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This paper investigates the existence of a separation principle between model identification and control design in the context of model predictive control. First, we elucidate that the separation principle holds asymptotically in the number of data in a Fisherian setting, and universally in a Bayesian setting. Then, by formulating model predictive control within a Gaussian regression framework, we describe how the Bayesian separation principle can be used to derive explicit, uncertainty-aware expressions for the control cost and optimal input sequence, thereby bridging direct and indirect data-driven approaches., Comment: 13 pages, 1 figure

This report describes our proposed solution for the second AI Olympics competition held at IROS 2024. Our solution is based on a recent Model-Based Reinforcement Learning algorithm named MC-PILCO. Besides briefly reviewing the algorithm, we discuss the most critical aspects of the MC-PILCO implementation in the tasks at hand.

In the following report, we describe the solution we propose for the AI Olympics competition held at IROS 2024. Our solution is based on a Model-free Deep Reinforcement Learning approach combined with an evolutionary strategy. We will briefly describe the algorithms that have been used and then provide details of the approach

The ability to achieve precise and smooth trajectory tracking is crucial for ensuring the successful execution of various tasks involving robotic manipulators. State-of-the-art techniques require accurate mathematical models of the robot dynamics, and robustness to model uncertainties is achieved by relying on precise bounds on the model mismatch. In this paper, we propose a novel adaptive robust feedback linearization scheme able to compensate for model uncertainties without any a-priori knowledge on them, and we provide a theoretical proof of convergence under mild assumptions. We evaluate the method on a simulated RR robot. First, we consider a nominal model with known model mismatch, which allows us to compare our strategy with state-of-the-art uncertainty-aware methods. Second, we implement the proposed control law in combination with a learned model, for which uncertainty bounds are not available. Results show that our method leads to performance comparable to uncertainty-aware methods while requiring less prior knowledge.

Multi-agent systems are increasingly widespread in a range of application domains, with optimization and learning underpinning many of the tasks that arise in this context. Different approaches have been proposed to enable the cooperative solution of these optimization and learning problems, including first- and second-order methods, and dual (or Lagrangian) methods, all of which rely on consensus and message-passing. In this article we discuss these algorithms through the lens of non-expansive operator theory, providing a unifying perspective. We highlight the insights that this viewpoint delivers, and discuss how it can spark future original research.

Accurate dynamic models are crucial for many robotic applications. Traditional approaches to deriving these models are based on the application of Lagrangian or Newtonian mechanics. Although these methods provide a good insight into the physical behaviour of the system, they rely on the exact knowledge of parameters such as inertia, friction and joint flexibility. In addition, the system is often affected by uncertain and nonlinear effects, such as saturation and dead zones, which can be difficult to model. A popular alternative is the application of Machine Learning (ML) techniques - e.g., Neural Networks (NNs) - in the context of a "black-box" methodology. This paper reports on our experience with this approach for a real-life 6 degrees of freedom (DoF) manipulator. Specifically, we considered several NN architectures: single NN, multiple NNs, and cascade NN. We compared the performance of the system by using different policies for selecting the NN hyperparameters. Our experiments reveal that the best accuracy and performance are obtained by a cascade NN, in which we encode our prior physical knowledge about the dependencies between joints, complemented by an appropriate optimisation of the hyperparameters., Comment: 6 pages, 5 figures, submitted to CASE 2024

Continuous control Deep Reinforcement Learning (RL) approaches are known to suffer from estimation biases, leading to suboptimal policies. This paper introduces innovative methods in RL, focusing on addressing and exploiting estimation biases in Actor-Critic methods for continuous control tasks, using Deep Double Q-Learning. We design a Bias Exploiting (BE) mechanism to dynamically select the most advantageous estimation bias during training of the RL agent. Most State-of-the-art Deep RL algorithms can be equipped with the BE mechanism, without hindering performance or computational complexity. Our extensive experiments across various continuous control tasks demonstrate the effectiveness of our approaches. We show that RL algorithms equipped with this method can match or surpass their counterparts, particularly in environments where estimation biases significantly impact learning. The results underline the importance of bias exploitation in improving policy learning in RL.

