A robust iterative learning control for continuous-time nonlinear systems with disturbances

In this paper, we study the trajectory tracking problem using iterative learning control for continuous-time nonlinear systems with a generic fixed relative degree in the presence of disturbances. This class of controllers iteratively refine the control input relying on the tracking error of the previous trials and some properly tuned learning gains. Sufficient conditions on these gains guarantee the monotonic convergence of the iterative process. However, the choice of the gains is heuristically hand-tuned given an approximated system model and no information on the disturbances. Thus, in the cases of inaccurate knowledge of the model or iteration-varying measurement errors, external disturbances, and delays, the convergence condition is unlikely to be verified at every iteration. To overcome this issue, we propose a robust convergence condition, which ensures the applicability of the pure feedforward control even if other classical conditions are not fulfilled for some trials due to the presence of disturbances. Furthermore, we quantify the upper bound of the nonrepetitive disturbance that the iterative algorithm is able to handle. Finally, we validate the convergence condition simulating the dynamics of a two degrees of freedom underactuated arm with elastic joints, where one is active, and the other is passive, and a Franka Emika Panda manipulator

Active Sensing as Bayes-Optimal Sequential Decision Making

Sensory inference under conditions of uncertainty is a major problem in both machine learning and computational neuroscience. An important but poorly understood aspect of sensory processing is the role of active sensing. Here, we present a Bayes-optimal inference and control framework for active sensing, C-DAC (Context-Dependent Active Controller). Unlike previously proposed algorithms that optimize abstract statistical objectives such as information maximization (Infomax) [Butko & Movellan, 2010] or one-step look-ahead accuracy [Najemnik & Geisler, 2005], our active sensing model directly minimizes a combination of behavioral costs, such as temporal delay, response error, and effort. We simulate these algorithms on a simple visual search task to illustrate scenarios in which context-sensitivity is particularly beneficial and optimization with respect to generic statistical objectives particularly inadequate. Motivated by the geometric properties of the C-DAC policy, we present both parametric and non-parametric approximations, which retain context-sensitivity while significantly reducing computational complexity. These approximations enable us to investigate the more complex problem involving peripheral vision, and we notice that the difference between C-DAC and statistical policies becomes even more evident in this scenario.Comment: Scheduled to appear in UAI 201

Performance Improvement of Low-Cost Iterative Learning-Based Fuzzy Control Systems for Tower Crane Systems

This paper is dedicated to the memory of Prof. Ioan Dzitac, one of the fathers of this journal and its founding Editor-in-Chief till 2021. The paper addresses the performance improvement of three Single Input-Single Output (SISO) fuzzy control systems that control separately the positions of interest of tower crane systems, namely the cart position, the arm angular position and the payload position. Three separate low-cost SISO fuzzy controllers are employed in terms of first order discrete-time intelligent Proportional-Integral (PI) controllers with Takagi-Sugeno-Kang Proportional-Derivative (PD) fuzzy terms. Iterative Learning Control (ILC) system structures with PD learning functions are involved in the current iteration SISO ILC structures. Optimization problems are defined in order to tune the parameters of the learning functions. The objective functions are defined as the sums of squared control errors, and they are solved in the iteration domain using the recent metaheuristic Slime Mould Algorithm (SMA). The experimental results prove the performance improvement of the SISO control systems after ten iterations of SMA

A Low-Cost Robust Distributed Linearly Constrained Beamformer for Wireless Acoustic Sensor Networks with Arbitrary Topology

We propose a new robust distributed linearly constrained beamformer which utilizes a set of linear equality constraints to reduce the cross power spectral density matrix to a block-diagonal form. The proposed beamformer has a convenient objective function for use in arbitrary distributed network topologies while having identical performance to a centralized implementation. Moreover, the new optimization problem is robust to relative acoustic transfer function (RATF) estimation errors and to target activity detection (TAD) errors. Two variants of the proposed beamformer are presented and evaluated in the context of multi-microphone speech enhancement in a wireless acoustic sensor network, and are compared with other state-of-the-art distributed beamformers in terms of communication costs and robustness to RATF estimation errors and TAD errors

Relaxing Fundamental Assumptions in Iterative Learning Control

Iterative learning control (ILC) is perhaps best decribed as an open loop feedforward control technique where the feedforward signal is learned through repetition of a single task. As the name suggests, given a dynamic system operating on a finite time horizon with the same desired trajectory, ILC aims to iteratively construct the inverse image (or its approximation) of the desired trajectory to improve transient tracking. In the literature, ILC is often interpreted as feedback control in the iteration domain due to the fact that learning controllers use information from past trials to drive the tracking error towards zero. However, despite the significant body of literature and powerful features, ILC is yet to reach widespread adoption by the control community, due to several assumptions that restrict its generality when compared to feedback control. In this dissertation, we relax some of these assumptions, mainly the fundamental invariance assumption, and move from the idea of learning through repetition to two dimensional systems, specifically repetitive processes, that appear in the modeling of engineering applications such as additive manufacturing, and sketch out future research directions for increased practicality: We develop an L1 adaptive feedback control based ILC architecture for increased robustness, fast convergence, and high performance under time varying uncertainties and disturbances. Simulation studies of the behavior of this combined L1-ILC scheme under iteration varying uncertainties lead us to the robust stability analysis of iteration varying systems, where we show that these systems are guaranteed to be stable when the ILC update laws are designed to be robust, which can be done using existing methods from the literature. As a next step to the signal space approach adopted in the analysis of iteration varying systems, we shift the focus of our work to repetitive processes, and show that the exponential stability of a nonlinear repetitive system is equivalent to that of its linearization, and consequently uniform stability of the corresponding state space matrix.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133232/1/altin_1.pd