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In this paper, a Bayesian inference problem is set up to infer the time delay and the resistance models from the dynamics of a connected automated vehicle. The delayed rejection adaptive Metropolis Markov chain Monte Carlo method is applied to obtain the posterior distributions of time delay and resistance parameters simultaneously using experimental data. The estimations of the time delay are shown to be consistent among multiple datasets and different resistance models. The distribution of the posterior indicates that there exist multiple modes in time delay, corresponding to different behaviors in acceleration and deceleration.

Integration-based Gaussian filters such as un-scented, cubature, and Gauss-Hermite filters are effective ways to assimilate data and models within nonlinear systems. Traditionally, these filters have only been applicable for systems with a handful of states due to stability and scalability issues. In this paper, we present a new integration method for scaling quadrature-based filters to higher dimensions. Our approach begins by decomposing the dynamics and observation models into separated, low-rank tensor formats. Once in low-rank tensor format, adaptive integration techniques may be used to efficiently propagate the mean and covariance of the distribution of the system state with computational complexity that is polynomial in dimension and rank. Simulation results are shown on nonlinear chaotic systems with 20 state variables.

© 2018 AACC. Zero-sum differential games constitute a prominent research topic in several fields ranging from economics to motion planning. Unfortunately, analytical techniques for differential games can address only simple, illustrative problem instances, and most existing computational methods suffer from the curse of dimensionality, i.e., the computational requirements grow exponentially with the dimensionality of the state space. In order to alleviate the curse of dimensionality for a certain class of two-player pursuit-evasion games, we propose a novel dynamic-programming-based algorithm that uses a continuous tensor-train approximation to represent the value function. In this way, the algorithm can represent high-dimensional tensors using computational resources that grow only polynomially with dimensionality of the state space and with the rank of the value function. The proposed algorithm is shown to converge to optimal solutions. It is demonstrated in several problem instances; in case of a seven-dimensional game, the value function representation was obtained with seven orders of magnitude savings in computational and memory cost, when compared to standard value iteration.

© 2017 IEEE. Integration-based Gaussian filters such as un-scented, cubature, and Gauss-Hermite filters are effective ways to assimilate data and models within nonlinear systems. Traditionally, these filters have only been applicable for systems with a handful of states due to stability and scalability issues. In this paper, we present a new integration method for scaling quadrature-based filters to higher dimensions. Our approach begins by decomposing the dynamics and observation models into separated, low-rank tensor formats. Once in low-rank tensor format, adaptive integration techniques may be used to efficiently propagate the mean and covariance of the distribution of the system state with computational complexity that is polynomial in dimension and rank. Simulation results are shown on nonlinear chaotic systems with 20 state variables.

We develop new approximation algorithms and data structures for representing and computing with multivariate functions using the functional tensor-train (FT), a continuous extension of the tensor-train (TT) decomposition. The FT represents functions using a tensor-train ansatz by replacing the three-dimensional TT cores with univariate matrix-valued functions. The main contribution of this paper is a framework to compute the FT that employs adaptive approximations of univariate fibers, and that is not tied to any tensorized discretization. The algorithm can be coupled with any univariate linear or nonlinear approximation procedure. We demonstrate that this approach can generate multivariate function approximations that are several orders of magnitude more accurate, for the same cost, than those based on the conventional approach of compressing the coefficient tensor of a tensor-product basis. Our approach is in the spirit of other continuous computation packages such as Chebfun, and yields an algorithm which requires the computation of “continuous” matrix factorizations such as the LU and QR decompositions of vector-valued functions. To support these developments, we describe continuous versions of an approximate maximum-volume cross approximation algorithm and of a rounding algorithm that re-approximates an FT by one of lower ranks. We demonstrate that our technique improves accuracy and robustness, compared to TT and quantics-TT approaches with fixed parameterizations, of high-dimensional integration, differentiation, and approximation of functions with local features such as discontinuities and other nonlinearities. ©2018, National Science Foundation (Grant IIS-1452019), US Department of Energy, Office of Advanced Scientific Computing Research (Award no. DE-SC0007099)

Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately, most existing algorithms that guarantee convergence to optimal solutions suffer from the curse of dimensionality: the run time of the algorithm grows exponentially with the dimension of the state space of the system. We propose novel dynamic programming algorithms that alleviate the curse of dimensionality in problems that exhibit certain low-rank structure. The proposed algorithms are based on continuous tensor decompositions recently developed by the authors. Essentially, the algorithms represent high-dimensional functions (e.g. the value function) in a compressed format, and directly perform dynamic programming computations (e.g. value iteration, policy iteration) in this format. Under certain technical assumptions, the new algorithms guarantee convergence towards optimal solutions with arbitrary precision. Furthermore, the run times of the new algorithms scale polynomially with the state dimension and polynomially with the ranks of the value function. This approach realizes substantial computational savings in “compressible” problem instances, where value functions admit low-rank approximations. We demonstrate the new algorithms in a wide range of problems, including a simulated six-dimensional agile quadcopter maneuvering example and a seven-dimensional aircraft perching example. In some of these examples, we estimate computational savings of up to 10 orders of magnitude over standard value iteration algorithms. We further demonstrate the algorithms running in real time on board a quadcopter during a flight experiment under motion capture. Keywords: Stochastic optimal control; motion planning; dynamic programming; tensor decompositions, National Science Foundation (U.S.) (Grant IIS-1452019), United States. Department of Energy (Award DE-SC0007099)