The Infinite Time Regulator Problem MCQ

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• The regulators that convert the non-linear stability into linear stability:
  ক

  Linear

  খ

  Sub-optimal

  গ

  Finite

  ঘ

  Infinite
• Tracking problem can be in:
  ক

  Infinite state regulators

  খ

  Finite state regulator

  গ

  Sub-optimal state regulators

  ঘ

  Non-linear regulators
• If Q is positive semi- definite:
  ক

  The optimal closed loop system is asymptotically stable

  খ

  The asymptotic stability is not guaranteed

  গ

  The system is stable

  ঘ

  The system is unstable
• The solution of the modified riccati equation may be:
  ক

  Independent

  খ

  Dependent

  গ

  Unique

  ঘ

  Non-unique
• The differential term in the riccati equation in infinite regulator is:
  ক

  Finite

  খ

  Positive

  গ

  Infinite

  ঘ

  Zero
• In Infinite regulator the optimal control cannot be differentiated from other controls.
  ক

  True

  খ

  False
• Performance index can become infinite if:
  ক

  One or more state are uncontrollable

  খ

  The uncontrollable states are uncontrollable

  গ

  The unstable states are reflected in system performance index

  ঘ

  All of the mentioned
• In finite time regulator:
  ক

  There is no restriction on the controllability of the plant

  খ

  Performance index is infinite

  গ

  Instability imposes problem in finite-interval control

  ঘ

  No restriction on controllability and performance index
• When time and the state variables tend to infinity then the system becomes:
  ক

  Unstable

  খ

  Stable

  গ

  Marginally stable

  ঘ

  Conditionally stable
• In infinite time regulator for the final time is:
  ক

  t1

  খ

  t0

  গ

  Infinite

  ঘ

  Zero