A. Bemporad

IMT Institute for Advanced Studies Lucca, Lucca, Tuscany, Italy

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Publications (177)98.25 Total impact

  • Panagiotis Patrinos, Lorenzo Stella, Alberto Bemporad
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    ABSTRACT: We propose a new approach for analyzing convergence of the Douglas-Rachford splitting method for solving convex composite optimization problems. The approach is based on a continuously differentiable function, the Douglas-Rachford Envelope (DRE), whose stationary points correspond to the solutions of the original (possibly nonsmooth) problem. The Douglas-Rachford splitting method is shown to be equivalent to a scaled gradient method on the DRE, and so results from smooth unconstrained optimization are employed to analyze its convergence and optimally choose parameter {\gamma} and to derive an accelerated variant of Douglas-Rachford splitting.
    07/2014;
  • Panagiotis Patrinos, Lorenzo Stella, Alberto Bemporad
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    ABSTRACT: This paper proposes two proximal Newton-CG methods for convex nonsmooth optimization problems in composite form. The algorithms are based on a a reformulation of the original nonsmooth problem as the unconstrained minimization of a continuously differentiable function, namely the forward-backward envelope (FBE). The first algorithm is based on a standard line search strategy, whereas the second one combines the global efficiency estimates of the corresponding first-order methods, while achieving fast asymptotic convergence rates. Furthermore, they are computationally attractive since each Newton iteration requires the approximate solution of a linear system of usually small dimension.
    02/2014;
  • P. Patrinos, A. Bemporad
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    ABSTRACT: This paper proposes a dual fast gradient-projection method for solving quadratic programming problems that arise in model predictive control of linear systems subject to general polyhedral constraints on inputs and states. The proposed algorithm is well suited for embedded control applications in that: 1) it is extremely simple and easy to code; 2) the number of iterations to reach a given accuracy in terms of optimality and feasibility of the primal solution can be tightly estimated; and 3) the computational cost per iteration increases only linearly with the prediction horizon.
    IEEE Transactions on Automatic Control 01/2014; 59(1):18-33. · 2.72 Impact Factor
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    ABSTRACT: This paper develops an approach for driver-aware vehicle control based on stochastic model predictive control with learning (SMPCL). The framework combines the on-board learning of a Markov chain that represents the driver behavior, a scenario-based approach for stochastic optimization, and quadratic programming. By using quadratic programming, SMPCL can handle, in general, larger state dimension models than stochastic dynamic programming, and can reconfigure in real-time for accommodating changes in driver behavior. The SMPCL approach is demonstrated in the energy management of a series hybrid electrical vehicle, aimed at improving fuel efficiency while enforcing constraints on battery state of charge and power. The SMPCL controller allocates the power from the battery and the engine to meet the driver power request. A Markov chain that models the power request dynamics is learned in real-time to improve the prediction capabilities of model predictive control (MPC). Because of exploiting the learned pattern of the driver behavior, the proposed approach outperforms conventional model predictive control and shows performance close to MPC with full knowledge of future driver power request in standard and real-world driving cycles.
    IEEE Transactions on Control Systems Technology 01/2014; 22(3):1018-1031. · 2.00 Impact Factor
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    ABSTRACT: Vehicle active safety receives ever increasing attention in the attempt to achieve zero accidents on the road. In this paper, we investigate a control architecture that has the potential of improving yaw stability control by achieving faster convergence and reduced impact on the longitudinal dynamics. We consider a system where active front steering and differential braking are available and propose a model predictive control (MPC) strategy to coordinate the actuators. We formulate the vehicle dynamics with respect to the tire slip angles and use a piecewise affine (PWA) approximation of the tire force characteristics. The resulting PWA system is used as prediction model in a hybrid MPC strategy. After assessing the benefits of the proposed approach, we synthesize the controller by using a switched MPC strategy, where the tire conditions (linear/saturated) are assumed not to change during the prediction horizon. The assessment of the controller computational load and memory requirements indicates that it is capable of real-time execution in automotive-grade electronic control units. Experimental tests in different maneuvers executed on low-friction surfaces demonstrate the high performance of the controller.
    IEEE Transactions on Control Systems Technology 06/2013; 21:1236-1248. · 2.00 Impact Factor
  • Source
    R. Krenn, A. Gibbesch, G. Binet, A. Bemporad
    05/2013;
  • M. Rubagotti, P. Patrinos, A. Bemporad
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    ABSTRACT: This paper describes a model predictive control (MPC) approach for discrete-time linear systems with hard constraints on control and state variables. The finite-horizon optimal control problem is formulated as a quadratic program (QP), and solved using a recently proposed dual fast gradient-projection method. More precisely, in a finite number of iterations of the mentioned optimization algorithm, a solution with bounded levels of infeasibility and suboptimality is determined for an alternative problem. This solution is shown to be a feasible suboptimal solution for the original problem, leading to exponential stability of the closed-loop system. The proposed strategy is particularly useful in embedded control applications, for which real-time constraints and limited computing resources can impose tight bounds on the possible number of iterations that can be performed within the scheduled sampling time.
    Control Conference (ECC), 2013 European; 01/2013
  • P. Patrinos, A. Guiggiani, A. Bemporad
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    ABSTRACT: Although linear Model Predictive Control has gained increasing popularity for controlling dynamical systems subject to constraints, the main barrier that prevents its widespread use in embedded applications is the need to solve a Quadratic Program (QP) in real-time. This paper proposes a dual gradient projection (DGP) algorithm specifically tailored for implementation on fixed-point hardware. A detailed convergence rate analysis is presented in the presence of round-off errors due to fixed-point arithmetic. Based on these results, concrete guidelines are provided for selecting the minimum number of fractional and integer bits that guarantee convergence to a suboptimal solution within a prespecified tolerance, therefore reducing the cost and power consumption of the hardware device.
    Control Conference (ECC), 2013 European; 01/2013
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    ABSTRACT: In this paper we present control strategies for solving the problems of risk-averse bidding on the electricity markets, focusing on the Day-Ahead and Ancillary Services market, and of optimal real-time power dispatch from the point of view of a market participant, or Balance Responsible Party (BRP). For what concerns the bidding problem, the proposed algorithms are based on two-stage stochastic programming and are aimed at finding the optimal allocation of production between the day-ahead exchange market and the ancillary services market. For the real-time power dispatch problem, we devised a two-level hierarchical control strategy, where the upper-level computes economically optimal power set-points for the generators, and the lower level tracks them while considering constraints and dynamical models of the plant. Simulation results based on realistic data modeling the Dutch transmission network are shown to evaluate the effectiveness of the approach.
