One algorithm for testing annulling of mixed trigonometric polynomial functions on boundary points

This paper considers one problem of modern automated theorem provers. While there are many different numerical methods for computation of real roots of polynomials, theorem provers require higher level of assurances of result correctness. In this paper is shown one method that circumvents limitations of application of Sturm’s theorem for such tasks

Non-Gaussian Uncertainty Minimization Based Control of Stochastic Nonlinear Robotic Systems

In this paper, we consider the closed-loop control problem of nonlinear robotic systems in the presence of probabilistic uncertainties and disturbances. More precisely, we design a state feedback controller that minimizes deviations of the states of the system from the nominal state trajectories due to uncertainties and disturbances. Existing approaches to address the control problem of probabilistic systems are limited to particular classes of uncertainties and systems such as Gaussian uncertainties and processes and linearized systems. We present an approach that deals with nonlinear dynamics models and arbitrary known probabilistic uncertainties. We formulate the controller design problem as an optimization problem in terms of statistics of the probability distributions including moments and characteristic functions. In particular, in the provided optimization problem, we use moments and characteristic functions to propagate uncertainties throughout the nonlinear motion model of robotic systems. In order to reduce the tracking deviations, we minimize the uncertainty of the probabilistic states around the nominal trajectory by minimizing the trace and the determinant of the covariance matrix of the probabilistic states. To obtain the state feedback gains, we solve deterministic optimization problems in terms of moments, characteristic functions, and state feedback gains using off-the-shelf interior-point optimization solvers. To illustrate the performance of the proposed method, we compare our method with existing probabilistic control methods.Comment: International Conference on Intelligent Robots and Systems (IROS), 202