Optimal Trajectory Tracking Of Nonlinear Dynamical Systems

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Optimal Trajectory Tracking Of Nonlinear Dynamical Systems


Optimal Trajectory Tracking Of Nonlinear Dynamical Systems
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Optimal Trajectory Tracking Of Nonlinear Dynamical Systems


Optimal Trajectory Tracking Of Nonlinear Dynamical Systems
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Author : Jakob Löber
language : en
Publisher: Springer
Release Date : 2016-12-20

Optimal Trajectory Tracking Of Nonlinear Dynamical Systems written by Jakob Löber and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-20 with Science categories.


By establishing an alternative foundation of control theory, this thesis represents a significant advance in the theory of control systems, of interest to a broad range of scientists and engineers. While common control strategies for dynamical systems center on the system state as the object to be controlled, the approach developed here focuses on the state trajectory. The concept of precisely realizable trajectories identifies those trajectories that can be accurately achieved by applying appropriate control signals. The resulting simple expressions for the control signal lend themselves to immediate application in science and technology. The approach permits the generalization of many well-known results from the control theory of linear systems, e.g. the Kalman rank condition to nonlinear systems. The relationship between controllability, optimal control and trajectory tracking are clarified. Furthermore, the existence of linear structures underlying nonlinear optimal control is revealed, enabling the derivation of exact analytical solutions to an entire class of nonlinear optimal trajectory tracking problems. The clear and self-contained presentation focuses on a general and mathematically rigorous analysis of controlled dynamical systems. The concepts developed are visualized with the help of particular dynamical systems motivated by physics and chemistry.

On The Time Optimal Trajectory Planning Along Predetermined Geometric Paths And Optimal Control Synthesis For Trajectory Tracking Of Robot Manipulators


On The Time Optimal Trajectory Planning Along Predetermined Geometric Paths And Optimal Control Synthesis For Trajectory Tracking Of Robot Manipulators
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Author : Pedro Reynoso Mora
language : en
Publisher:
Release Date : 2013

On The Time Optimal Trajectory Planning Along Predetermined Geometric Paths And Optimal Control Synthesis For Trajectory Tracking Of Robot Manipulators written by Pedro Reynoso Mora and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.