Learning the inverse dynamics of robots directly from data, adopting a black-box approach, is interesting for several real-world scenarios where limited knowledge about the system is available. In this paper, we propose a black-box model based on Gaussian Process (GP) Regression for the identification of the inverse dynamics of robotic manipulators. The proposed model relies on a novel multidimensional kernel, called \textit{Lagrangian Inspired Polynomial} (\kernelInitials{}) kernel. The \kernelInitials{} kernel is based on two main ideas. First, instead of directly modeling the inverse dynamics components, we model as GPs the kinetic and potential energy of the system. The GP prior on the inverse dynamics components is derived from those on the energies by applying the properties of GPs under linear operators. Second, as regards the energy prior definition, we prove a polynomial structure of the kinetic and potential energy, and we derive a polynomial kernel that encodes this property. As a consequence, the proposed model allows also to estimate the kinetic and potential energy without requiring any label on these quantities. Results on simulation and on two real robotic manipulators, namely a 7 DOF Franka Emika Panda, and a 6 DOF MELFA RV4FL, show that the proposed model outperforms state-of-the-art black-box estimators based both on Gaussian Processes and Neural Networks in terms of accuracy, generality and data efficiency. The experiments on the MELFA robot also demonstrate that our approach achieves performance comparable to fine-tuned model-based estimators, despite requiring less prior information.

In this paper we focus on the solution of online problems with time-varying, linear equality and inequality constraints. Our approach is to design a novel online algorithm by leveraging the tools of control theory. In particular, for the case of equality constraints only, using robust control we design an online algorithm with asymptotic convergence to the optimal trajectory, differently from the alternatives that achieve non-zero tracking error. When also inequality constraints are present, we show how to modify the proposed algorithm to account for the wind-up induced by the nonnegativity constraints on the dual variables. We report numerical results that corroborate the theoretical analysis, and show how the proposed approach outperforms state-of-the-art algorithms both with equality and inequality constraints.

In this paper, we propose a novel distributed algorithm for consensus optimization over networks and a robust extension tailored to deal with asynchronous agents and packet losses. Indeed, to robustly achieve dynamic consensus on the solution estimates and the global descent direction, we embed in our algorithms a distributed implementation of the Alternating Direction Method of Multipliers (ADMM). Such a mechanism is suitably interlaced with a local proportional action steering each agent estimate to the solution of the original consensus optimization problem. First, in the case of ideal networks, by using tools from system theory, we prove the linear convergence of the scheme with strongly convex costs. Then, by exploiting the averaging theory, we extend such a first result to prove that the robust extension of our method preserves linear convergence in the case of asynchronous agents and packet losses. Further, by using the notion of Input-to-State Stability, we also guarantee the robustness of the schemes with respect to additional, generic errors affecting the agents' updates. Finally, some numerical simulations confirm our theoretical findings and compare our algorithms with other distributed schemes in terms of speed and robustness.

In this paper, we propose to estimate the forward dynamics equations of mechanical systems by learning a model of the inverse dynamics and estimating individual dynamics components from it. We revisit the classical formulation of rigid body dynamics in order to extrapolate the physical dynamical components, such as inertial and gravitational components, from an inverse dynamics model. After estimating the dynamical components, the forward dynamics can be computed in closed form as a function of the learned inverse dynamics. We tested the proposed method with several machine learning models based on Gaussian Process Regression and compared them with the standard approach of learning the forward dynamics directly. Results on two simulated robotic manipulators, a PANDA Franka Emika and a UR10, show the effectiveness of the proposed method in learning the forward dynamics, both in terms of accuracy as well as in opening the possibility of using more structured~models.

