Alberto Bemporad

• IMT School for Advanced Studies Lucca

Despite recent advances in computing hardware and optimization algorithms, solving model predictive control (MPC) problems in real time still poses some technical challenges when long prediction and control horizons are used, due to the presence of several optimization variables and constraints. In this paper, we propose to reduce the computational...

In this paper we present a data-driven approach for synthesizing optimal switching controllers directly from experimental data, without the need of a global model of the dynamics of the process. The set of controllers and the switching law are learned by using a coordinate descent strategy: for a fixed switching law, the controllers are sequentiall...

Industrial systems deployed in mass production, such as automobiles, can greatly benefit from sharing selected data among them through the cloud, when asked to self-adapt their control laws. The reason is that in mass production, systems are clones of each other, designed, constructed, and calibrated by the manufacturer in the same way, and thus th...

For all its successes, Reinforcement Learning (RL) still struggles to deliver formal guarantees on the closed-loop behavior of the learned policy. Among other things, guaranteeing the safety of RL with respect to safety-critical systems is a very active research topic. Some recent contributions propose to rely on projections of the inputs delivered...

Active-set (AS) methods for quadratic programming (QP) are particularly suitable for real-time optimization, as they provide a high-quality solution in a finite number of iterations. However, they add or remove one constraint at each iteration, which makes them inefficient when the number of constraints and variables grows. Block principal pivoting...

Providing the users information on the energy consumed in the household at the appliance level is of major importance for increasing their awareness of their consumption behavior. In this paper, we propose a technique based on Kalman filters to estimate the devices’ consumption patterns from aggregate readings, i.e., to solve the so called disaggre...

Energy disaggregation aims at reconstructing the power consumed by each electric appliance available in a household from the aggregate power readings collected by a single-point smart meter. With the ultimate goal of fully automatizing this procedure, we first estimate a set of jump models, each of them describing the consumption behaviour of each...

We describe a new framework for fitting jump models to a sequence of data. The key idea is to alternate between minimizing a loss function to fit multiple model parameters, and minimizing a discrete loss function to determine which set of model parameters is active at each data point. The framework is quite general and encompasses popular classes o...

Optimal control theory and machine learning techniques are combined to formulate and solve in closed form an optimal control formulation of online learning from supervised examples with regularization of the updates. The connections with the classical linear quadratic gaussian (LQG) optimal control problem, of which the proposed learning paradigm i...

This paper presents an integrated control approach for autonomous driving comprising a corridor path planner that determines constraints on vehicle position, and a linear time-varying model predictive controller combining path planning and tracking in a road-aligned coordinate frame. The capabilities of the approach are illustrated in obstacle-free...

This paper presents the design of a Model Predictive Control (MPC) scheme to optimally manage the thermal and electrical subsystems of a small-size building (“smart house”), with the objective of minimizing the expense for buying energy from the grid, while keeping the room temperature within given time-varying bounds. The system, for which an expe...

A hierarchical method for the approximate computation of the consensus state of a network of agents is investigated. The method is motivated theoretically by spectral graph theory arguments. In a first phase, the graph is divided into a number of subgraphs with good spectral properties, i.e., a fast convergence toward the local consensus state of e...

In nonlinear regression choosing an adequate model structure is often a challenging problem. While simple models (such as linear functions) may not be able to capture the underlying relationship among the variables, over-parametrized models described by a large set of nonlinear basis functions tend to overfit the training data, leading to poor gene...

The optimization of process economics within the model predictive control (MPC) formulation has given rise to a new control paradigm known as economic MPC (EMPC). Several authors have discussed the closed-loop properties of EMPC-controlled deterministic systems, however, little have uncertain systems been studied. In this paper we propose EMPC form...

This paper proposes a method to design robust model predictive control (MPC) laws for discrete-time linear systems with hard mixed constraints on states and inputs, in case of only an inexact solution of the associated quadratic program is available, because of real-time requirements. By using a recently proposed dual gradient-projection algorithm,...

