Optimal input design for non-linear dynamic systems: a graph theory approach

In this article a new algorithm for the design of stationary input sequences for system identification is presented. The stationary input signal is generated by optimizing an approximation of a scalar function of the information matrix, based on stationary input sequences generated from prime cycles, which describe the set of finite Markov chains of a given order. This method can be used for solving input design problems for nonlinear systems. In particular it can handle amplitude constraints on the input. Numerical examples show that the new algorithm is computationally attractive and that is consistent with previously reported results.Comment: 6 pages, 6 figures. Accepted for publication in the 52nd IEEE Conference on Decision and Control, Florence, Italy (CDC 2013

Optimal Experiment Design in Nonlinear Parameter Estimation with Exact Confidence Regions

A model-based optimal experiment design (OED) of nonlinear systems is studied. OED represents a methodology for optimizing the geometry of the parametric joint-confidence regions (CRs), which are obtained in an a posteriori analysis of the least-squares parameter estimates. The optimal design is achieved by using the available (experimental) degrees of freedom such that more informative measurements are obtained. Unlike the commonly used approaches, which base the OED procedure upon the linearized CRs, we explore a path where we explicitly consider the exact CRs in the OED framework. We use a methodology for a finite parametrization of the exact CRs within the OED problem and we introduce a novel approximation technique of the exact CRs using inner- and outer-approximating ellipsoids as a computationally less demanding alternative. The employed techniques give the OED problem as a finite-dimensional mathematical program of bilevel nature. We use two small-scale illustrative case studies to study various OED criteria and compare the resulting optimal designs with the commonly used linearization-based approach. We also assess the performance of two simple heuristic numerical schemes for bilevel optimization within the studied problems.Comment: 12 pages, 9 figure

A robust extended H-infinity filtering approach to multi-robot cooperative localization in dynamic indoor environments

Multi-robot cooperative localization serves as an essential task for a team of mobile robots to work within an unknown environment. Based on the real-time laser scanning data interaction, a robust approach is proposed to obtain optimal multi-robot relative observations using the Metric-based Iterative Closest Point (MbICP) algorithm, which makes it possible to utilize the surrounding environment information directly instead of placing a localization-mark on the robots. To meet the demand of dealing with the inherent non-linearities existing in the multi-robot kinematic models and the relative observations, a robust extended H∞ filtering (REHF) approach is developed for the multi-robot cooperative localization system, which could handle non-Gaussian process and measurement noises with respect to robot navigation in unknown dynamic scenes. Compared with the conventional multi-robot localization system using extended Kalman filtering (EKF) approach, the proposed filtering algorithm is capable of providing superior performance in a dynamic indoor environment with outlier disturbances. Both numerical experiments and experiments conducted for the Pioneer3-DX robots show that the proposed localization scheme is effective in improving both the accuracy and reliability of the performance within a complex environment.This work was supported inpart by the National Natural Science Foundation of China under grants 61075094, 61035005 and 61134009

On Robust Computation of Koopman Operator and Prediction in Random Dynamical Systems

In the paper, we consider the problem of robust approximation of transfer Koopman and Perron-Frobenius (P-F) operators from noisy time series data. In most applications, the time-series data obtained from simulation or experiment is corrupted with either measurement or process noise or both. The existing results show the applicability of algorithms developed for the finite dimensional approximation of deterministic system to a random uncertain case. However, these results hold true only in asymptotic and under the assumption of infinite data set. In practice the data set is finite, and hence it is important to develop algorithms that explicitly account for the presence of uncertainty in data-set. We propose a robust optimization-based framework for the robust approximation of the transfer operators, where the uncertainty in data-set is treated as deterministic norm bounded uncertainty. The robust optimization leads to a min-max type optimization problem for the approximation of transfer operators. This robust optimization problem is shown to be equivalent to regularized least square problem. This equivalence between robust optimization problem and regularized least square problem allows us to comment on various interesting properties of the obtained solution using robust optimization. In particular, the robust optimization formulation captures inherent tradeoffs between the quality of approximation and complexity of approximation. These tradeoffs are necessary to balance for the proposed application of transfer operators, for the design of optimal predictor. Simulation results demonstrate that our proposed robust approximation algorithm performs better than the Extended Dynamic Mode Decomposition (EDMD) and DMD algorithms for a system with process and measurement noise.Comment: arXiv admin note: text overlap with arXiv:1803.0855

A Near-Optimal Separation Principle for Nonlinear Stochastic Systems Arising in Robotic Path Planning and Control