We propose a Model-Based Reinforcement Learning (MBRL) algorithm named VF-MC-PILCO, specifically designed for application to mechanical systems where velocities cannot be directly measured. This circumstance, if not adequately considered, can compromise the success of MBRL approaches. To cope with this problem, we define a velocity-free state formulation which consists of the collection of past positions and inputs. Then, VF-MC-PILCO uses Gaussian Process Regression to model the dynamics of the velocity-free state and optimizes the control policy through a particle-based policy gradient approach. We compare VF-MC-PILCO with our previous MBRL algorithm, MC-PILCO4PMS, which handles the lack of direct velocity measurements by modeling the presence of velocity estimators. Results on both simulated (cart-pole and UR5 robot) and real mechanical systems (Furuta pendulum and a ball-and-plate rig) show that the two algorithms achieve similar results. Conveniently, VF-MC-PILCO does not require the design and implementation of state estimators, which can be a challenging and time-consuming activity to be performed by an expert user., Comment: Accepted at the 2023 American Control Conference (ACC)

In this paper we propose a model-based approach to the design of online optimization algorithms, with the goal of improving the tracking of the solution trajectory (trajectories) w.r.t. state-of-the-art methods. We focus first on quadratic problems with a time-varying linear term, and use digital control tools (a robust internal model principle) to propose a novel online algorithm that can achieve zero tracking error by modeling the cost with a dynamical system. We prove the convergence of the algorithm for both strongly convex and convex problems. We further discuss the sensitivity of the proposed method to model uncertainties and quantify its performance. We discuss how the proposed algorithm can be applied to general (non-quadratic) problems using an approximate model of the cost, and analyze the convergence leveraging the small gain theorem. We present numerical results that showcase the superior performance of the proposed algorithms over previous methods for both quadratic and non-quadratic problems.

In this work we consider the problem of mobile robots that need to manipulate/transport an object via cables or robotic arms. We consider the scenario where the number of manipulating robots is redundant, i.e. a desired object configuration can be obtained by different configurations of the robots. The objective of this work is to show that communication can be used to implement cooperative local feedback controllers in the robots to improve disturbance rejection and reduce structural stress in the object. In particular we consider the realistic scenario where measurements are sampled and transmitted over wireless, and the sampling period is comparable with the system dynamics time constants. We first propose a kinematic model which is consistent with the overall systems dynamics under high-gain control and then we provide sufficient conditions for the exponential stability and monotonic decrease of the configuration error under different norms. Finally, we test the proposed controllers on the full dynamical systems showing the benefit of local communication., Comment: 8 pages, 6 figures

In this paper, we propose an inverse-kinematics controller for a class of multi-robot systems in the scenario of sampled communication. The goal is to make a group of robots perform trajectory tracking in a coordinated way when the sampling time of communications is much larger than the sampling time of low-level controllers, disrupting theoretical convergence guarantees of standard control design in continuous time. Given a desired trajectory in configuration space which is precomputed offline, the proposed controller receives configuration measurements, possibly via wireless, to re-compute velocity references for the robots, which are tracked by a low-level controller. We propose joint design of a sampled proportional feedback plus a novel continuous-time feedforward that linearizes the dynamics around the reference trajectory: this method is amenable to distributed communication implementation where only one broadcast transmission is needed per sample. Also, we provide closed-form expressions for instability and stability regions and convergence rate in terms of proportional gain $k$ and sampling period $T$. We test the proposed control strategy via numerical simulations in the scenario of cooperative aerial manipulation of a cable-suspended load using a realistic simulator (Fly-Crane). Finally, we compare our proposed controller with centralized approaches that adapt the feedback gain online through smart heuristics, and show that it achieves comparable performance., Comment: 23 pages (main article: 14 pages; appendix: 9 pages), 18 figures; accepted for publication on Automatica; final accepted version

The energy sustainability of multi-access edge computing (MEC) platforms is here addressed by developing Energy-Aware job Scheduling at the Edge (EASE), a computing resource scheduler for edge servers co-powered by renewable energy resources and the power grid. The scenario under study involves the optimal allocation and migration of time-sensitive computing tasks in a resource-constrained internet of vehicles (IoV) context. This is achieved by tackling, as the main objective, the minimization of the carbon footprint of the edge network, whilst delivering adequate quality of service (QoS) to the end users (e.g., meeting task execution deadlines). EASE integrates i) a centralized optimization step, solved through model predictive control (MPC), to manage the renewable energy that is locally collected at the edge servers and their local computing resources, estimating their future availability, and ii) a distributed consensus step, solved via dual ascent in closed form, to reach agreement on service migrations. EASE is compared with four existing migration strategies. Quantitative results demonstrate its greater energy efficiency, which often gets close to complete carbon neutrality, while also improving the QoS., Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