In this dissertation, we study two important subjects in robotics: (i) time-optimal trajectory planning, and (ii) optimal control synthesis methodologies for trajectory tracking. In the first subject, we concentrate on a rather specific sub-class of problems, the time-optimal trajectory planning along predetermined geometric paths. In this kind of problem, a purely geometric path is already known, and the task is to find out how to move along this path in the shortest time physically possible. In order to generate the true fastest solutions achievable by the actual robot manipulator, the complete nonlinear dynamic model should be incorporated into the problem formulation as a constraint that must be satisfied by the generated trajectories and feedforward torques. This important problem was studied in the 1980s, with many related methods for addressing it based on the so-called velocity limit curve and variational methods. Modern formulations directly discretize the problem and obtain a large-scale mathematical optimization problem, which is a prominent approach to tackle optimal control problems that has gained popularity over variational methods, mainly because it allows to obtain numerical solutions for harder problems. We contribute to the referred problem of time-optimal trajectory planning, by extending and improving the existing mathematical optimization formulations. We successfully incorporate the complete nonlinear dynamic model, including viscous friction because for the fastest motions it becomes even more significant than Coulomb friction; of course, Coulomb friction is likewise accommodated for in our formulation. We develop a framework that guarantees exact dynamic feasibility of the generated time-optimal trajectories and feedforward torques. Our initial formulation is carefully crafted in a rather specific manner, so that it allows to naturally propose a convex relaxation that solves exactly the original problem formulation, which is non-convex and therefore hard to solve. In order to numerically solve the proposed formulation, a discretization scheme is also developed. Unlike traditional and modern formulations, we motivate the incorporation of additional criteria to our original formulation, with simulation and experimental studies of three crucial variables for a 6-axis industrial manipulator. Namely, the resulting applied torques, the readings of a 3-axis accelerometer mounted at the manipulator end-effector, and the detrimental effects on the tracking errors induced by pure time-optimal solutions. We therefore emphasize the significance of penalizing a measure of total jerk and of imposing acceleration constraints. These two criteria are incorporated without destroying convexity. The final formulation generates near time-optimal trajectories and feedforward torques with traveling times that are slightly larger than those of pure time-optimal solutions. Nevertheless, the detrimental effects induced by pure time-optimality are eliminated. Experimental results on a 6-axis industrial manipulator confirm that our formulation generates the fastest solutions that can actually be implemented in the real robot manipulator. Following the work done on near time-optimal trajectories, we explore two controller synthesis methodologies for trajectory tracking, which are more suitable to achieve trajectory-tracking under such fast trajectories. In the first approach, we approximate the discrete-time nonlinear dynamics of robot manipulators, moving along the state-reference trajectory, as an affine time-varying (ATV) dynamical system in discrete-time. Therefore, the problem of trajectory tracking for robot manipulators is posed as a linear quadratic (LQ) optimal control problem for a class of discrete-time ATV dynamical systems. Then, an ATV control law to achieve trajectory tracking on the ATV system is developed, which uses LQ methods for linear time-varying (LTV) systems. Since the ATV dynamical system approximates the nonlinear robot dynamics along the state-reference trajectory, the resulting time-varying control law is suitable to achieve trajectory tracking on the robot manipulator. The ATV control law is implemented in experiments for the 6-axis industrial manipulator, tracking the near time-optimal trajectory. Experimental results verify the better performance achieved with the ATV control law, but also expose its shortcomings. The second approach to address trajectory tracking is related in spirit, but different in crucial aspects, which ultimately endow this approach with its superior features. In this novel approach, the highly nonlinear dynamic model of robot manipulators, moving along a state-reference trajectory, is approximated as a class of piecewise affine (PWA) dynamical systems. We propose a framework to construct the referred PWA system, which consists in: (i) choosing strategic operating points on the state-reference trajectory with their respective (local) linearized system dynamics, (ii) constructing ellipsoidal regions centered at the operating points, whose purpose is to facilitate the scheduling strategy of controller gains designed for each local dynamics. Likewise, in order to switch controller gains as the robot state traverses in the direction of the state-reference trajectory, a simple scheduling strategy is proposed. The controller synthesis near each operating point is an LQR-type that takes into account the local coupled dynamics. The referred PWA control law is implemented in experiments for the 6-axis manipulator tracking the near time-optimal trajectory. The experimental results show the feasibility and superiority of the PWA control law over the typical PID controller and the ATV control law.

Discrete Time Inverse Optimal Control For Nonlinear Systems


Discrete Time Inverse Optimal Control For Nonlinear Systems
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Author : Edgar N. Sanchez
language : en
Publisher: CRC Press
Release Date : 2017-12-19

Discrete Time Inverse Optimal Control For Nonlinear Systems written by Edgar N. Sanchez and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-19 with Technology & Engineering categories.


Discrete-Time Inverse Optimal Control for Nonlinear Systems proposes a novel inverse optimal control scheme for stabilization and trajectory tracking of discrete-time nonlinear systems. This avoids the need to solve the associated Hamilton-Jacobi-Bellman equation and minimizes a cost functional, resulting in a more efficient controller. Design More Efficient Controllers for Stabilization and Trajectory Tracking of Discrete-Time Nonlinear Systems The book presents two approaches for controller synthesis: the first based on passivity theory and the second on a control Lyapunov function (CLF). The synthesized discrete-time optimal controller can be directly implemented in real-time systems. The book also proposes the use of recurrent neural networks to model discrete-time nonlinear systems. Combined with the inverse optimal control approach, such models constitute a powerful tool to deal with uncertainties such as unmodeled dynamics and disturbances. Learn from Simulations and an In-Depth Case Study The authors include a variety of simulations to illustrate the effectiveness of the synthesized controllers for stabilization and trajectory tracking of discrete-time nonlinear systems. An in-depth case study applies the control schemes to glycemic control in patients with type 1 diabetes mellitus, to calculate the adequate insulin delivery rate required to prevent hyperglycemia and hypoglycemia levels. The discrete-time optimal and robust control techniques proposed can be used in a range of industrial applications, from aerospace and energy to biomedical and electromechanical systems. Highlighting optimal and efficient control algorithms, this is a valuable resource for researchers, engineers, and students working in nonlinear system control.

Reinforcement Learning For Optimal Feedback Control


Reinforcement Learning For Optimal Feedback Control
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Author : Rushikesh Kamalapurkar
language : en
Publisher: Springer
Release Date : 2018-05-10

Reinforcement Learning For Optimal Feedback Control written by Rushikesh Kamalapurkar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-10 with Technology & Engineering categories.