Linear model predictive control (MPC) can be currently deployed at outstanding speeds, thanks to recent progress in algorithms for solving online the underlying structured quadratic programs. In contrast, nonlinear MPC (NMPC) requires the deployment of more elaborate algorithms, which require longer computation times than linear MPC. Nonetheless, c...

We introduce a new stochastic gradient algorithm, SAAGA, and investigate its employment for solving Stochastic MPC problems and multi-stage stochastic optimization programs in general. The method is particularly attractive for scenario-based formulations that involve a large number of scenarios, for which “batch” formulations may become inefficient...

Least Squares Support Vector Machine (LS-SVM) is a computationally efficient kernel-based regression approach which has been recently applied to nonparametric identification of Linear Parameter Varying (LPV) systems. In contrast to parametric LPV identification approaches, LS-SVM based methods obviate the need to parameterize the scheduling depende...

Piecewise affine (PWA) regression is a supervised learning method which aims at estimating, from a set of training data, a PWA map approximating the relationship between a set of explanatory variables (commonly called regressors) and continuous-valued outputs. In this paper, we describe a recursive and numerically efficient PWA regression algorithm...

Despite the proven advantages of scenario-based stochastic model predictive control for the operational control of water networks, its applicability is limited by its considerable computational footprint. In this paper we fully exploit the structure of these problems and solve them using a proximal gradient algorithm parallelizing the involved oper...

We propose a decentralised hierarchical multi-rate control scheme for the control of large-scale systems with state and input constraints. The large-scale system is partitioned into sub-systems each one of which is locally controlled by a stabilising linear controller which does not account for the prescribed constraints. A higher-layer controller...

This paper proposes a new algorithm for solving Mixed-Integer Quadratic Programming (MIQP) problems. The algorithm is particularly tailored to solving small-scale MIQPs such as those that arise in embedded hybrid Model Predictive Control (MPC) applications. The approach combines branch and bound (B&B) with nonnegative least squares (NNLS), that are...

Model predictive control (MPC) is one of the most successful techniques adopted in industry to control multivariable systems under constraints on input and output variables. To circumvent the main drawback of MPC, i.e., the need to solve a Quadratic Program (QP) on line to compute the control action, explicit MPC was proposed in the past to precomp...

This paper analyses stability of discrete-time piecewise-affine systems, defined on possibly non-invariant domains, taking into account the possible presence of multiple dynamics in each of the polytopic regions of the system. An algorithm based on linear programming is proposed, in order to prove exponential stability of the origin and to find a p...

In this paper we propose a fast optimization algorithm for approximately minimizing convex quadratic functions over the intersection of affine and separable constraints (i.e., the Cartesian product of possibly nonconvex real sets). This problem class contains many NP-hard problems such as mixed-integer quadratic programming. Our heuristic is based...

In the consensus problem on multi-agent systems, in which the states of the agents represent opinions, the agents aim at reaching a common opinion (or consensus state) through local exchange of information. An important design problem is to choose the degree of interconnection of the subsystems to achieve a good trade-off between a small number of...

This paper describes the modeling and control of heat and electricity flows in a smart house equipped with a solar heating system, PV panels, and lead-acid batteries for energy storage. The goal is to minimize electricity costs, making best use of renewable sources of heat and electricity. The system model is obtained via system identification from...

Future safety critical space missions call for increasing levels of embedded spacecraft autonomy. Spacecraft and mission responsiveness will be highly improved via onboard automation and autonomy functions, simplifying operations and ground control capabilities. Recently developed real-time embedded MPC guidance and control strategies have a great...

In this paper, we combine optimal control theory and machine learning techniques to propose and solve an optimal control formulation of online learning from supervised examples, which are used to learn an unknown vector parameter modeling the relationship between the input examples and their outputs. We show some connections of the problem investig...