This paper proposes a framework to study the convergence of stochastic optimization and learning algorithms. The framework is modeled over the different challenges that these algorithms pose, such as (i) the presence of random additive errors (e.g. due to stochastic gradients), and (ii) random coordinate updates (e.g. due to asynchrony in distributed set-ups). The paper covers both convex and strongly convex problems, and it also analyzes online scenarios, involving changes in the data and costs. The paper relies on interpreting stochastic algorithms as the iterated application of stochastic operators, thus allowing us to use the powerful tools of operator theory. In particular, we consider operators characterized by additive errors with sub-Weibull distribution (which parameterize a broad class of errors by their tail probability), and random updates. In this framework we derive convergence results in mean and in high probability, by providing bounds to the distance of the current iteration from a solution of the optimization or learning problem. The contributions are discussed in light of federated learning applications., Comment: To appear in IEEE Transactions on Automatic Control

In this paper, we consider the use of black-box Gaussian process (GP) models for trajectory tracking control based on feedback linearization, in the context of mechanical systems. We considered two strategies. The first computes the control input directly by using the GP model, whereas the second computes the input after estimating the individual components of the dynamics. We tested the two strategies on a simulated manipulator with seven degrees of freedom, also varying the GP kernel choice. Results show that the second implementation is more robust w.r.t. the kernel choice and model inaccuracies. Moreover, as regards the choice of kernel, the obtained performance shows that the use of a structured kernel, such as a polynomial kernel, is advantageous, because of its effectiveness with both strategies.

In this paper, we present a Model-Based Reinforcement Learning (MBRL) algorithm named \emph{Monte Carlo Probabilistic Inference for Learning COntrol} (MC-PILCO). The algorithm relies on Gaussian Processes (GPs) to model the system dynamics and on a Monte Carlo approach to estimate the policy gradient. This defines a framework in which we ablate the choice of the following components: (i) the selection of the cost function, (ii) the optimization of policies using dropout, (iii) an improved data efficiency through the use of structured kernels in the GP models. The combination of the aforementioned aspects affects dramatically the performance of MC-PILCO. Numerical comparisons in a simulated cart-pole environment show that MC-PILCO exhibits better data efficiency and control performance w.r.t. state-of-the-art GP-based MBRL algorithms. Finally, we apply MC-PILCO to real systems, considering in particular systems with partially measurable states. We discuss the importance of modeling both the measurement system and the state estimators during policy optimization. The effectiveness of the proposed solutions has been tested in simulation and on two real systems, a Furuta pendulum and a ball-and-plate rig., Comment: Accepted in IEEE Transactions on Robotics. MC-PILCO code is publicly available at https://www.merl.com/research/license/MC-PILCO

In this paper, we propose a Model-Based Reinforcement Learning (MBRL) algorithm for Partially Measurable Systems (PMS), i.e., systems where the state can not be directly measured, but must be estimated through proper state observers. The proposed algorithm, named Monte Carlo Probabilistic Inference for Learning COntrol for Partially Measurable Systems (MC-PILCO4PMS), relies on Gaussian Processes (GPs) to model the system dynamics, and on a Monte Carlo approach to update the policy parameters. W.r.t. previous GP-based MBRL algorithms, MC-PILCO4PMS models explicitly the presence of state observers during policy optimization, allowing to deal PMS. The effectiveness of the proposed algorithm has been tested both in simulation and in two real systems., Comment: Accepted to 3rd Robot Learning Workshop: Grounding Machine Learning Development in the Real World (NeurIPS 2020)

This paper introduces a dual-regularized ADMM approach to distributed, time-varying optimization. The proposed algorithm is designed in a prediction-correction framework, in which the computing nodes predict the future local costs based on past observations, and exploit this information to solve the time-varying problem more effectively. In order to guarantee linear convergence of the algorithm, a regularization is applied to the dual, yielding a dual-regularized ADMM. We analyze the convergence properties of the time-varying algorithm, as well as the regularization error of the dual-regularized ADMM. Numerical results show that in time-varying settings, despite the regularization error, the performance of the dual-regularized ADMM can outperform inexact gradient-based methods, as well as exact dual decomposition techniques, in terms of asymptotical error and consensus constraint violation., Comment: Presented at Asilomar Conference on Signals, Systems, and Computers 2020

