arXiv subjects

Andrea Iannelli

Publications and source records attributed to Andrea Iannelli.

At least 55 records · Page 3Linked to original sources

arXiv2023

An Online Learning Analysis of Minimax Adaptive Control

We present an online learning analysis of minimax adaptive control for the case where the uncertainty includes a finite set of linear dynamical systems. Precisely, for each system inside the uncertainty set, we define the model-based regret by comparing the state and input trajectories from the minimax adaptive controller against that of an optimal controller in hindsight that knows the true dynamics. We then define the total regret as the worst case model-based regret with respect to all models in the considered uncertainty set. We study how the total regret accumulates over time and its effect on the adaptation mechanism employed by the controller. Moreover, we investigate the effect of the disturbance on the growth of the regret over time and draw connections between robustness of the controller and the associated regret rate.

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arXiv2023

Implications of Regret on Stability of Linear Dynamical Systems

The setting of an agent making decisions under uncertainty and under dynamic constraints is common for the fields of optimal control, reinforcement learning, and recently also for online learning. In the online learning setting, the quality of an agent's decision is often quantified by the concept of regret, comparing the performance of the chosen decisions to the best possible ones in hindsight. While regret is a useful performance measure, when dynamical systems are concerned, it is important to also assess the stability of the closed-loop system for a chosen policy. In this work, we show that for linear state feedback policies and linear systems subject to adversarial disturbances, linear regret implies asymptotic stability in both time-varying and time-invariant settings. Conversely, we also show that bounded input bounded state stability and summability of the state transition matrices imply linear regret.

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arXiv2023

A Dual System-Level Parameterization for Identification from Closed-Loop Data

This work presents a dual system-level parameterization (D-SLP) method for closed-loop system identification. The recent system-level synthesis framework parameterizes all stabilizing controllers via linear constraints on closed-loop response functions, known as system-level parameters. It was demonstrated that several structural, locality, and communication constraints on the controller can be posed as convex constraints on these system-level parameters. In the current work, the identification problem is treated as a {\em dual} of the system-level synthesis problem. The plant model is identified from the dual system-level parameters associated to the plant. In comparison to existing closed-loop identification approaches (such as the dual-Youla parameterization), the D-SLP framework neither requires the knowledge of a nominal plant that is stabilized by the known controller, nor depends upon the choice of factorization of the nominal plant and the stabilizing controller. Numerical simulations demonstrate the efficacy of the proposed D-SLP method in terms of identification errors, compared to existing closed-loop identification techniques.

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arXiv2023

A quantitative and constructive proof of Willems' Fundamental Lemma and its implications

Willems' Fundamental Lemma provides a powerful data-driven parametrization of all trajectories of a controllable linear time-invariant system based on one trajectory with persistently exciting (PE) input. In this paper, we present a novel proof of this result which is inspired by the classical adaptive control literature and differs from existing proofs in multiple aspects. The proof involves a quantitative and directional PE notion, allowing to characterize robust PE properties via singular value bounds, as opposed to binary rank-based PE conditions. Further, the proof is constructive, i.e., we derive an explicit PE lower bound for the generated data. As a contribution of independent interest, we generalize existing PE results from the adaptive control literature and reveal a crucial role of the system's zeros.

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arXiv2022

Dual adaptive MPC using an exact set-membership reformulation

Adaptive model predictive control (MPC) methods using set-membership identification to reduce parameter uncertainty are considered in this work. Strong duality is used to reformulate the set-membership equations exactly within the MPC optimization. A predicted worst-case cost is then used to enable performance-oriented exploration. The proposed approach guarantees robust constraint satisfaction and recursive feasibility. It is shown that method can be implemented using homothetic tube and flexible tube parameterizations of state tubes, and a simulation study demonstrates performance improvement over state-of-the-art controllers.

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arXiv2022

Computationally efficient robust MPC using optimized constraint tightening

A robust model predictive control (MPC) method is presented for linear, time-invariant systems affected by bounded additive disturbances. The main contribution is the offline design of a disturbance-affine feedback gain whereby the resulting constraint tightening is minimized. This is achieved by formulating the constraint tightening problem as a convex optimization problem with the feedback term as a variable. The resulting MPC controller has the computational complexity of nominal MPC, and guarantees recursive feasibility, stability and constraint satisfaction. The advantages of the proposed approach compared to existing robust MPC methods are demonstrated using numerical examples.

