Probabilistic control of switched linear systems with chance constraints

This paper proposes an approach to algorithmically synthesize control strategies for set-to-set transitions of uncertain discrete-time switched linear systems based on reachable set computations in a stochastic setting. The initial state and disturbances are assumed to be normally distributed, and a time-variant hybrid control law stabilizes the system towards a goal set. The algorithmic solution computes sequences of discrete states via tree search, and the continuous controls are obtained from solving embedded semi-definite programs (SDP). These programs take polytopic input constraints as well as time-varying probabilistic state constraints into account. An example for demonstrating the principles of the solution procedure with focus on handling the chance constraints is included.

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