This paper studies an important aspect of attitude control for a launcher's upper stage: the minimum impulse bit (MIB), that is, the minimum torque that can be exerted by the thrusters. We model this effect using principles of hybrid systems theory and we design a hybrid model predictive control scheme for the attitude control of a launcher during...

In this paper we propose a Model Predictive Controller for spacecraft attitude tracking with reaction wheel actuators. The controller is designed for desaturation of the reaction wheels. In contrast with standard desaturation techniques, which rely on the activation of thrusters, the proposed strategy does not need to consume fuel as it exploits ex...

In this tutorial paper we present a novel modeling methodology to derive a nonlinear dynamical model which adequately describes the effect of fuel sloshing on the attitude dynamics of a spacecraft. We model the impulsive thrusters using mixed logic and dynamics leading to a hybrid formulation. We design a hybrid model predictive control scheme for...

This paper revisits the fundamental equations for the solution of the frictionless unilateral normal contact problem between a rough rigid surface and a linear elastic half-plane using the boundary element method (BEM). After recasting the resulting Linear Complementarity Problem (LCP) as a convex quadratic program (QP) with nonnegative constraints...

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 tailore...

The Internet of Things (IoT) is the interconnection of embedded devices and offers the possibility of exploiting cloud-based services to improve control functions. But how much cloud control is possible when facing real-time challenges in a safety-critical environment? This paper provides first insights and data into cloud-based control by means of...

This paper combines predictive control and setmembership state estimation techniques, for input/state hard constraints fulfilment. Linear systems with unknown but bounded disturbances and partial state information are considered. The adopted worst-case approach guarantees that the constraints are satisfied for all the states which are compatible wi...

This paper proposes a novel model predictive control (MPC) scheme based on multiobjective optimization. At each sampling time, the MPC control action is chosen among the set of Pareto optimal solutions based on a time-varying and state-dependent decision criterion. After recasting the optimization problem associated with the multiobjective MPC cont...

This paper proposes a novel decentralized model predictive control (MPC) design approach for open-loop asymptotically stable processes whose dynamics are not necessarily decoupled. A set of partially decoupled approximate prediction models are defined and used by different MPC controllers. Rather than looking for a-priori conditions for asymptotic...

In this paper a Model Predictive Control (MPC) method for torque control of a Permanent Magnet Synchronous Motor (PMSM) is presented. The proposed approach takes into account constraints on voltages and currents, and allows the use of modulation techniques that eliminate the side effects caused by the direct transistor actuation performed by Model...

This paper proposes to decouple performance optimization and enforcement of asymptotic convergence in Model Predictive Control (MPC) so that convergence to a given terminal set is achieved independently of how much performance is optimized at each sampling step. By embedding an explicit decreasing condition in the MPC constraints and thanks to a no...

This technical note proposes an active set method based on nonnegative least squares (NNLS) to solve strictly convex quadratic programming (QP) problems, such as those that arise in Model Predictive Control (MPC). The main idea is to rephrase the QP problem as a Least Distance Problem (LDP) that is solved via a NNLS reformulation.While the method i...

This paper proposes an explicit model predictive control design approach for regulation of linear time-invariant systems subject to both state and control constraints, in the presence of additive disturbances. The proposed control law is implemented as a piecewise-affine function defined on a regular simplicial partition, and has two main positive...

In the “consensus problem” on multi-agent systems, in which the states of the agents are “opinions”, the agents aim at reaching a common opinion (or “consensus state”) through local exchange of information. An important design problem is to choose the degree of interconnection of the subsystems so as to achieve a good trade-off between a small numb...

The paper develops a Model Predictive Controller for constrained control of spacecraft attitude with reaction wheel actuators. The controller exploits a special formulation of the cost with the reference governor like term, a low complexity addition of integral action to guarantee offset-free tracking of attitude set points, and a fixed-point, onli...

Ferroelectric Random Access Memory (FRAM) by Texas Instruments (TI) is a non-volatile memory which allows lower power and faster data throughput compared to other nonvolatile solutions. These features have accelerated the interest in this technology as the future of embedded unified memory, in particular in data logging, remote sensing and Wireless...