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arXiv2022

Infinite-Dimensional Sparse Learning in Linear System Identification

Regularized methods have been widely applied to system identification problems without known model structures. This paper proposes an infinite-dimensional sparse learning algorithm based on atomic norm regularization. Atomic norm regularization decomposes the transfer function into first-order atomic models and solves a group lasso problem that selects a sparse set of poles and identifies the corresponding coefficients. The difficulty in solving the problem lies in the fact that there are an infinite number of possible atomic models. This work proposes a greedy algorithm that generates new candidate atomic models maximizing the violation of the optimality condition of the existing problem. This algorithm is able to solve the infinite-dimensional group lasso problem with high precision. The algorithm is further extended to reduce the bias and reject false positives in pole location estimation by iteratively reweighted adaptive group lasso and complementary pairs stability selection respectively. Numerical results demonstrate that the proposed algorithm performs better than benchmark parameterized and regularized methods in terms of both impulse response fitting and pole location estimation.

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arXiv2022

Kernel-Based Identification of Local Limit Cycle Dynamics with Linear Periodically Parameter-Varying Models

Limit cycle oscillations are phenomena arising in nonlinear dynamical systems and characterized by periodic, locally-stable, and self-sustained state trajectories. Systems controlled in a closed loop along a periodic trajectory can also be modelled as systems experiencing limit cycle behavior. The goal of this work is to identify from data, the local dynamics around the limit cycle using linear periodically parameter-varying models. Using a coordinate transformation onto transversal surfaces, the dynamics are decomposed into two parts: one along the limit cycle, and one on the transversal surfaces. Then, the model is identified from trajectory data using kernel-based methods with a periodic kernel design. The kernel-based model is extended to also account for variations in system parameters associated with different operating conditions. The performance of the proposed identification method is demonstrated on a benchmark nonlinear system and on a simplified airborne wind energy model. The method provides accurate model parameter estimation, compared to the analytical linearization, and good prediction capability.

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arXiv2022

On the Regret of $\mathcal{H}_{\infty}$ Control

The $\mathcal{H}_{\infty}$ synthesis approach is a cornerstone robust control design technique, but is known to be conservative in some cases. The objective of this paper is to quantify the additional cost the controller incurs planning for the worst-case scenario, by adopting an approach inspired by regret from online learning. We define the \textit{disturbance-reality gap} as the difference between the predicted worst-case disturbance signal and the actual realization. The regret is shown to scale with the norm of this \textit{gap}, which turns out to have a similar structure to that of the certainty equivalent controller with inaccurate predictions, obtained here in terms of the \textit{prediction error} norm.

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arXiv2022

Scalable tube model predictive control of uncertain linear systems using ellipsoidal sets

This work proposes a novel robust model predictive control (MPC) algorithm for linear systems affected by dynamic model uncertainty and exogenous disturbances. The uncertainty is modeled using a linear fractional perturbation structure with a time-varying perturbation matrix, enabling the algorithm to be applied to a large model class. The MPC controller constructs a state tube as a sequence of parameterized ellipsoidal sets to bound the state trajectories of the system. The proposed approach results in a semidefinite program to be solved online, whose size scales linearly with the order of the system. The design of the state tube is formulated as an offline optimization problem, which offers flexibility to impose desirable features such as robust invariance on the terminal set. This contrasts with most existing tube MPC strategies using polytopic sets in the state tube, which are difficult to design and whose complexity grows combinatorially with the system order. The algorithm guarantees constraint satisfaction, recursive feasibility, and stability of the closed loop. The advantages of the algorithm are demonstrated using two simulation studies.

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arXiv2022

Stochastic MPC with robustness to bounded parametric uncertainty

The performance of model-based control techniques strongly depends on the quality of the employed dynamics model. If strong guarantees are desired, it is therefore common to robustly treat all possible sources of uncertainty, such as model inaccuracies or external disturbances. This, however, can result in overly conservative control strategies. In this paper, we present a stochastic model predictive control approach for discrete-time LTI systems subject to bounded parametric uncertainty and potentially unbounded stochastic additive noise. The proposed scheme makes use of homothetic tubes along the prediction horizon for a robust treatment of parametric uncertainty. Stochastic noise is handled by non-conservatively tightening constraints using the concept of probabilistic reachable sets (PRS). In order to accommodate all possible parametric uncertainties, we provide a strategy for generating "robustified" PRS based only on first and second moments of the noise sequence. In the case of quadratic cost functions, and under a further i.i.d. assumption on the noise distribution, we also provide an average asymptotic performance bound for the l2-norm of the closed-loop state. Finally, we demonstrate our scheme on both an illustrative example, and in a building temperature control problem.

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arXiv2022

Regret Analysis of Online Gradient Descent-based Iterative Learning Control with Model Mismatch

In Iterative Learning Control (ILC), a sequence of feedforward control actions is generated at each iteration on the basis of partial model knowledge and past measurements with the goal of steering the system toward a desired reference trajectory. This is framed here as an online learning task, where the decision-maker takes sequential decisions by solving a sequence of optimization problems having only partial knowledge of the cost functions. Having established this connection, the performance of an online gradient-descent based scheme using inexact gradient information is analyzed in the setting of dynamic and static regret, standard measures in online learning. Fundamental limitations of the scheme and its integration with adaptation mechanisms are further investigated, followed by numerical simulations on a benchmark ILC problem.

