NONLINEAR ADAPTIVE CONTROL

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NONLINEAR ADAPTIVE CONTROL

• RICCARDO MARINO
• UNIVERSITA DI ROMA TOR VERGATA

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NONLINEAR ADAPTIVE CONTROL

• ADAPTIVE CONTROL OF LINEAR SYSTEMS
• ADAPTIVE CONTROL OF NONLINEAR SYSTEMS
• ADAPTIVE CONTROL OF TIME-VARYING SYSTEMS

• ADAPTIVE DISTURBANCE ATTENUATION/ REJECTION
• ADAPTIVE REGULATION
• LEARNING CONTROL

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Adaptive control of linear systems

• Given a family of linear time-invariant systems
  (minimum phase, known upper bound on system
  order, known relative degree, known sign of high
  frequency gain), design an output feedback
  tracking control such that ANY smooth bounded
  output reference signal is asymptotically tracked
  from any initial condition with transient
  specifications the resulting control is
  NONLINEAR.

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Adaptive control of nonlinear systems

• Given a family of systems with KNOWN
  nonlinearities, design an output feedback control
  which solves an output tracking problem with
  transient specifications.
• If the nonlinearities depend on the measured
  output, the problem has been solved for a class
  of nonlinear minimum phase systems which
  strictly contains the linear ones.

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• The model is required to be LINEARLY
  parametrized with respect to unknown constant
  parameters while this is natural for linear
  systems, it may be a strong assumption for
  nonlinear systems.
• The control contains parameter estimates which
  are adapted on the basis of the tracking error.
  They may or may not converge to the true values
  depending on persistency of excitation.
  Nevertheless, asymptotic tracking is achieved.

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Adaptive control of time- varying systems

• Adaptation really means to adapt with respect to
  systems time variations and to changes from the
  environment.
• From a technical viewpoint this implies time
  varying parameters and time varying disturbances
  and poses many difficulties in adaptive control
  design what does adaptation mean if asymptotic
  tracking cannot be achieved?

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Adaptive disturbance attenuation/rejection

• Given an additive sinusoidal disturbance of
  unknown frequency acting on a stable/stabilizable
  system, design an output feedback control which
  asymptotically rejects the influence of the
  disturbance on the output.
• More generally the disturbance is the sum of a
  bias and unknown sinusoids.

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Adaptive regulation

• Given a controllable and observable system with
  additive disturbances and output reference
  generated by a linear stable exosystem with
  UNKNOWN parameters, design an output feedback
  regulator which achieves asymptotic regulation
  and disturbance rejection.

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Learning control

• Learning control deals with repetitive tasks,
  i.e. asymptotic tracking of PERIODIC reference
  signals (and not any smooth bounded as adaptive
  control does).
• The goal of learning control is to learn the
  unknown reference (periodic) input and not to
  identify systems parameters.

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• OPEN PROBLEMS IN NONLINEAR ADAPTIVE/LEARNING
  CONTROL If the unknown nonlinearities
  are not linearly parametrized, can we still track
  a time varying (for instance periodic) reference
  signal? Can we learn the required reference
  input? How do we
  hold the system in the adaptive/learning phase?