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We develop a procedure for computing viable (also known as controlled invariant) polytopes of a given subset of the state space under linear dynamics. The advantage of the proposed algorithm is that at every step it maintains a polytope that is itself viable. Therefore, even if the algorithm is stopped before termination it will still return a viable polytope, that can be subsequently used for controller...
Impulse differential inclusions are introduced as a formalism for modelling hybrid phenomena and their connection to some standard problems in area of hybrid systems is discussed. Conditions are derived that allow one to determine whether a set of states is viable or invariant under the action of an impulse differential inclusion. The results are demonstrated on examples.
We establish convergence guarantees for a recently proposed Markov Chain Monte Carlo (MCMC) method to locate source(s) of a certain concentration field. Our method utilizes a Markovian controller to control the motion of autonomous vehicles on a compact search domain. The distribution of the resulting discrete-time Markov chain is used to estimate the locations of the sources. To guarantee the correctness...
In this work a framework for camera-based autonomous surveillance is introduced based on the theory of stochastic reachability and random sets. We consider set-valued models of a single pan-tilt-zoom (PTZ) camera (pursuer) and multiple targets that need to be tracked (evaders). We define the stochastic pursuer process and the stochastic evader processes and consider the problem of maximizing the probability...
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