arXiv subjects

Simone Formentin

Publications and source records attributed to Simone Formentin.

52 records · Page 3Linked to original sources

arXiv2022

Data-driven predictive control in a stochastic setting: a unified framework

Data-driven predictive control (DDPC) has been recently proposed as an effective alternative to traditional model-predictive control (MPC) for its unique features of being time-efficient and unbiased with respect to the oracle solution. Nonetheless, it has also been observed that noise may strongly jeopardize the final closed-loop performance since it affects both the data-based system representation and the control update computed from the online measurements. Recent studies have shown that regularization is potentially a successful tool to counteract the effect of noise. At the same time, regularization requires the tuning of a set of penalty terms, whose choice might be practically difficult without closed-loop experiments. In this paper, by means of subspace identification tools, we pursue a three-fold goal: $(i)$ we set up a unified framework for the existing regularized data-driven predictive control schemes for stochastic systems; $(ii)$ we introduce $γ$-DDPC, an efficient two-stage scheme that splits the optimization problem into two parts: fitting the initial conditions and optimizing the future performance, while guaranteeing constraint satisfaction; $(iii)$ we discuss the role of regularization for data-driven predictive control, providing new insight on $when$ and $how$ it should be applied. A benchmark numerical case study finally illustrates the performance of $γ$-DDPC, showing how controller design can be simplified in terms of tuning effort and computational complexity when benefiting from the insights coming from the subspace identification realm.

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arXiv2022

Hourly operation of a regulated lake via Model Predictive Control

The optimal operation of regulated lakes is a challenging task involving conflicting objectives, ranging from controlling lake levels to avoid floods and low levels to water supply downstream. The traditional approach to operation policy design is based on an offline optimization, where a feedback control rule mapping lake storage into daily release decisions is identified over a set of observational data. In this paper, we propose a receding-horizon policy for a more frequent, online regulation of the lake level, and we discuss its tuning as compared to benchmark approaches. As side contributions, we provide a daily alternative based on the same rationale, and we show that this is still valid under some assumptions on the water inflow. Numerical simulations are used to show the effectiveness of the proposed approach. We demonstrate the approach on the regulated lake Como, Italy.

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arXiv2022

Data-driven design of explicit predictive controllers using model-based priors

In this paper, we propose a data-driven approach to derive explicit predictive control laws, without requiring any intermediate identification step. The keystone of the presented strategy is the exploitation of available priors on the control law, coming from model-based analysis. Specifically, by leveraging on the knowledge that the optimal predictive controller is expressed as a piecewise affine (PWA) law, we directly optimize the parameters of such an analytical controller from data, instead of running an on-line optimization problem. As the proposed method allows us to automatically retrieve also a model of the closed-loop system, we show that we can apply model-based techniques to perform a stability check prior to the controller deployment. The effectiveness of the proposed strategy is assessed on two benchmark simulation examples, through which we also discuss the use of regularization and its combination with averaging techniques to handle the presence of noise.

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arXiv2021

On the design of regularized explicit predictive controllers from input-output data

On the wave of recent advances in data-driven predictive control, we present an explicit predictive controller that can be constructed from a batch of input/output data only. The proposed explicit law is build upon a regularized implicit data-driven predictive control problem, so as to guarantee the uniqueness of the explicit predictive controller. As a side benefit, the use of regularization is shown to improve the capability of the explicit law in coping with noise on the data. The effectiveness of the retrieved explicit law and the repercussions of regularization on noise handling are analyzed on two benchmark simulation case studies, showing the potential of the proposed regularized explicit controller.

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arXiv2021

Direct data-driven model-reference control with Lyapunov stability guarantees

In this work, we introduce a novel data-driven model-reference control design approach for unknown linear systems with fully measurable state. The proposed control action is composed by a static feedback term and a reference tracking block, which are shaped from data to reproduce the desired behavior in closed-loop. By focusing on the case where the reference model and the plant share the same order, we propose an optimal design procedure with Lyapunov stability guarantees, tailored to handle state measurements with additive noise. Two simulation examples are finally illustrated to show the potential of the proposed strategy as compared to the state of the art approaches.

