arXiv subjects

Alberto Bemporad

Publications and source records attributed to Alberto Bemporad.

90 records · Page 5Linked to original sources

arXiv2019

Active preference learning based on radial basis functions

This paper proposes a method for solving optimization problems in which the decision-maker cannot evaluate the objective function, but rather can only express a preference such as "this is better than that" between two candidate decision vectors. The algorithm described in this paper aims at reaching the global optimizer by iteratively proposing the decision maker a new comparison to make, based on actively learning a surrogate of the latent (unknown and perhaps unquantifiable) objective function from past sampled decision vectors and pairwise preferences. The surrogate is fit by means of radial basis functions, under the constraint of satisfying, if possible, the preferences expressed by the decision maker on existing samples. The surrogate is used to propose a new sample of the decision vector for comparison with the current best candidate based on two possible criteria: minimize a combination of the surrogate and an inverse weighting distance function to balance between exploitation of the surrogate and exploration of the decision space, or maximize a function related to the probability that the new candidate will be preferred. Compared to active preference learning based on Bayesian optimization, we show that our approach is superior in that, within the same number of comparisons, it approaches the global optimum more closely and is computationally lighter. MATLAB and a Python implementations of the algorithms described in the paper are available at http://cse.lab.imtlucca.it/~bemporad/idwgopt.

cs.LG↗

arXiv2019

Uncertainty-aware demand management of water distribution networks in deregulated energy markets

We present an open-source solution for the operational control of drinking water distribution networks which accounts for the inherent uncertainty in water demand and electricity prices in the day-ahead market of a volatile deregulated economy. As increasingly more energy markets adopt this trading scheme, the operation of drinking water networks requires uncertainty-aware control approaches that mitigate the effect of volatility and result in an economic and safe operation of the network that meets the consumers' need for uninterrupted water supply. We propose the use of scenario-based stochastic model predictive control: an advanced control methodology which comes at a considerable computation cost which is overcome by harnessing the parallelization capabilities of graphics processing units (GPUs) and using a massively parallelizable algorithm based on the accelerated proximal gradient method.

math.OC↗

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.

math.OC↗

arXiv2019

Practical Reinforcement Learning of Stabilizing Economic MPC

Reinforcement Learning (RL) has demonstrated a huge potential in learning optimal policies without any prior knowledge of the process to be controlled. Model Predictive Control (MPC) is a popular control technique which is able to deal with nonlinear dynamics and state and input constraints. The main drawback of MPC is the need of identifying an accurate model, which in many cases cannot be easily obtained. Because of model inaccuracy, MPC can fail at delivering satisfactory closed-loop performance. Using RL to tune the MPC formulation or, conversely, using MPC as a function approximator in RL allows one to combine the advantages of the two techniques. This approach has important advantages, but it requires an adaptation of the existing algorithms. We therefore propose an improved RL algorithm for MPC and test it in simulations on a rather challenging example.

eess.SY↗

arXiv2018

Risk-averse model predictive control

Risk-averse model predictive control (MPC) offers a control framework that allows one to account for ambiguity in the knowledge of the underlying probability distribution and unifies stochastic and worst-case MPC. In this paper we study risk-averse MPC problems for constrained nonlinear Markovian switching systems using generic cost functions, and derive Lyapunov-type risk-averse stability conditions by leveraging the properties of risk-averse dynamic programming operators. We propose a controller design procedure to design risk-averse stabilizing terminal conditions for constrained nonlinear Markovian switching systems. Lastly, we cast the resulting risk-averse optimal control problem in a favorable form which can be solved efficiently and thus deems risk-averse MPC suitable for applications.

math.OC↗

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.

math.OC↗

arXiv2018

A posteriori multi-stage optimal trading under transaction costs and a diversification constraint

This paper presents a simple method for a posteriori (historical) multi-variate multi-stage optimal trading under transaction costs and a diversification constraint. Starting from a given amount of money in some currency, we analyze the stage-wise optimal allocation over a time horizon with potential investments in multiple currencies and various assets. Three variants are discussed, including unconstrained trading frequency, a fixed number of total admissable trades, and the waiting of a specific time-period after every executed trade until the next trade. The developed methods are based on efficient graph generation and consequent graph search, and are evaluated quantitatively on real-world data. The fundamental motivation of this work is preparatory labeling of financial time-series data for supervised machine learning.

q-fin.PM↗

arXiv2017

Stock Trading via Feedback Control: Stochastic Model Predictive or Genetic?

We seek a discussion about the most suitable feedback control structure for stock trading under the consideration of proportional transaction costs. Suitability refers to robustness and performance capability. Both are tested by considering different one-step ahead prediction qualities, including the ideal case, correct prediction of the direction of change in daily stock prices and the worst-case. Feedback control structures are partitioned into two general classes: stochastic model predictive control (SMPC) and genetic. For the former class three controllers are discussed, whereby it is distinguished between two Markowitz- and one dynamic hedging-inspired SMPC formulation. For the latter class five trading algorithms are disucssed, whereby it is distinguished between two different moving average (MA) based, two trading range (TR) based, and one strategy based on historical optimal (HistOpt) trajectories. This paper also gives a preliminary discussion about how modified dynamic hedging-inspired SMPC formulations may serve as alternatives to Markowitz portfolio optimization. The combinations of all of the eight controllers with five different one-step ahead prediction methods are backtested for daily trading of the 30 components of the German stock market index DAX for the time period between November 27, 2015 and November 25, 2016.

