Fast optimizing control for non-convex state constraints using homotopy properties

For optimal point-to-point control of linear systems, this paper investigates how control strategies should be rendered online if non-convex state constraints are suddenly detected during execution. The challenge is to compute a modified strategy with low effort while maintaining a close-to-optimal control performance. The proposed solution is to synthesize offline a range of trajectories which are homotopic to the optimal unconstrained solution. Upon detection of the state constraints (which may represent an obstacle to be circumvented by a mobile vehicle), a sub-optimal yet feasible homotopic trajectory is selected by a fast iteration which avoids to solve a time-demanding constrained optimization problem online.

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