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In this study, we consider a controller of the parallel wheeled inverted pendulum named Beauto Balancer Duo. The mathematical model of the inverted pendulum is derived by using the Euler Lagrange formula. Kinetic coefficients of the motor are derived from a specification sheet. The inverted pendulum has an uncertain viscous friction coefficient around the wheel, that causes perturbation of the dynamics. Therefore, an upper bound and a lower bound of the viscous friction coefficient are estimated by several experiments. Two controllers are synthesized in order to compare by simulations and experiments. One controller provides optimal performance only for a nominal model, and other controller has a robustness for the range of the viscous friction coefficient. From comparing two controllers, an accuracy of the derived mathematical model and an accuracy of the estimated viscous friction coefficient are verified. [ABSTRACT FROM PUBLISHER]

Agents rarely act in isolation -- their behavioral history, in particular, is public to others. We seek a nonasymptotic understanding of how a leader agent should shape this history to its maximal advantage, knowing that follower agent(s) will be learning and responding to it. We study Stackelberg leader-follower games with finite observations of the leader commitment, which commonly models security games and network routing in engineering, and persuasion mechanisms in economics. First, we formally show that when the game is not zero-sum and the vanilla Stackelberg commitment is mixed, it is not robust to observational uncertainty. We propose observation-robust, polynomial-time-computable commitment constructions for leader strategies that approximate the Stackelberg payoff, and also show that these commitment rules approximate the maximum obtainable payoff (which could in general be greater than the Stackelberg payoff). [ABSTRACT FROM AUTHOR]