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arXiv2021

Learning explicit predictive controllers: theory and applications

In this paper, we deal with data-driven predictive control of linear time-invariant (LTI) systems. Specifically, we show for the first time how explicit predictive laws can be learnt directly from data, without needing to identify the system to control. To this aim, we resort to the Willems' fundamental lemma and we derive the explicit formulas by suitably elaborating the constrained optimization problem under investigation. The resulting optimal controller turns out to be a piecewise affine system coinciding with the solution of the original model-based problem in case of noiseless data. Such an equivalence is proven to hold asymptotically also in presence of measurement noise, thus making the proposed method a computationally efficient (but model-free) alternative to the state of the art predictive controls. The above statements are further supported by numerical simulations on three benchmark examples.

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arXiv2021

Learning-based hierarchical control of water reservoir systems

The optimal control of a water reservoir systems represents a challenging problem, due to uncertain hydrologic inputs and the need to adapt to changing environment and varying control objectives. In this work, we propose a real-time learning-based control strategy based on a hierarchical predictive control architecture. Two control loops are implemented: the inner loop is aimed to make the overall dynamics similar to an assigned linear through data-driven control design, then the outer economic model-predictive controller compensates for model mismatches, enforces suitable constraints, and boosts the tracking performance. The effectiveness of the proposed approach as compared to traditional dynamic programming strategies is illustrated on an accurate simulator of the Hoa Binh reservoir in Vietnam. Results show that the proposed approach performs better than the one based on stochastic dynamic programming.

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arXiv2020

Experimental Automatic Calibration of a Semi-Active Suspension Controller via Bayesian Optimization

The End-of-Line (EoL) calibration of semi-active suspension systems for road vehicles is usually a critical and expensive task, needing a team of vehicle and control experts as well as many hours of professional driving. In this paper, we propose a purely data-based tuning method enabling the automatic calibration of the parameters of a proprietary suspension controller by relying on little experimental time and exploiting Bayesian Optimization tools. A detailed methodology on how to select the most critical degrees of freedom of the algorithm is also provided. The effectiveness of the proposed approach is assessed on a commercial multi-body simulator as well as on a real car.

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arXiv2019

Performance-oriented model learning for data-driven MPC design

Model Predictive Control (MPC) is an enabling technology in applications requiring controlling physical processes in an optimized way under constraints on inputs and outputs. However, in MPC closed-loop performance is pushed to the limits only if the plant under control is accurately modeled; otherwise, robust architectures need to be employed, at the price of reduced performance due to worst-case conservative assumptions. In this paper, instead of adapting the controller to handle uncertainty, we adapt the learning procedure so that the prediction model is selected to provide the best closed-loop performance. More specifically, we apply for the first time the above "identification for control" rationale to hierarchical MPC using data-driven methods and Bayesian optimization.

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arXiv2018

Direct data-driven control of constrained linear parameter-varying systems: A hierarchical approach

In many nonlinear control problems, the plant can be accurately described by a linear model whose operating point depends on some measurable variables, called scheduling signals. When such a linear parameter-varying (LPV) model of the open-loop plant needs to be derived from a set of data, several issues arise in terms of parameterization, estimation, and validation of the model before designing the controller. Moreover, the way modeling errors affect the closed-loop performance is still largely unknown in the LPV context. In this paper, a direct data-driven control method is proposed to design LPV controllers directly from data without deriving a model of the plant. The main idea of the approach is to use a hierarchical control architecture, where the inner controller is designed to match a simple and a-priori specified closed-loop behavior. Then, an outer model predictive controller is synthesized to handle input/output constraints and to enhance the performance of the inner loop. The effectiveness of the approach is illustrated by means of a simulation and an experimental example. Practical implementation issues are also discussed.

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arXiv2018

Data-Driven Inversion-Based Control: closed-loop stability analysis for MIMO systems

Data-Driven Inversion-Based Control (D$^{2}$-IBC) is a recently introduced control design method for uncertain nonlinear systems, relying on a two degree-of-freedom architecture, with a nonlinear controller and a linear controller running in parallel. In this paper, extending to the MIMO case a previous result holding for the SISO case, we derive a finite-gain stability sufficient condition for a closed-loop system formed by a nonlinear MIMO plant, connected in feedback with a D$^{2}$-IBC controller.

