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254   Control theory in biomedical engineering


          Additionally, these strategies can be used for evaluating or studying subject
          movements and performance improvement. In these modes, theoretically,
          the patient should not feel the presence of the exoskeleton robot. Therefore,
          the subject is completely active and the exoskeleton robot should not affect
          the movement.
             However, these devices are still part of an emerging area and present many
          challenges. In fact, these robots have an additional complexity compared to
          conventional robotic manipulators due to their complex mechanical struc-
          ture designed for human use, types of assistive motion, and the sensitivity
          of the interaction with a large diversity of human wearers. As a result, these
          conditions make the robot system vulnerable to dynamic uncertainties and
          externaldisturbancessuchassaturation,frictionforces,backlash,andpayload.
          Likewise, the interactionbetween the human and the exoskeleton subjectthe
          system to external disturbances due to different physiological conditions of
          the subjects, such as different weights of upper limbs for each patient (Brahmi
          et al., 2018a, b). During a rehabilitation movement, the nonlinear uncertain
          dynamic model and external forces can turn into an unknown function that
          can affect the performance of the exoskeleton robot.
             The control of uncertain nonlinear dynamics is one of the challenges of
          nonlinear control engineering problems. In particular, a control system
          should be developed to ensure the stability of the system. In addition, its per-
          formance should not be affected by the disturbances generated from the var-
          iation of internal parameters of the system, unmodeled dynamics
          stimulation, and external disturbances (Slotine et al., 1991; Khalil and Griz-
          zle, 1996). Many studies discussing the problem of modeling and control of
          exoskeleton robot manipulator based on centralized approaches have been
          given in Rahman et al. (2013b), Ueda et al. (2010), and Lee et al. (2012).
          Nevertheless, in the previously cited studies, the control design is model-
          based, in which the control law requires the full dynamic model of the exo-
          skeleton robot. The estimation of the dynamic parameters is one of the open
          problems in exoskeleton manipulators, notably, with high DOFs (Krstic
          et al., 1995), and in the presence of human-robot interaction. Conventional
          control approaches consider that the dynamic model of the upper arm
          manipulator is known. However, in practice, it becomes very difficult to
          get the exact model and uncertainty may still exist. To overcome this prob-
          lem, robust control approaches based on the Lyapunov theory are developed
          to ensure the stability of the full system (Khan et al., 2016a, b, 2017; Huang
          and Chien, 2010; Luna et al., 2016). However, these controllers are very
          complicated due to the complexity of the regression matrix (Huang and
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