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Moving horizon estimation (MHE) is a widely studied state estimation approach in several practical applications. In the MHE problem, the state estimates are obtained via the solution of an approximated nonlinear optimization problem. However, this optimization step is known to be computationally complex. Given this limitation, this paper investigates the idea of iteratively preconditioned gradient-descent (IPG) to solve MHE problem with the aim of an improved performance than the existing solution techniques. To our knowledge, the preconditioning technique is used for the first time in this paper to reduce the computational cost and accelerate the crucial optimization step for MHE. The convergence guarantee of the proposed iterative approach for a class of MHE problems is presented. Additionally, sufficient conditions for the MHE problem to be convex are also derived. Finally, the proposed method is implemented on a unicycle localization example. The simulation results demonstrate that the proposed approach can achieve better accuracy with reduced computational costs.

Adaptive gradient methods have become popular in optimizing deep neural networks; recent examples include AdaGrad and Adam. Although Adam usually converges faster, variations of Adam, for instance, the AdaBelief algorithm, have been proposed to enhance Adam's poor generalization ability compared to the classical stochastic gradient method. This paper develops a generic framework for adaptive gradient methods that solve non-convex optimization problems. We first model the adaptive gradient methods in a state-space framework, which allows us to present simpler convergence proofs of adaptive optimizers such as AdaGrad, Adam, and AdaBelief. We then utilize the transfer function paradigm from classical control theory to propose a new variant of Adam, coined AdamSSM. We add an appropriate pole-zero pair in the transfer function from squared gradients to the second moment estimate. We prove the convergence of the proposed AdamSSM algorithm. Applications on benchmark machine learning tasks of image classification using CNN architectures and language modeling using LSTM architecture demonstrate that the AdamSSM algorithm improves the gap between generalization accuracy and faster convergence than the recent adaptive gradient methods.

Empirical experiences have shown that simultaneous (rather than conventional sequential) plant and controller design procedure leads to an improvement in performance and saving of plant resources. Such a simultaneous synthesis procedure is called as "co-design". In this letter we study the co-design problem for a class of Lipschitz nonlinear dynamical systems having a quadratic control objective and state-feedback controller. We propose a novel time independent reformulation of the co-design optimization problem whose constraints ensure stability of the system. We also present a gradient-based co-design solution procedure which involves system coordinate transformation and whose output is provably stable solution for the original system. We show the efficacy of the solution procedure through co-design of a single-link robot.

This paper considers the multi-agent distributed linear least-squares problem. The system comprises multiple agents, each agent with a locally observed set of data points, and a common server with whom the agents can interact. The agents' goal is to compute a linear model that best fits the collective data points observed by all the agents. In the server-based distributed settings, the server cannot access the data points held by the agents. The recently proposed Iteratively Pre-conditioned Gradient-descent (IPG) method has been shown to converge faster than other existing distributed algorithms that solve this problem. In the IPG algorithm, the server and the agents perform numerous iterative computations. Each of these iterations relies on the entire batch of data points observed by the agents for updating the current estimate of the solution. Here, we extend the idea of iterative pre-conditioning to the stochastic settings, where the server updates the estimate and the iterative pre-conditioning matrix based on a single randomly selected data point at every iteration. We show that our proposed Iteratively Pre-conditioned Stochastic Gradient-descent (IPSG) method converges linearly in expectation to a proximity of the solution. Importantly, we empirically show that the proposed IPSG method's convergence rate compares favorably to prominent stochastic algorithms for solving the linear least-squares problem in server-based networks., Changes in the replacement: Application to distributed state estimation problem has been added in Appendix B. Related articles: arXiv:2003.07180v2 [math.OC] and arXiv:2008.02856v1 [math.OC]

We present a distributed average consensus protocol that preserves the privacy of agents' inputs. Unlike the differential privacy mechanisms, the presented protocol does not affect the accuracy of the output. It is shown that the protocol preserves the information-theoretic privacy of the agents' inputs against colluding passive adversarial (or honest-but-curious) agents in the network, if the adversarial agents do not constitute a vertex cut in the underlying communication network. This implies that we can guarantee information-theoretic privacy of all the honest agents' inputs against $t$ arbitrary colluding passive adversarial agents if the network is $(t+1)$-connected. The protocol is constructed by composing a distributed privacy mechanism that we propose with any (non-private) distributed average consensus algorithm., Related to the prior work (1) Gupta, Nirupam, Jonathan Kat, and Nikhil Chopra. "Statistical Privacy in Distributed Average Consensus on Bounded Real Inputs." 2019 IEEE American Control Conference, and (2) Gupta, Nirupam, Jonathan Katz, and Nikhil Chopra. "Privacy in distributed average consensus." IFAC-PapersOnLine 2017. Comprises 7 pages (two-column format), and 3 figures

International audience; In this paper, we present a quadrotor formation control, whose simplified dynamics is represented by integrators in cascade. A system transformation is presented that reduces the input-output behavior of a chain of integrators into a single integrator. Therefore the standard coordination control algorithms can be directly applied. A second strategy is proposed consisting in transforming the chain of integrators into an SPR system and then an algorithm is proposed for the formation control of SPR systems. The proposed algorithm is illustrated in simulation.

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