In this paper, we focus on the solution of online optimization problems that arise often in signal processing and machine learning, in which we have access to streaming sources of data. We discuss algorithms for online optimization based on the prediction-correction paradigm, both in the primal and dual space. In particular, we leverage the typical regularized least-squares structure appearing in many signal processing problems to propose a novel and tailored prediction strategy, which we call extrapolation-based. By using tools from operator theory, we then analyze the convergence of the proposed methods as applied both to primal and dual problems, deriving an explicit bound for the tracking error, that is, the distance from the time-varying optimal solution. We further discuss the empirical performance of the algorithm when applied to signal processing, machine learning, and robotics problems., Comment: To be published in Elsevier Signal Processing

We consider the problem of PMU-based state estimation combining information coming from ubiquitous power demand time series and only a limited number of PMUs. Conversely to recent literature in which synchrophasor devices are often assumed perfectly synchronized with the Coordinated Universal Time (UTC), we explicitly consider the presence of time-synchronization errors in the measurements due to different non-ideal causes such as imperfect satellite localization and internal clock inaccuracy. We propose a recursive Kalman-based algorithm which allows for the explicit offline computation of the expected performance and for the real-time compensation of possible frequency mismatches among different PMUs. Based on the IEEE C37.118.1 standard on PMUs, we test the proposed solution and compare it with alternative approaches on both synthetic data from the IEEE 123 node standard distribution feeder and real-field data from a small medium voltage distribution feeder located inside the EPFL campus in Lausanne., Comment: 10 page, 7 figures

In this paper, we propose, discuss, and validate an online Nonlinear Model Predictive Control (NMPC) method for multi-rotor aerial systems with arbitrarily positioned and oriented rotors which simultaneously addresses the local reference trajectory planning and tracking problems. This work brings into question some common modeling and control design choices that are typically adopted to guarantee robustness and reliability but which may severely limit the attainable performance. Unlike most of state of the art works, the proposed method takes advantages of a unified nonlinear model which aims to describe the whole robot dynamics by explicitly including a realistic physical description of the actuator dynamics and limitations. As a matter of fact, our solution does not resort to common simplifications such as: 1) linear model approximation, 2) cascaded control paradigm used to decouple the translational and the rotational dynamics of the rigid body, 3) use of low-level reactive trackers for the stabilization of the internal loop, and 4) unconstrained optimization resolution or use of fictitious constraints. More in detail, we consider as control inputs the derivatives of the propeller forces and propose a novel method to suitably identify the actuator limitations by leveraging experimental data. Differently from previous approaches, the constraints of the optimization problem are defined only by the real physics of the actuators, avoiding conservative -- and often not physical -- input/state saturations which are present, e.g., in cascaded approaches. The control algorithm is implemented using a state-of-the-art Real Time Iteration (RTI) scheme with partial sensitivity update method. CONTINUES..., Comment: cs.RO cs.SY math.OC math.DS

Volterra series are especially useful for nonlinear system identification, also thanks to their capability to approximate a broad range of input-output maps. However, their identification from a finite set of data is hard, due to the curse of dimensionality. Recent approaches have shown how regularized kernel-based methods can be useful for this task. In this paper, we propose a new regularization network for Volterra models identification. It relies on a new kernel given by the product of basic building blocks. Each block contains some unknown parameters that can be estimated from data using marginal likelihood optimization. In comparison with other algorithms proposed in the literature, numerical experiments show that our approach allows to better select the monomials that really influence the system output, much increasing the prediction capability of the model.