This paper proposes a dynamic controller structure and a systematic design procedure for stabilizing discrete-time hybrid systems. The proposed approach is based on the concept of control Lyapunov functions (CLFs), which, when available, can be used to design a stabilizing state-feedback control law. In general, the construction of a CLF for hybrid...

In this paper we study constrained stochastic optimal control problems for Markovian switching systems, an extension of Markovian jump linear systems (MJLS), where the subsystems are allowed to be nonlinear. We develop appropriate notions of invariance and stability for such systems and provide terminal conditions for stochastic model predictive co...

Drinking Water Networks (DWN) are large-scale multiple-input multiple-output systems with uncertain disturbances (such as the water demand from the consumers) and involve components of linear, non-linear and switching nature. Operating, safety and quality constraints deem it important for the state and the input of such systems to be constrained in...

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 com...

Extending the success of model predictive control (MPC) technologies in embedded applications heavily depends on the capability of improving quadratic programming (QP) solvers. Improvements can be done in two directions: better algorithms that reduce the number of arithmetic operations required to compute a solution, and more efficient architecture...

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 D...

This note describes a model predictive control (MPC) formulation for discrete-time linear systems with hard constraints on control and state variables, under the assumption that the solution of the associated quadratic program is neither optimal nor satisfies the inequality constraints. This is common in embedded control applications, for which rea...

This paper describes a Model Predictive Control (MPC) design for the thermal management of cabin heat in Hybrid Electric Vehicles (HEVs). Due to the augmented complexity of the energy flow in recent energy-efficient vehicles in comparison to conventional vehicles, control degrees of freedom are increased, as many components can achieve the same fun...

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, SMP...

Autonomy is being defined as the capability of a vehicle by means of its on board systems to perform functions without external support. Focusing on stabilization and guidance, in this paper we investigate the use of the Model Predictive Control (MPC) technique as a candidate technology to help bringing more autonomy to future space systems. By mea...

This paper is focused on the theoretical development and the hardware implementation of low-complexity piecewise-affine direct virtual sensors for the estima-tion of unmeasured variables of interest of nonlinear systems. The direct virtual sensor is designed directly from measured inputs and outputs of the system and does not require a dynamical mo...

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 st...

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)...

In this paper we investigate the problem of optimal real-time power dispatch of an interconnection of conventional power generation plants, renewable resources and energy storage systems. The objective is to minimize imbalance costs and maximize profits whilst satisfying user demand. The managing company is able to trade energy on an electricity ma...

Model Predictive Control (MPC) is an optimization-based control strategy that is considered extremely attractive in the autonomous space rendezvous scenarios. The Online Recon¦guration Control System and Avionics Architecture (ORCSAT) study addresses its applicability in Mars Sample Return (MSR) mission, including the implementation of the develope...

This paper proposes two proximal Newton methods for convex nonsmooth optimization problems in composite form. The algorithms are based on a new continuously differentiable exact penalty function, namely the Composite Moreau Envelope. The first algorithm is based on a standard line search strategy, whereas the second one combines the global efficien...

The need for reduced-order approximations of dynamical systems emerges naturally in model-based control of very large-scale systems, such as those arising from the discretisation of partial differential equation models. The controller based on the reduced-order model, when in closed-loop with the large-scale system, ought to endow certain propertie...

This note proposes a method to analyze uniform asymptotic stability and uniform ultimate boundedness of uncertain piecewise affine systems whose dynamics are only defined in a bounded and possibly non-invariant set X of states. The approach relies on introducing fake dynamics outside X and on synthesizing a piecewise affine and possibly discontinuo...

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 i...

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 tailore...

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 steerin...

Results of the ESA project RobMPC (Robust Model Predictive Control for Space Constraint Systems) could successfully demonstrate that model predictive control (MPC) is definitively applicable for space systems with high dynamics like wheeled vehicles exploring a planetary surface. In the context of RobMPC a rover control hierarchy for guidance, traj...