    European Energy Market (EEM), 2013 10th International Conference on the; 01/2013
  • L. Puglia, A. Bemporad, A. Jokic, A. Virag
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    ABSTRACT: The aim of this paper is to present a market design for trading capacity reserves (also called Ancillary Services, AS) and to introduce a strategy for the optimal bidding problem in such a scenario. In the deregulated market, the presence of several market participants or Balance Responsible Parties (BRPs) entitled for trading energy, together with the increasing integration of renewable sources and price-elastic loads, shift the focus on decentralized control and reliable forecast techniques. The main feature of the considered market design is its double-sided nature. In addition to portfolio-based supply bids and based on prediction of their stochastic production and load, BRPs are allowed to submit risk-limiting requests. Requesting capacity from the AS market corresponds to giving to the market an estimate of the possible deviation from the daily production schedule resulting from the day-ahead auction and from bilateral contracts, named E-Program. In this way each BRP is responsible for the balanced and safe operation of the electric grid. On the other hand, at each Program Time Unit (PTU) BRPs must also offer their available capacity under the form of bids. In this paper, a bidding strategy to the double-sided market is described, where the risk is minimized and all the constraints are fulfilled. The algorithms devised are tested in a simulation environment and compared to the current practice, where the double-sided auction is not contemplated. Results in terms of expected imbalances and reliability are presented.
    European Energy Market (EEM), 2013 10th International Conference on the; 01/2013
  • Source
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    ABSTRACT: Hybrid Petri nets represent a powerful modeling formalism that offers the possibility of integrating, in a natural way, continuous and discrete dynamics in a single net model. Usual control approaches for hybrid nets can be divided into discrete-time and continuous-time approaches. Continuous-time approaches are usually more precise, but can be computationally prohibitive. Discrete-time approaches are less complex, but can entail mode-mismatch errors due to fixed time discretization. This work proposes an optimization-based event-driven control approach that applies on continuous time models and where the control actions change when discrete events occur. Such an approach is computationally feasible for systems of interest in practice and avoids mode-mismatch errors. In order to handle modelling errors and exogenous disturbances, the proposed approach is implemented in a closed-loop strategy based on event-driven model predictive control. Copyright © 2013 John Wiley & Sons, Ltd.
    International Journal of Robust and Nonlinear Control 01/2013; · 1.90 Impact Factor
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    ABSTRACT: Linear Impulsive Control Systems have been extensively studied with respect to their equilibrium points which, in most cases, are no other than the origin. As a result the trajectory of the system cannot be stabilized to arbitrary desired points which imposes a significant restriction towards their utilization in various applications such as drug administration. In this paper, we study the equilibrium of Linear Impulsive Systems in light of target-sets instead of the standard equilibrium point approach. We properly extend the notion of invariant sets which is crucial in designing asymptotically stable Model Predictive Controllers (MPC).
    51st Conference on Decision and Control; 12/2012
  • 4th IFAC Conference on Nonlinear Model Predictive Control; 08/2012
  • Source
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    ABSTRACT: This paper proposes piecewise affine (PWA) virtual sensors for the estimation of unmeasured variables of nonlinear systems with unknown dynamics. The estimation functions are designed directly from measured inputs and outputs and have two important features. First, they enjoy convergence and optimality properties, based on classical results on parametric identification. Second, the PWA structure is based on a simplicial partition of the measurement space and allows one to implement very effectively the virtual sensor on a digital circuit. Due to the low cost of the required hardware for the implementation of such a particular structure and to the very high sampling frequencies that can be achieved, the approach is applicable to a wide range of industrial problems.
    IEEE Transactions on Industrial Electronics 02/2012; 59(2):1228-1237. · 6.50 Impact Factor
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    ABSTRACT: Derivative contracts require the replication of the product by means of a dynamic portfolio composed of simpler, more liquid securities. For a broad class of options encountered in financial engineering we propose a solution to the problem of finding a hedging portfolio using a discrete-time stochastic model predictive control and receding horizon optimization. By employing existing option pricing engines for estimating future option prices (possibly in an approximate way, to increase computation speed), in the absence of transaction costs the resulting stochastic optimization problem is easily solved at each trading date as a least-squares problem with as many variables as the number of traded assets and as many constraints as the number of predicted scenarios. As shown through numerical examples, the approach is particularly useful and numerically viable for exotic options where closed-form results are not available, as well as relatively long expiration dates where tree-based stochastic approaches are excessively complex.
    Quantitative Finance. 01/2012; 2012(pp. 1–13).
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    ABSTRACT: In this paper, a piecewise-affine direct virtual sensor is proposed for the estimation of unmeasured outputs of nonlinear systems whose dynamical model is unknown. In order to overcome the lack of a model, the virtual sensor is designed directly from measured inputs and outputs. The proposed approach generalizes a previous contribution, allowing one to design lower-complexity estimators. Indeed, the reduced-complexity approach strongly reduces the effect of the so-called “curse of dimensionality”, and can be applied to relatively high-order systems, while enjoying all the convergence and optimality properties of the original approach.
    Decision and Control (CDC), 2012 IEEE 51st Annual Conference on; 01/2012
  • A. Bemporad, A. Oliveri, T. Poggi, M. Storace
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    ABSTRACT: This paper investigates the use of canonical piecewise affine (PWA) functions for approximation and fast implementation of linear MPC controllers. The control law is approximated in an optimal way over a regular simplicial partition of a given set of states of interest. The stability properties of the resulting closed-loop system are analyzed by constructing a suitable PWA Lyapunov function. The main advantage of the proposed approach to the implementation of MPC controllers is that the resulting stabilizing approximate MPC controller can be implemented on chip with sampling times in the order of tens of nanoseconds.
    IEEE Transactions on Automatic Control 01/2012; · 2.72 Impact Factor
  • Source
    G. Binet, R. Krenn, A. Bemporad
    01/2012;
  • M. Rubagotti, L. Zaccarian, A. Bemporad
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    ABSTRACT: This paper analyzes stability of discrete-time piecewise-affine systems defined on non-invariant domains. An algorithm based on linear programming is proposed, in order to prove the exponential stability of the origin and to find a positively invariant estimate of the region of attraction. The theoretical results are based on the definition of a piecewise-affine, possibly discontinuous, Lyapunov function. The proposed method presents a relatively low computational burden, and is proven to lead to feasible solutions in a broader range of cases with respect to a previously proposed approach.
    Decision and Control (CDC), 2012 IEEE 51st Annual Conference on; 01/2012
  • Source
    18th IFAC World Congress; 09/2011