In this paper, we introduce a novel data-driven inverse dynamics estimator based on Gaussian Process Regression. Driven by the fact that the inverse dynamics can be described as a polynomial function on a suitable input space, we propose the use of a novel kernel, called Geometrically Inspired Polynomial Kernel (GIP). The resulting estimator behaves similarly to model-based approaches as concerns data efficiency. Indeed, we proved that the GIP kernel defines a finite-dimensional Reproducing Kernel Hilbert Space that contains the inverse dynamics function computed through the Rigid Body Dynamics. The proposed kernel is based on the recently introduced Multiplicative Polynomial Kernel, a redefinition of the classical polynomial kernel equipped with a set of parameters that allows for a higher regularization. We tested the proposed approach in a simulated environment, and also in real experiments with a UR10 robot. The obtained results confirm that, compared to other data-driven estimators, the proposed approach is more data-efficient and exhibits better generalization properties. Instead, with respect to model-based estimators, our approach requires less prior information and is not affected by model bias.

In this paper we present a novel algorithm to solve the robot kinematic structure identification problem. Given a time series of data, typically obtained processing a set of visual observations, the proposed approach identifies the ordered sequence of links associated to the kinematic chain, the joint type interconnecting each couple of consecutive links, and the input signal influencing the relative motion. Compared to the state of the art, the proposed algorithm has reduced computational costs, and is able to identify also the joints' type sequence.

We address the solution of time-varying optimization problems characterized by the sum of a time-varying strongly convex function and a time-invariant nonsmooth convex function. We design an online algorithmic framework based on prediction-correction, which employs splitting methods to solve the sampled instances of the time-varying problem. We describe the prediction-correction scheme and two splitting methods, the forward-backward and the Douglas-Rachford. Then by using a result for generalized equations, we prove convergence of the generated sequence of approximate optimizers to a neighborhood of the optimal solution trajectory. Simulation results for a leader following formation in robotics assess the performance of the proposed algorithm., Comment: To be presented at the European Control Conference 2019

We present an algorithm for minimizing the sum of a strongly convex time-varying function with a time-invariant, convex, and nonsmooth function. The proposed algorithm employs the prediction-correction scheme alongside the forward-backward envelope, and we are able to prove the convergence of the solutions to a neighborhood of the optimizer that depends on the sampling time. Numerical simulations for a time-varying regression problem with elastic net regularization highlight the effectiveness of the algorithm., Comment: Full version of the paper to be presented at ICASSP'19

In this work we focus on the problem of minimizing the sum of convex cost functions in a distributed fashion over a peer-to-peer network. In particular, we are interested in the case in which communications between nodes are prone to failures and the agents are not synchronized among themselves. We address the problem proposing a modified version of the relaxed ADMM, which corresponds to the Peaceman-Rachford splitting method applied to the dual. By exploiting results from operator theory, we are able to prove the almost sure convergence of the proposed algorithm under general assumptions on the distribution of communication loss and node activation events. By further assuming the cost functions to be strongly convex, we prove the linear convergence of the algorithm in mean to a neighborhood of the optimal solution, and provide an upper bound to the convergence rate. Finally, we present numerical results testing the proposed method in different scenarios., Comment: To appear in IEEE Transactions on Automatic Control

In this work we address the problem of distributed optimization of the sum of convex cost functions in the context of multi-agent systems over lossy communication networks. Building upon operator theory, first, we derive an ADMM-like algorithm that we refer to as relaxed ADMM (R-ADMM) via a generalized Peaceman-Rachford Splitting operator on the Lagrange dual formulation of the original optimization problem. This specific algorithm depends on two parameters, namely the averaging coefficient $\alpha$ and the augmented Lagrangian coefficient $\rho$. We show that by setting $\alpha=1/2$ we recover the standard ADMM algorithm as a special case of our algorithm. Moreover, by properly manipulating the proposed R-ADMM, we are able to provide two alternative ADMM-like algorithms that present easier implementation and reduced complexity in terms of memory, communication and computational requirements. Most importantly the latter of these two algorithms provides the first ADMM-like algorithm which has guaranteed convergence even in the presence of lossy communication under the same assumption of standard ADMM with lossless communication. Finally, this work is complemented with a set of compelling numerical simulations of the proposed algorithms over cycle graphs and random geometric graphs subject to i.i.d. random packet losses., Comment: Full version of the paper presented at European Control Conference (ECC) 2018

