A Primal-Dual Method for Optimal Control and Trajectory Generation in High-Dimensional Systems

Presented is a method for efficient computation of the Hamilton-Jacobi (HJ) equation for time-optimal control problems using the generalized Hopf formula. Typically, numerical methods to solve the HJ equation rely on a discrete grid of the solution space and exhibit exponential scaling with dimension. The generalized Hopf formula avoids the use of grids and numerical gradients by formulating an unconstrained convex optimization problem. The solution at each point is completely independent, and allows a massively parallel implementation if solutions at multiple points are desired. This work presents a primal-dual method for efficient numeric solution and presents how the resulting optimal trajectory can be generated directly from the solution of the Hopf formula, without further optimization. Examples presented have execution times on the order of milliseconds and experiments show computation scales approximately polynomial in dimension with very small high-order coefficients.Comment: Updated references and funding sources. To appear in the proceedings of the 2018 IEEE Conference on Control Technology and Application

Higher order sigma point filter: A new heuristic for nonlinear time series filtering

In this paper we present some new results related to the higher order sigma point filter (HOSPoF), introduced in [1] for filtering nonlinear multivariate time series. This paper makes two distinct contributions. Firstly, we propose a new algorithm to generate a discrete statistical distribution to match exactly a specified mean vector, a specified covariance matrix, the average of specified marginal skewness and the average of specified marginal kurtosis. Both the sigma points and the probability weights are given in closed-form and no numerical optimization is required. Combined with HOSPoF, this random sigma point generation algorithm provides a new method for generating proposal density which propagates the information about higher order moments. A numerical example on nonlinear, multivariate time series involving real financial market data demonstrates the utility of this new algorithm. Secondly, we show that HOSPoF achieves a higher order estimation accuracy as compared to UKF for smooth scalar nonlinearities. We believe that this new filter provides a new and powerful alternative heuristic to existing filtering algorithms and is useful especially in econometrics and in engineering applications

Results of the attitude reconstruction for the UniSat-6 microsatellite using in-orbit data

UniSat-6 is a civilian microsatellite that was launched in orbit on the 19th of June, 2014. Its main mission consisted in the in-orbit release of a number of on-board carried Cubesats and in the transmission to the UniSat-6 ground station of telemetry data and images from an on-board mounted camera. The spacecraft is equipped with a passive magnetic attitude control system. Gyros and magnetometers provide the information about the attitude of the spacecraft. The importance of reconstructing the attitude motion of UniSat-6 lies in the dual possibility, for future missions, of:controlling the direction of ejection of the on-board carried satelliteshaving an accurate pointing for remote sensing operation.The reconstruction of the attitude motion of UniSat-6 is based on the data of the on-board Commercial Off The Shelf (COTS) gyros and magnetometers, downloaded at the passages over the ground station in Roma, Italy. At ground, these data have been processed with the UnScented QUaternion Estimator (USQUE) algorithm. This estimator is an adaptation of the Unscented Filter to the problem of spacecraft attitude estimation. The USQUE is based on a dual attitude representation, which involves both quaternions and Generalized Rodrigues Parameters. In this work, the propagation phase of the algorithm contains only a kinematic model of the motion of the spacecraft. This paper presents the results of the reconstruction of the UniSat-6 attitude using on-board measurements. The results show that the spacecraft effectively stabilized its attitude motion thanks to the on-board magnetic devices

Model Prediction-Based Approach to Fault Tolerant Control with Applications

Abstract— Fault-tolerant control (FTC) is an integral component in industrial processes as it enables the system to continue robust operation under some conditions. In this paper, an FTC scheme is proposed for interconnected systems within an integrated design framework to yield a timely monitoring and detection of fault and reconfiguring the controller according to those faults. The unscented Kalman filter (UKF)-based fault detection and diagnosis system is initially run on the main plant and parameter estimation is being done for the local faults. This critical information\ud is shared through information fusion to the main system where the whole system is being decentralized using the overlapping decomposition technique. Using this parameter estimates of decentralized subsystems, a model predictive control (MPC) adjusts its parameters according to the\ud fault scenarios thereby striving to maintain the stability of the system. Experimental results on interconnected continuous time stirred tank reactors (CSTR) with recycle and quadruple tank system indicate that the proposed method is capable to correctly identify various faults, and then controlling the system under some conditions