This paper is devoted to the autonomous Lagrange problem of the calculus of variations with a discontinuous Lagrangian. We prove that every minimizer is Lipschitz continuous if the Lagrangian is coercive and locally bounded. The main difference with respect to the previous works in the literature is that we do not assume that the Lagrangian is convex in the velocity. We also show that, under so...

Abstract. Given a compact parameter set Y ⊂ Rp, we consider polynomial optimization problems (Py) on Rn whose description depends on the parameter y ∈ Y. We assume that one can compute all moments of some probability measure φ on Y, absolutely continuous with respect to the Lebesgue measure (e.g. Y is a box or a simplex and φ is uniformly distributed). We then provide a hierarchy of semidefinit...

The power grid is a complex and vital system that necessitates careful reliability management. Managing the grid is a difficult problem with multiple time scales of decision making and stochastic behavior due to renewable energy generations, variable demand and unplanned outages. Solving this problem in the face of uncertainty requires a new methodology with tractable algorithms. In this work, ...

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This section formalizes the encoding of an agent’s environment and goal into a Markov decision problem (MDP), and describes how this MDP can be solved efficiently by algorithms for rational planning. Let π be an agent’s plan, referred to here (and in the MDP literature) as a policy, such that Pπ(at|st, g, w) is a probability distribution over actions at at time t, given the agent’s state st at ...

Large industrial-scale databases tend to be poorly structured, dirty, and very confusing. There are many reasons for this disorder, not the least of which is that the application domains themselves are poorly structured, dirty and confusing. As data analysts, we are often called upon to mine, clean, or otherwise analyze these databases. In this article, we describe the types of problems we have...

This paper proposes an adaptive control method for robotic manipulators with input toque uncertainties. For each link of manipulators, it is assumed that the input torque uncertainties can be divided into unknown parameters term and bounded disturbance term. In addition, all the parameters for input torque uncertainties and robot are unknown. The proposed method ensures that the unknown paramet...

This paper examines the problem of link position tracking control for robot manipulators with input toque uncertainty. It is assumed that the input torque uncertainty can be regarded as dead-zone phenomena at each link of manipulator and all the system parameters for robotic manipulator and dead-zone model are unknown. The proposed method ensures that the unknown parameters are estimated adapti...

This article considers the problem of learning the correct temporal sequence of discrete behaviors from a finite behavior set that will lead to completion of a complex task, using only stochastic reinforcement from the environment. A trial-and-error learning algorithm is proposed that is inspired by backward chaining from the animal training discipline. The procedure is analytically formulated ...