Abstract
Abstract We introduce a new control synthesis approach to solve reach-avoid problems occurring in many fields, such as autonomous driving or robot motion planning. Our control approach steers a set of initial states as close as possible to a given target state while provably satisfying constraints on both inputs and states. We compute a control law consisting of a state-dependent, piecewise constant feedforward controller and a continuous feedback controller. The feedforward controller can be polynomial in the state and steers the initial set of states as close as possible to the target state for an undisturbed system, while the feedback controller minimizes the effect of disturbances and abstraction errors. Compared to other formal synthesis approaches, our approach can be verified in polynomial time and generates nonlinear feedforward control laws. The achievable control performance is demonstrated by two use cases.
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