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 propos...

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 design of stabilizing controllers for hybrid systems is particularly challenging due to the heterogeneity present within the system itself. In this paper we propose a constructive procedure to design stabilizing dynamic controllers for a fairly general class of hybrid systems. The proposed technique is based on the concept of a hybrid control L...

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 a...

This paper is concerned with L2-gain optimal control approach for coordinating the active front steering and differential braking to improve vehicle yaw stability and cornering control. The vehicle dynamics with respect to the tire slip angles is formulated and disturbances are added on the front and rear cornering forces characteristics modelling,...

This paper investigates the dynamics of networks of systems achieving rendezvous under linear quadratic optimal control. While the dynamics of rendezvous were studied extensively for the symmetric case, where all systems have exactly the same dynamics (such as simple integrators), this paper investigates the rendezvous dynamics for the general case...

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 pi...

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 on...

In this paper we review a dual fast gradient-projection approach to solving quadratic programming (QP) problems recently proposed in [Patrinos and Bemporad, 2012] that is particularly useful for embedded model predictive control (MPC) of linear systems subject to linear constraints on inputs and states. We show that the method has a computational e...

This paper describes a MATLAB Toolbox for the integrated design of Model Predictive Control (MPC) state-feedback control laws and the digital circuits implementing them. Explicit MPC laws can be designed using optimal and sub-optimal formulations, directly taking into account the specifications of the digital circuit implementing the control law (s...

Model predictive control (MPC) is one of the few advanced control methodologies that have proven to be very successful in real-life applications. An attractive feature of MPC is its capability of explicitly taking state and input constraints into account. Recently, there has been an increasing interest in the usage of MPC schemes to control electri...

In this paper, the numerical algorithm based on conjugate gradient method to solve a finite- horizon min-max optimization problem arising in the H_infinity control of nonlinear systems is presented. The feedback control and disturbance variables are formulated as a linear combination of basis functions. The proposed algorithm, which has a backward-...

This paper investigates stochastic stabilization procedures based on quadratic and piecewise linear Lyapunov functions for discrete-time linear systems affected by multiplicative disturbances and subject to linear constraints on inputs and states. A stochastic model predictive control (SMPC) design approach is proposed to optimize closed-loop perfo...

In this paper, we study the stability of Networked Control Systems (NCSs) that are subject to time-varying transmission intervals, time-varying transmission delays, packet dropouts and communication constraints. The transmission intervals and transmission delays are described by a sequence of continuous random variables. The complexity that the con...

To meet increasingly stringent emission regulations modern internal combustion engines require highly accurate control of the air-to-fuel ratio. The performance of the conventional air-to-fuel ratio feedback loop is limited by the combustion delay between fuel injection and engine exhaust, and by the transport delay for the exhaust gas to propagate...

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...

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 para...

Wireless sensor networks (WSNs) are becoming fundamental components of modern control systems due to their flexibility, ease of deployment and low cost. However, the energy-constrained nature of WSNs poses new issues in control design; in particular the discharge of batteries of sensor nodes, which is mainly due to radio communications, must be tak...

A hierarchical and decentralised model predictive control (DMPC) strategy for drinking water networks (DWN) is proposed. The DWN is partitioned into a set of subnetworks using a partitioning algorithm that makes use of the topology of the network, historic information about the actuator usage and heuristics. A suboptimal DMPC strategy was derived,...

Idle speed control is a landmark application of feedback control in automotive vehicles that continues to be of significant interest to automotive industry practitioners, since improved idle performance and robustness translate into better fuel economy, emissions and drivability. In this paper, we develop a model predictive control (MPC) strategy f...

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 co...

Explicit model predictive controllers computed exactly by multi-parametric optimization techniques often lead to piecewise affine (PWA) state feedback controllers with highly complex and irregular partitionings of the feasible set. In many cases complexity prohibits the implementation of the resulting MPC control law for fast or large-scale system....