In this paper we propose a distributed implementation of the relaxed Alternating Direction Method of Multipliers algorithm (R-ADMM) for optimization of a separable convex cost function, whose terms are stored by a set of interacting agents, one for each agent. Specifically the local cost stored by each node is in general a function of both the state of the node and the states of its neighbors, a framework that we refer to as `partition-based' optimization. This framework presents a great flexibility and can be adapted to a large number of different applications. We show that the partition-based R-ADMM algorithm we introduce is linked to the relaxed Peaceman-Rachford Splitting (R-PRS) operator which, historically, has been introduced in the literature to find the zeros of sum of functions. Interestingly, making use of non expansive operator theory, the proposed algorithm is shown to be provably robust against random packet losses that might occur in the communication between neighboring nodes. Finally, the effectiveness of the proposed algorithm is confirmed by a set of compelling numerical simulations run over random geometric graphs subject to i.i.d. random packet losses., Comment: Full version of the paper to be presented at Conference on Decision and Control (CDC) 2018

In this work, we present the equivalent of many theorems available for continuous time systems. In particular, the theory is applied to Averaging Theory and Separation of time scales. In particular the proofs developed for Averaging Theory and Separation of time scales departs from those typically used in continuous time systems that are based on twice differentiable change of variables and the multiple use of the Implicit Function Theorem and Mean Value Theorem. More specifically, by constructing a suitable Lyapunov function only Lipschitz conditions are necessary. Finally, it is shown that under mild condition on the so-called "interconnection conditions" the proposed tools can guarantee semi-global exponential stability rather than the more stringent local exponential stability typically found in the literature

In this paper we consider a novel partitioned framework for distributed optimization in peer-to-peer networks. In several important applications the agents of a network have to solve an optimization problem with two key features: (i) the dimension of the decision variable depends on the network size, and (ii) cost function and constraints have a sparsity structure related to the communication graph. For this class of problems a straightforward application of existing consensus methods would show two inefficiencies: poor scalability and redundancy of shared information. We propose an asynchronous distributed algorithm, based on dual decomposition and coordinate methods, to solve partitioned optimization problems. We show that, by exploiting the problem structure, the solution can be partitioned among the nodes, so that each node just stores a local copy of a portion of the decision variable (rather than a copy of the entire decision vector) and solves a small-scale local problem.

We address the problem of distributed convex unconstrained optimization over networks characterized by asynchronous and possibly lossy communications. We analyze the case where the global cost function is the sum of locally coupled local strictly convex cost functions. As discussed in detail in a motivating example, this class of optimization objectives is, for example, typical in localization problems and in partition-based state estimation. Inspired by a generalized gradient descent strategy, namely the block Jacobi iteration, we propose a novel solution which is amenable for a distributed implementation and which, under a suitable condition on the step size, is provably locally resilient to communication failures. The theoretical analysis relies on the separation of time scales and Lyapunov theory. In addition, to show the flexibility of the proposed algorithm, we derive a resilient gradient descent iteration and a resilient generalized gradient for quadratic programming as two natural particularizations of our strategy. In this second case, global robustness is provided. Finally, the proposed algorithm is numerically tested on the IEEE 123 nodes distribution feeder in the context of partition-based smart grid robust state estimation in the presence of measurements outliers., Comment: 20 pages, 5 figures

In this work we study the problem of unconstrained convex-optimization in a fully distributed multi-agent setting which includes asynchronous computation and lossy communication. In particular, we extend a recently proposed algorithm named Newton-Raphson Consensus by integrating it with a broadcast-based average consensus algorithm which is robust to packet losses. We show via the separation of time scales principle that under mild conditions (i.e., persistency of the agents activation and bounded consecutive communication failures) the proposed algorithm is proved to be locally exponentially stable with respect to the optimal global solution. Finally, we complement the theoretical analysis with numerical simulations that are based on real datasets.

