The problem of behaviour prediction for linear parameter-varying systems is considered in the interval framework. It is assumed that the system is subject to uncertain inputs and the vector of scheduling parameters is unmeasurable, but all uncertainties take values in a given admissible set. Then an interval predictor is designed and its stability is guaranteed applying Lyapunov function with a novel structure. The conditions of stability are formulated in the form of linear matrix inequalities. Efficiency of the theoretical results is demonstrated in the application to safe motion planning for autonomous vehicles.

Reward-free exploration is a reinforcement learning setting recently studied by Jin et al. [17], who address it by running several algorithms with regret guarantees in parallel. In our work, we instead propose a more adaptive approach for reward-free exploration which directly reduces upper bounds on the maximum MDP estimation error. We show that, interestingly, our reward-free UCRL algorithm can be seen as a variant of an algorithm of Fiechter from 1994 [11], originally proposed for a different objective that we call best-policy identification. We prove that RF-UCRL needs O (SAH 4 /ε 2 ) log(1/δ) episodes to output, with probability 1 − δ, an ε-approximation of the optimal policy for any reward function. We empirically compare it to oracle strategies using a generative model. 1 We use the shorthand [n] = {1, . . . , n} for every integer n ∈ N * Preprint. Under review.

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