Nonlinear control systems - A brief overview of historical and recent advances <s> Nonlinear adaptive control <s> Robot Manipulator Control offers a complete survey of control systems for serial-link robot arms and acknowledges how robotic device performance hinges upon a well-developed control system. Containing over 750 essential equations, this thoroughly up-to-date Second Edition, the book explicates theoretical and mathematical requisites for controls design and summarizes current techniques in computer simulation and implementation of controllers. It also addresses procedures and issues in computed-torque, robust, adaptive, neural network, and force control. New chapters relay practical information on commercial robot manipulators and devices and cutting-edge methods in neural network control. <s> BIB001 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Nonlinear adaptive control <s> Safety is very important for physical human-robot interaction. Compliance control can solve an important aspect of the safety problem by dealing with impact and other forces arising during close contact between humans and robots. <s> BIB002 </s> Nonlinear control systems - A brief overview of historical and recent advances <s> Nonlinear adaptive control <s> We survey some of the rich history of control over the past century with a focus on the major milestones in adaptive systems. We review classic methods and examples in adaptive linear systems for both control and observation/identification. The focus is on linear plants to facilitate understanding, but we also provide the tools necessary for many classes of nonlinear systems. We discuss practical issues encountered in making these systems stable and robust with respect to additive and multiplicative uncertainties. We discuss various perspectives on adaptive systems and their role in various fields. Finally, we present some of the ongoing research and expose problems in the field of adaptive control. <s> BIB003
The most effective and advanced nonlinear control schemes are the adaptive controllers. The basic idea of an adaptive controller is to estimate uncertain parameters and to tune the controller online to adopt to the dynamic situation where the variations in the system parameters or environment are significant. Adaptive control got more popularity in 1950s in the aerospace control community. However, due to lack of well-understood stability tools and proper hardware, it lost its charm. Another particular reason for this loss of interest was incident of the plane crash which was controlled by an adaptive law BIB003 . Nevertheless, interest in adaptive control has revived especially in social robotic because of its suitability for a highly nonlinear, unstructured and dynamic human environment as compared to the controlled and well-ordered industrial work cells. In general, there are two main types of adaptive control schemes i.e. Model Reference Adaptive Control (MRAC) (see Fig. 8 ) and Self Tuning Adaptive Control (STAC) (Fig. 9) . In MRAC, the adaptation mechanism estimates suitable parameters, so that the system behave the same as the reference model. In STAC, the slowly varying parameters or unknown constants are optimized so as to minimize/ maximize an objective function typically minimization of error or maximization of efficiency. BIB002 Adaptive controllers may employ dynamic model and estimate the uncertain parameters BIB001 or may be dynamic model free. Model based adaptive controllers can be easily tuned and their performance is usually better as observed be Khan et al. BIB002 . However, dynamic model becomes very cumbersome as the DOF increases. This may results in computational and communication issues thus making the implementation of dynamic model based adaptive schemes more challenging. Therefore, dynamic model free adaptive controllers can be the best choice for a high DOF plant, eliminating the need for a dynamic model.