Real-Time Convex-lifting-based Robust Control Using Approximated Control Law

Convex-lifting-based robust control evaluates manipulated variable by (i) solving linear programming, when the input/state constraints are active, or (ii) by linear state feedback control law when no constraints are active. This paper addresses the problem of switching linear feedback when multiple linear control laws are considered. As the sudden switching might be undesirable, the approximated control law is introduced into the real-time convex-lifting-based robust control approach, to avoid switching. This approximation of control law replaces the switching control law and ensures smoother, gain-scheduling-like, evaluation of the state feedback gain matrix. Linear interpolation is considered to approximate the switching control law. The properties of the proposed control strategy are experimentally investigated and compared to the original control approach without approximation of the control law. The laboratory device Flexy serves to experimentally demonstrate that the proposed approach outperforms the original approach.

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