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arXiv2022

An explicit dual control approach for constrained reference tracking of uncertain linear systems

A finite horizon optimal tracking problem is considered for linear dynamical systems subject to parametric uncertainties in the state-space matrices and exogenous disturbances. A suboptimal solution is proposed using a model predictive control (MPC) based explicit dual control approach which enables active uncertainty learning. A novel algorithm for the design of robustly invariant online terminal sets and terminal controllers is presented. Set membership identification is used to update the parameter uncertainty online. A predicted worst-case cost is used in the MPC optimization problem to model the dual effect of the control input. The cost-to-go is estimated using contractivity of the proposed terminal set and the remaining time horizon, so that the optimizer can estimate future benefits of exploration. The proposed dual control algorithm ensures robust constraint satisfaction and recursive feasibility, and navigates the exploration-exploitation trade-off using a robust performance metric.

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arXiv2021

Maximum Likelihood Estimation in Data-Driven Modeling and Control

Recently, various algorithms for data-driven simulation and control have been proposed based on the Willems' fundamental lemma. However, when collected data are noisy, these methods lead to ill-conditioned data-driven model structures. In this work, we present a maximum likelihood framework to obtain an optimal data-driven model, the signal matrix model, in the presence of output noise. Data compression and noise level estimation schemes are also proposed to apply the algorithm efficiently to large datasets and unknown noise level scenarios. Two approaches in system identification and receding horizon control are developed based on the derived optimal estimator. The first one identifies a finite impulse response model. This approach improves the least-squares estimator with less restrictive assumptions. The second one applies the signal matrix model as the predictor in predictive control. The control performance is shown to be better than existing data-driven predictive control algorithms, especially under high noise levels. Both approaches demonstrate that the derived estimator provides a promising framework to apply data-driven algorithms to noisy data.

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arXiv2021

Maximum Likelihood Signal Matrix Model for Data-Driven Predictive Control

The paper presents a data-driven predictive control framework based on an implicit input-output mapping derived directly from the signal matrix of collected data. This signal matrix model is derived by maximum likelihood estimation with noise-corrupted data. By linearizing online, the implicit model can be used as a linear constraint to characterize possible trajectories of the system in receding horizon control. The signal matrix can also be updated online with new measurements. This algorithm can be applied to large datasets and slowly time-varying systems, possibly with high noise levels. An additional regularization term on the prediction error can be introduced to enhance the predictability and thus the control performance. Numerical results demonstrate that the proposed signal matrix model predictive control algorithm is effective in multiple applications and performs better than existing data-driven predictive control algorithm.

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arXiv2021

Data-Driven Prediction with Stochastic Data: Confidence Regions and Minimum Mean-Squared Error Estimates

Recently, direct data-driven prediction has found important applications for controlling unknown systems, particularly in predictive control. Such an approach provides exact prediction using behavioral system theory when noise-free data are available. For stochastic data, although approximate predictors exist based on different statistical criteria, they fail to provide statistical guarantees of prediction accuracy. In this paper, confidence regions are provided for these stochastic predictors based on the prediction error distribution. Leveraging this, an optimal predictor which achieves minimum mean-squared prediction error is also proposed to enhance prediction accuracy. These results depend on some true model parameters, but they can also be replaced with an approximate data-driven formulation in practice. Numerical results show that the derived confidence region is valid and smaller prediction errors are observed for the proposed minimum mean-squared error estimate, even with the approximate data-driven formulation.

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arXiv2021

Design of input for data-driven simulation with Hankel and Page matrices

The paper deals with the problem of designing informative input trajectories for data-driven simulation. First, the excitation requirements in the case of noise-free data are discussed and new weaker conditions, which assume the simulated input to be known in advance, are provided. Then, the case of noisy data trajectories is considered and an input design problem based on a recently proposed maximum likelihood estimator is formulated. A Bayesian interpretation is provided, and the implications of using Hankel and Page matrix representations are demonstrated. Numerical examples show the impact of the designed input on the predictive accuracy.

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arXiv2021

Decentralized trajectory optimization for multi-agent exploration

Autonomous exploration is an application of growing importance in robotics. A promising strategy is ergodic trajectory planning, whereby an agent spends in each area a fraction of time which is proportional to its probability information density function. In this paper, a decentralized ergodic multi-agent trajectory planning algorithm featuring limited communication constraints is proposed. The agents' trajectories are designed by optimizing a weighted cost encompassing ergodicity, control energy and close-distance operation objectives. To solve the underlying optimal control problem, a second-order descent iterative method coupled with a projection operator in the form of an optimal feedback controller is used. Exhaustive numerical analyses show that the multi-agent solution allows a much more efficient exploration in terms of completion task time and control energy distribution by leveraging collaboration among agents.

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