally. And a reduced 3R arm was modeled and tested as a flexible joint robot (FJR). Evaluations of load carrying capacity and operation time were investigated to assess the capability of this approach, both of which showed significant improvement.

Finite-time state-dependent Riccati equation for time-varying nonaffine systems: rigid and flexible joint manipulator control.

Nonlinear suboptimal control of fully coupled non-affine six-DOF autonomous underwater vehicle using the state-dependent Riccati equation

This work studies an optimal control problem using the state-dependent Riccati equation (SDRE) in differential form to track for time-varying systems with state and control nonlinearities. The trajectory tracking structure provides two nonlinear differential equations: the state-dependent differential Riccati equation (SDDRE) and the feed-forward differential equation. The independence of the governing equations and stability of the controller are proven along the trajectory using the Lyapunov approach. Backward integration (BI) is capable of solving the equations as a numerical solution; however, the forward solution methods require the closed-form solution to fulfill the task. A closed-form solution is introduced for SDDRE, but the feed-forward differential equation has not yet been obtained. Different ways of solving the problem are expressed and analyzed. These include BI, closed-form solution with corrective assumption, approximate solution, and forward integration. Application of the tracking problem is investigated to control robotic manipulators possessing rigid or flexible joints. The intention is to release a general program for automatic implementation of an SDDRE controller for any manipulator that obeys the Denavit–Hartenberg (D–H) principle when only D–H parameters are received as input data.

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

Tutorial and Review on the State-dependent Riccati Equation

This work proposes an algorithm besides output feedback linearization method for controlling a wheeled mobile robot with two manipulators. To control such a mobile robot, three desired trajectories (or fixed points for regulation) are needed: two for the arms and one for the base. Improper choice in base path leads to singularity, low performance and failure. To prevent singularities and to attain a smooth motion, an algorithm is introduced as a local path planning process for the base. It consists of two parts which helps the robot to maintain the desired configuration. The first part of the algorithm mainly focuses on the position and orientation of the base in future time based on the arms configuration, and the second part adjusts the movement of the arms for obtaining a consistent motion. This maintenance reduces and preserves the norm of applied torques, which consequently leads to an increase in the performance of the robot and its dynamic load carrying capacity (DLCC). Also, it is no longer required to define a trajectory or an end point for the base movement since they will be calculated automatically by the algorithm.

Saeed Rafee Nekoo

Papers

Finite-time state-dependent Riccati equation for time-varying nonaffine systems: rigid and flexible joint manipulator control.

Nonlinear suboptimal control of fully coupled non-affine six-DOF autonomous underwater vehicle using the state-dependent Riccati equation

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

Tutorial and Review on the State-dependent Riccati Equation

Path planning algorithm in wheeled mobile manipulators based on motion of arms