We consider nonlinear stochastic systems that arise in path planning and control of mobile robots. As is typical of almost all nonlinear stochastic systems, the optimally solving problem is intractable. We provide a design approach which yields a tractable design that is quantifiably near-optimal. We exhibit a "separation" principle under a small noise assumption consisting of the optimal open-loop design of nominal trajectory followed by an optimal feedback law to track this trajectory, which is different from the usual effort of separating estimation from control. As a corollary, we obtain a trajectory-optimized linear quadratic regulator design for stochastic nonlinear systems with Gaussian noise.Comment: 7 pages, 4 Figures, Submitted to 56th IEEE Conference on Decision and Control (CDC), 201

Minimax Iterative Dynamic Game: Application to Nonlinear Robot Control Tasks

Multistage decision policies provide useful control strategies in high-dimensional state spaces, particularly in complex control tasks. However, they exhibit weak performance guarantees in the presence of disturbance, model mismatch, or model uncertainties. This brittleness limits their use in high-risk scenarios. We present how to quantify the sensitivity of such policies in order to inform of their robustness capacity. We also propose a minimax iterative dynamic game framework for designing robust policies in the presence of disturbance/uncertainties. We test the quantification hypothesis on a carefully designed deep neural network policy; we then pose a minimax iterative dynamic game (iDG) framework for improving policy robustness in the presence of adversarial disturbances. We evaluate our iDG framework on a mecanum-wheeled robot, whose goal is to find a ocally robust optimal multistage policy that achieve a given goal-reaching task. The algorithm is simple and adaptable for designing meta-learning/deep policies that are robust against disturbances, model mismatch, or model uncertainties, up to a disturbance bound. Videos of the results are on the author's website, http://ecs.utdallas.edu/~opo140030/iros18/iros2018.html, while the codes for reproducing our experiments are on github, https://github.com/lakehanne/youbot/tree/rilqg. A self-contained environment for reproducing our results is on docker, https://hub.docker.com/r/lakehanne/youbotbuntu14/Comment: 2018 International Conference on Intelligent Robots and System

PLD-Based Reconfigurable Controllers for Feedback Systems

Recently, interest has grown for application of reconfigurable devices in robust and adaptive control systems. The main advantage of such devices is that its structure is not fixed and may be varied depending on the currently used control algorithm. In this paper a new PC-based reconfigurable microcontrollers (RMC) are offered for Experimental Physics control systems.Comment: Poster, ICALEPCS2001 PSN#WEAP05

Ergodic Exploration of Distributed Information

This paper presents an active search trajectory synthesis technique for autonomous mobile robots with nonlinear measurements and dynamics. The presented approach uses the ergodicity of a planned trajectory with respect to an expected information density map to close the loop during search. The ergodic control algorithm does not rely on discretization of the search or action spaces, and is well posed for coverage with respect to the expected information density whether the information is diffuse or localized, thus trading off between exploration and exploitation in a single objective function. As a demonstration, we use a robotic electrolocation platform to estimate location and size parameters describing static targets in an underwater environment. Our results demonstrate that the ergodic exploration of distributed information (EEDI) algorithm outperforms commonly used information-oriented controllers, particularly when distractions are present.Comment: 17 page

Particle-based Gaussian process optimization for input design in nonlinear dynamical models

We propose a novel approach to input design for identification of nonlinear state space models. The optimal input sequence is obtained by maximizing a scalar cost function of the Fisher information matrix. Since the Fisher information matrix is unavailable in closed form, it is estimated using particle methods. In addition, we make use of Gaussian process optimization to find the optimal input and to mitigate the problem of a large computational cost incurred by the particle filter, as the method reduces the number of functional evaluations. Numerical examples are provided to illustrate the performance of the resulting algorithm.Comment: 6 pages, 3 figure

The inverted Pendulum: A fundamental Benchmark in Control Theory and Robotics

For at least fifty years, the inverted pendulum has been the most popular benchmark, among others, for teaching and researches in control theory and robotics. This paper presents the key motivations for the use of that system and explains, in details, the main reflections on how the inverted pendulum benchmark gives an effective and efficient application. Several real experiences, virtual models and web-based remote control laboratories will be presented with emphasis on the practical design implementation of this system. A bibliographical survey of different design control approaches and trendy robotic problems will be presented through applications to the inverted pendulum system. In total, 150 references in the open literature, dating back to 1960, are compiled to provide an overall picture of historical, current and challenging developments.Comment: IEEE International Conference on Education and e-Learning Innovations (ICEELI), 1-3 July 2012, Sousse, Tunisi