Publication Stats

4k Citations
98.25 Total Impact Points

Institutions

  • 2010–2013
    • IMT Institute for Advanced Studies Lucca
      Lucca, Tuscany, Italy
  • 2011
    • Università degli Studi di Trento
      • Departmental Area of Mechanical and Structural Engineering
      Trento, Trentino-Alto Adige, Italy
  • 2001–2010
    • Università degli Studi di Siena
      Siena, Tuscany, Italy
  • 2008
    • Polytechnic University of Catalonia
      • Department of Automatic Control (ESAII)
      Barcino, Catalonia, Spain
  • 2007
    • Università di Pisa
      Pisa, Tuscany, Italy
  • 2006
    • Università degli studi di Cagliari
      • Department of Electrical and Electronic Engineering
      Cagliari, Sardinia, Italy
    • SENER Ingeniería y Sistemas
      Madrid, Madrid, Spain
  • 2001–2006
    • Technische Universiteit Eindhoven
      • Department of Electrical Engineering
      Eindhoven, North Brabant, Netherlands
  • 1999–2006
    • ETH Zurich
      • Automatic Control Laboratory
      Zürich, ZH, Switzerland
  • 2005
    • Universidad de Sevilla
      • Departamento de Ingeniería de Sistemas y Automática
      Sevilla, Andalusia, Spain
  • 2001–2004
    • Norwegian University of Science and Technology
      • Department of Engineering Cybernetics
      Trondheim, Sor-Trondelag Fylke, Norway
  • 1994–1998
    • University of Florence
      • Dipartimento di Ingegneria dell'Informazione
      Florence, Tuscany, Italy
  • 1996
    • Sapienza University of Rome
      • Department of Computer Science
      Roma, Latium, Italy