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arXiv2016

Online wheel speed filtering for periodic disturbance reduction: a strategy for an advanced bicycle application

Due to geometrical errors and possible misalignment of the sensors, wheel speed measurements provided by incremental encoders in road vehicles are usually affected by significant periodic noises. This paper presents an online wheel speed filtering procedure, based on a model of the sensor, aimed at processing the speed measurement to make it suitable for advanced vehicle dynamics applications. In particular, differently from low-pass and notch filtering, this strategy is reliable for the cycling cadence estimation from the wheel speed on bicycles. Experimental data are used to show the effectiveness of the proposed approach.

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arXiv2016

Robust linear static anti-windup with probabilistic certificates

In this paper, we address robust static anti-windup compensator design and performance analysis for saturated linear closed loops in the presence of nonlinear probabilistic parameter uncertainties via randomized techniques. The proposed static anti-windup analysis and robust performance synthesis correspond to several optimization goals, ranging from minimization of the nonlinear input/output gain to maximization of the stability region or maximization of the domain of attraction. We also introduce a novel paradigm accounting for uncertainties in the energy of the disturbance inputs. Due to the special structure of linear static anti-windup design, wherein the design variables are decoupled from the Lyapunov certificates, we introduce a significant extension, called scenario with certificates (SwC), of the so-called scenario approach for uncertain optimization problems. This extension is of independent interest for similar robust synthesis problems involving parameter-dependent Lyapunov functions. We demonstrate that the scenario with certificates robust design formulation is appealing because it provides a way to implicitly design the parameter-dependent Lyapunov functions and to remove restrictive assumptions about convexity with respect to the uncertain parameters. Subsequently, to reduce the computational cost, we present a sequential randomized algorithm for iteratively solving this problem. The obtained results are illustrated by numerical examples.

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arXiv2015

Least costly energy management for series hybrid electric vehicles

Energy management of plug-in Hybrid Electric Vehicles (HEVs) has different challenges from non-plug-in HEVs, due to bigger batteries and grid recharging. Instead of tackling it to pursue energetic efficiency, an approach minimizing the driving cost incurred by the user - the combined costs of fuel, grid energy and battery degradation - is here proposed. A real-time approximation of the resulting optimal policy is then provided, as well as some analytic insight into its dependence on the system parameters. The advantages of the proposed formulation and the effectiveness of the real-time strategy are shown by means of a thorough simulation campaign.

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arXiv2014

Data-driven controller design for nonlinear systems: a two degrees of freedom architecture

In this paper, the D2-IBC (Data-Driven Inversion Based Control) approach for nonlinear control is introduced and analyzed. The method does not require any a-priori knowledge of the system dynamics and relies on a two degrees of freedom scheme, with a nonlinear controller and a linear controller running in parallel. In particular, the former is devoted to stabilize the system around a trajectory of interest, whereas the latter is used to boost the closed-loop performance. The paper also presents a thorough stability and performance analysis of the closed-loop system.

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arXiv2014

Scenario optimization with certificates and applications to anti-windup design

In this paper, we introduce a significant extension, called scenario with certificates (SwC), of the so-called scenario approach for uncertain optimization problems. This extension is motivated by the observation that in many control problems only some of the optimization variables are used in the design phase, while the other variables play the role of certificates. Examples are all those control problems that can be reformulated in terms of linear matrix inequalities involving parameter-dependent Lyapunov functions. These control problems include static anti-windup compensator design for uncertain linear systems with input saturation, where the goal is the minimization of the nonlinear gain from an exogenous input to a performance output. The main contribution of this paper is to show that randomization is a useful tool, specifically for anti-windup design, to make the overall approach less conservative compared to its robust counterpart. In particular, we demonstrate that the scenario with certificates reformulation is appealing because it provides a way to implicitly design the parameter-dependent Lyapunov functions. Finally, to further reduce the computational cost of this one-shot approach, we present a sequential randomized algorithm for iteratively solving this problem.

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