Quadratic Constraint for Semi-automatic Control
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The quadratic constraint, APRC or QDC, is implemented separately from the control algorithm in this chapter instead of integrating with the MPC optimisation as in previous chapters. The real-time value of the supply rate is monitored by an independent entity, called stabilising agent, while the quadratic constraint is continuously checked online by the associated semi-automatic control system. The stabilising agent will override the control actions of the controller, or of the human operator, if the quadratic constraint is violated, thus confine the closed-loop system within the QDC ellipsoidal boundary—a stabilising region. The closed-loop system will be asymptotically attractive, or stabilisable in the GDC sense, as a result of these overriding actions online.