Reinforcement Learning for Optimal Feedback Control develops model-based and data-driven reinforcement learning methods for solving optimal control problems in nonlinear deterministic dynamical systems. In order to achieve learning under uncertainty, data-driven methods for identifying system models in real-time are also developed. The book illustrates the advantages gained from the use of a model and the use of previous experience in the form of recorded data through simulations and experiments. The book’s focus on deterministic systems allows for an in-depth Lyapunov-based analysis of the performance of the methods described during the learning phase and during execution. To yield an approximate optimal controller, the authors focus on theories and methods that fall under the umbrella of actor–critic methods for machine learning. They concentrate on establishing stability during the learning phase and the execution phase, and adaptive model-based and data-driven reinforcement learning, to assist readers in the learning process, which typically relies on instantaneous input-output measurements. This monograph provides academic researchers with backgrounds in diverse disciplines from aerospace engineering to computer science, who are interested in optimal reinforcement learning functional analysis and functional approximation theory, with a good introduction to the use of model-based methods. The thorough treatment of an advanced treatment to control will also interest practitioners working in the chemical-process and power-supply industry.

Feedback Systems


Feedback Systems
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Author : Karl Johan Åström
language : en
Publisher: Princeton University Press
Release Date : 2021-02-02

Feedback Systems written by Karl Johan Åström and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-02 with Technology & Engineering categories.


The essential introduction to the principles and applications of feedback systems—now fully revised and expanded This textbook covers the mathematics needed to model, analyze, and design feedback systems. Now more user-friendly than ever, this revised and expanded edition of Feedback Systems is a one-volume resource for students and researchers in mathematics and engineering. It has applications across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl Åström and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. Åström and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. Features a new chapter on design principles and tools, illustrating the types of problems that can be solved using feedback Includes a new chapter on fundamental limits and new material on the Routh-Hurwitz criterion and root locus plots Provides exercises at the end of every chapter Comes with an electronic solutions manual An ideal textbook for undergraduate and graduate students Indispensable for researchers seeking a self-contained resource on control theory

Dynamics Of Underactuated Multibody Systems


Dynamics Of Underactuated Multibody Systems
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Author : Robert Seifried
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-08

Dynamics Of Underactuated Multibody Systems written by Robert Seifried and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-08 with Technology & Engineering categories.


Underactuated multibody systems are intriguing mechatronic systems, as they posses fewer control inputs than degrees of freedom. Some examples are modern light-weight flexible robots and articulated manipulators with passive joints. This book investigates such underactuated multibody systems from an integrated perspective. This includes all major steps from the modeling of rigid and flexible multibody systems, through nonlinear control theory, to optimal system design. The underlying theories and techniques from these different fields are presented using a self-contained and unified approach and notation system. Subsequently, the book focuses on applications to large multibody systems with multiple degrees of freedom, which require a combination of symbolical and numerical procedures. Finally, an integrated, optimization-based design procedure is proposed, whereby both structural and control design are considered concurrently. Each chapter is supplemented by illustrated examples.

Proceedings Of 2021 Chinese Intelligent Systems Conference


Proceedings Of 2021 Chinese Intelligent Systems Conference
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Author : Yingmin Jia
language : en
Publisher: Springer Nature
Release Date : 2021-10-06

Proceedings Of 2021 Chinese Intelligent Systems Conference written by Yingmin Jia and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-06 with Technology & Engineering categories.


This book presents the proceedings of the 17th Chinese Intelligent Systems Conference, held in Fuzhou, China, on Oct 16-17, 2021. It focuses on new theoretical results and techniques in the field of intelligent systems and control. This is achieved by providing in-depth study on a number of major topics such as Multi-Agent Systems, Complex Networks, Intelligent Robots, Complex System Theory and Swarm Behavior, Event-Triggered Control and Data-Driven Control, Robust and Adaptive Control, Big Data and Brain Science, Process Control, Intelligent Sensor and Detection Technology, Deep learning and Learning Control Guidance, Navigation and Control of Flight Vehicles and so on. The book is particularly suited for readers who are interested in learning intelligent system and control and artificial intelligence. The book can benefit researchers, engineers, and graduate students.