In this work we study the non-parametric reconstruction of spatio-temporal dynamical Gaussian processes (GPs) via GP regression from sparse and noisy data. GPs have been mainly applied to spatial regression where they represent one of the most powerful estimation approaches also thanks to their universal representing properties. Their extension to dynamical processes has been instead elusive so far since classical implementations lead to unscalable algorithms. We then propose a novel procedure to address this problem by coupling GP regression and Kalman filtering. In particular, assuming space/time separability of the covariance (kernel) of the process and rational time spectrum, we build a finite-dimensional discrete-time state-space process representation amenable of Kalman filtering. With sampling over a finite set of fixed spatial locations, our major finding is that the Kalman filter state at instant $t_k$ represents a sufficient statistic to compute the minimum variance estimate of the process at any $t \geq t_k$ over the entire spatial domain. This result can be interpreted as a novel Kalman representer theorem for dynamical GPs. We then extend the study to situations where the set of spatial input locations can vary over time. The proposed algorithms are finally tested on both synthetic and real field data, also providing comparisons with standard GP and truncated GP regression techniques., Comment: 26 pages, 12 figures. Submitted to IEEE Transactions on Pattern Analysis and Machine Intelligence

We extend a multi-agent convex-optimization algorithm named Newton-Raphson consensus to a network scenario that involves directed, asynchronous and lossy communications. We theoretically analyze the stability and performance of the algorithm and, in particular, provide sufficient conditions that guarantee local exponential convergence of the node-states to the global centralized minimizer even in presence of packet losses. Finally, we complement the theoretical analysis with numerical simulations that compare the performance of the Newton-Raphson consensus against asynchronous implementations of distributed subgradient methods on real datasets extracted from open-source databases.

In this paper, we define a general class of abstract aerial robotic systems named Laterally Bounded Force (LBF) vehicles, in which most of the control authority is expressed along a principal thrust direction, while in the lateral directions a (smaller and possibly null) force may be exploited to achieve full-pose tracking. This class approximates well platforms endowed with non-coplanar/non-collinear rotors that can use the tilted propellers to slightly change the orientation of the total thrust w.r.t. the body frame. For this broad class of systems, we introduce a new geometric control strategy in SE(3) to achieve, whenever made possible by the force constraints, the independent tracking of position-plus-orientation trajectories. The exponential tracking of a feasible full-pose reference trajectory is proven using a Lyapunov technique in SE(3). The method can deal seamlessly with both under- and fully-actuated LBF platforms. The controller guarantees the tracking of at least the positional part in the case that an unfeasible full-pose reference trajectory is provided. The paper provides several experimental tests clearly showing the practicability of the approach and the sharp improvement with respect to state of-the-art approaches.

A standard operational requirement in power systems is that the voltage magnitudes lie within prespecified bounds. Conventional engineering wisdom suggests that such a tightly-regulated profile, imposed for system design purposes and good operation of the network, should also guarantee a secure system, operating far from static bifurcation instabilities such as voltage collapse. In general however, these two objectives are distinct and must be separately enforced. We formulate an optimization problem which maximizes the distance to voltage collapse through injections of reactive power, subject to power flow and operational voltage constraints. By exploiting a linear approximation of the power flow equations we arrive at a convex reformulation which can be efficiently solved for the optimal injections. We also address the planning problem of allocating the resources by recasting our problem in a sparsity-promoting framework that allows us to choose a desired trade-off between optimality of injections and the number of required actuators. Finally, we present a distributed algorithm to solve the optimization problem, showing that it can be implemented on-line as a feedback controller. We illustrate the performance of our results with the IEEE30 bus network., Comment: 10 pages, 9 figures

In this paper we propose a novel partition-based distributed state estimation scheme for non-overlapping subsystems based on Kalman filter. The estimation scheme is designed in order to account, in a rigorous fashion, for dynamic coupling terms between subsystems, and for the uncertainty related to the state estimates performed by the neighboring subsystems. The online implementation of the proposed estimation scheme is scalable, since it involves (i) small-scale matrix operations to be carried out by the estimator embedded in each subsystem and (ii) neighbor-to-neighbor transmission of a limited amount of data. We provide theoretical conditions ensuring the estimation convergence. Reconfigurability of the proposed estimation scheme is allowed in case of plug and play operations. Simulation tests are provided to illustrate the effectiveness of the proposed algorithm.