cs.CE↗

arXiv2017

Cloud-aided collaborative estimation by ADMM-RLS algorithms for connected vehicle prognostics

As the connectivity of consumer devices is rapidly growing and cloud computing technologies are becoming more widespread, cloud-aided techniques for parameter estimation can be designed to exploit the theoretically unlimited storage memory and computational power of the cloud, while relying on information provided by multiple sources. With the ultimate goal of developing monitoring and diagnostic strategies, this report focuses on the design of a Recursive Least-Squares (RLS) based estimator for identification over a group of devices connected to the cloud. The proposed approach, that relies on Node-to-Cloud-to-Node (N2C2N) transmissions, is designed so that: (i) estimates of the unknown parameters are computed locally and (ii) the local estimates are refined on the cloud. The proposed approach requires minimal changes to local (pre-existing) RLS estimators.

eess.SY↗

arXiv2017

Trajectory Planning Under Vehicle Dimension Constraints Using Sequential Linear Programming

This paper presents a spatial-based trajectory planning method for automated vehicles under actuator, obstacle avoidance, and vehicle dimension constraints. Starting from a nonlinear kinematic bicycle model, vehicle dynamics are transformed to a road-aligned coordinate frame with path along the road centerline replacing time as the dependent variable. Space-varying vehicle dimension constraints are linearized around a reference path to pose convex optimization problems. Such constraints do not require to inflate obstacles by safety-margins and therefore maximize performance in very constrained environments. A sequential linear programming (SLP) algorithm is motivated. A linear program (LP) is solved at each SLP-iteration. The relation between LP formulation and maximum admissible traveling speeds within vehicle tire friction limits is discussed. The proposed method is evaluated in a roomy and in a tight maneuvering driving scenario, whereby a comparison to a semi-analytical clothoid-based path planner is given. Effectiveness is demonstrated particularly for very constrained environments, requiring to account for constraints and planning over the entire obstacle constellation space.

eess.SY↗

arXiv2016

LQG Online Learning

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 is a non-trivial variation as it involves random matrices, are investigated. The obtained optimal solutions are compared with the Kalman-filter estimate of the parameter vector to be learned. It is shown that the proposed algorithm is less sensitive to outliers with respect to the Kalman estimate (thanks to the presence of the regularization term), thus providing smoother estimates with respect to time. The basic formulation of the proposed online-learning framework refers to a discrete-time setting with a finite learning horizon and a linear model. Various extensions are investigated, including the infinite learning horizon and, via the so-called "kernel trick", the case of nonlinear models.

math.OC↗

arXiv2016

Stochastic economic model predictive control for Markovian switching systems

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 formulations for nonlinear Markovian switching systems which guarantee recursive feasibility, asymptotic performance bounds and constrained mean square (MS) stability.

math.OC↗

arXiv2016

GPU-accelerated stochastic predictive control of drinking water networks

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 operations. The proposed methodology is applied and validated on a case study: the water network of the city of Barcelona.

math.OC↗

arXiv2015

A Simple Effective Heuristic for Embedded Mixed-Integer Quadratic Programming

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 on a variation of the alternating direction method of multipliers (ADMM), an algorithm for solving convex optimization problems. We discuss the favorable computational aspects of our algorithm, which allow it to run quickly even on very modest computational platforms such as embedded processors. We give several examples for which an approximate solution should be found very quickly, such as management of a hybrid-electric vehicle drivetrain and control of switched-mode power converters. Our numerical experiments suggest that our method is very effective in finding a feasible point with small objective value; indeed, we find that in many cases, it finds the global solution.

math.OC↗

arXiv2015

A Convex Feasibility Approach to Anytime Model Predictive Control

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 novel and very easy-to-implement convex feasibility solver proposed in the paper, it is possible to run an outer performance optimization algorithm on top of the feasibility solver and optimize for an amount of time that depends on the available CPU resources within the current sampling step (possibly going open-loop at a given sampling step in the extreme case no resources are available) and still guarantee convergence to the terminal set. While the MPC setup and the solver proposed in the paper can deal with quite general classes of functions, we highlight the synthesis method and show numerical results in case of linear MPC and ellipsoidal and polyhedral terminal sets.

eess.SY↗

arXiv2015

Fixed-Point Constrained Model Predictive Control of Spacecraft Attitude

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 an online optimization algorithm for the solution of the Quadratic Programming problem which is tailored to run in fixed-point arithmetic. Simulations on a nonlinear spacecraft model demonstrate that the MPC controller achieves good tracking performance while satisfying reaction wheel torque constraints. The controller also has low computational complexity and is suitable for implementation in spacecrafts with fixed-point processors.

math.OC↗

arXiv2014

Douglas-Rachford Splitting: Complexity Estimates and Accelerated Variants

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. By proving the equivalence between the Douglas-Rachford splitting method and a scaled gradient method applied to the DRE, results from smooth unconstrained optimization are employed to analyze convergence properties of DRS, to tune the method and to derive an accelerated version of it.

math.OC↗

arXiv2014

Forward-backward truncated Newton methods for convex composite optimization

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.

math.OC↗