[Show abstract][Hide abstract] ABSTRACT: Lagrangian duality in mixed integer optimization is a useful framework for
problems decomposition and for producing tight lower bounds to the optimal
objective, but in contrast to the convex counterpart, it is generally unable to
produce optimal solutions directly. In fact, solutions recovered from the dual
may be not only suboptimal, but even infeasible. In this paper we concentrate
on large scale mixed--integer programs with a specific structure that is of
practical interest, as it appears in a variety of application domains such as
power systems or supply chain management. We propose a solution method for
these structures, in which the primal problem is modified in a certain way,
guaranteeing that the solutions produced by the corresponding dual are feasible
for the original unmodified primal problem. The modification is simple to
implement and the method is amenable to distributed computations. We also
demonstrate that the quality of the solutions recovered using our procedure
improves as the problem size increases, making it particularly useful for large
scale instances for which commercial solvers are inadequate. We illustrate the
efficacy of our method with extensive experimentations on a problem stemming
from power systems.
[Show abstract][Hide abstract] ABSTRACT: An adaptive control algorithm for open-loop stable, constrained, linear, multiple input multiple output systems is presented. The proposed approach can deal with both input and output constraints, as well as measurement noise and output disturbances. The adaptive controller consists of an iterative set membership identification algorithm, that provides a set of candidate plant models at each time step, and a model predictive controller, that enforces input and output constraints for all the plants inside the model set. The algorithm relies only on the solution of standard convex optimization problems that are guaranteed to be recursively feasible. The experimental results obtained by applying the proposed controller to a quad-tank testbed are presented.
[Show abstract][Hide abstract] ABSTRACT: This paper is concerned with the design of a linear control law for a linear system with stationary additive disturbances. The objective is to find a state feedback gain that minimizes a quadratic stage cost function, while observing chance constraints on the input and/or the state. Unlike most of the previous literature, the chance constraints (and the stage cost) are not considered on each input/state of the transient response. Instead, they refer to the input/state of the closed-loop system in its stationary mode of operation. Hence the control is optimized for the long-run, rather than for finite-horizon operation. The controller synthesis problem can be cast as a convex semi-definite program (SDP). The chance constraints appear as linear matrix inequalities. Both single chance constraints (SCCs) and joint chance constraints (JCCs) on the input and/or the state can be included. If the disturbance is Gaussian, this information can be used to improve the controller design. The presented approach can also be extended to the case of output feedback. The entire design procedure is flexible and easy to implement, as demonstrated on a short illustrative example.
[Show abstract][Hide abstract] ABSTRACT: The problem of experiment design for constrained linear systems with multiple inputs is addressed. A parametric model of the system is considered. The presented theoretical results provide a guideline on how to design experiments that minimize the worst-case identification error, as measured by the radius of information of the set of feasible model parameters, calculated in any norm. In addition, it is shown that an alternative, simpler approach can be employed when input constraints are symmetric and the worst-case identification error is minimized in either - or -norm. For such cases, on the basis of the derived results, a computationally tractable algorithm for the experiment design is proposed. The presented results are valid for a general model representation, which admits the commonly used finite impulse response model as a special case. The features of the presented method are illustrated in a numerical example.
[Show abstract][Hide abstract] ABSTRACT: Neuromodulation of spinal sensorimotor circuits improves motor control in animal models and humans with spinal cord injury. With common neuromodulation devices, electrical stimulation parameters are tuned manually and remain constant during movement. We developed a mechanistic framework to optimize neuromodulation in real time to achieve high-fidelity control of leg kinematics during locomotion in rats. We first uncovered relationships between neuromodulation parameters and recruitment of distinct sensorimotor circuits, resulting in predictive adjustments of leg kinematics. Second, we established a technological platform with embedded control policies that integrated robust movement feedback and feed-forward control loops in real time. These developments allowed us to conceive a neuroprosthetic system that controlled a broad range of foot trajectories during continuous locomotion in paralyzed rats. Animals with complete spinal cord injury performed more than 1000 successive steps without failure, and were able to climb staircases of various heights and lengths with precision and fluidity. Beyond therapeutic potential, these findings provide a conceptual and technical framework to personalize neuromodulation treatments for other neurological disorders.
Science translational medicine 09/2014; 6(255):255ra133. · 10.76 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Airborne wind energy systems aim to harvest the power of winds blowing at
altitudes higher than what conventional wind turbines reach. They employ a
tethered flying structure, usually a wing, and exploit the aerodynamic lift to
produce electrical power. In the case of ground-based systems, where the
traction force on the tether is used to drive a generator on the ground, a two
phase power cycle is carried out: one phase to produce power, where the tether
is reeled out under high traction force, and a second phase where the tether is
recoiled under minimal load. The problem of controlling a tethered wing in this
second phase, the retraction phase, is addressed here, by proposing two
possible control strategies. Theoretical analyses, numerical simulations, and
experimental results are presented to show the performance of the two
approaches. Finally, the experimental results of complete autonomous power
generation cycles are reported and compared with first-principle models.
[Show abstract][Hide abstract] ABSTRACT: Predictive control of hybrid systems is currently considered prohibitive using embedded computing platforms. To overcome this limitation for mixed logical dynamical systems of small to medium size, we propose to use 1) a standard branch-and-bound approach combined with a fast embedded interior point solver, 2) pre-processing heuristics, run once and offline, to significantly reduce the number of subproblems to be solved, and 3) relaxations of the original MPC problem that allow a trade off between computation time and closed-loop performance. A problem-specific ANSI C implementation of the proposed method can be automatically generated, and has a fixed memory footprint and a code size that is insignificantly larger than that of the subproblem solver. Two extensive numerical studies are presented, where problems with up to 60 binary variables are solved in less than 0.2 seconds with a performance deterioration of below 2 % when compared to an optimal MPC scheme.
Computers & Chemical Engineering 07/2014; · 2.09 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The recent increase in popularity of shared mobility systems, in which users take a bicycle or car from a geographically-dispersed public pool in order to complete part of a journey, is due in part to improved technologies for tracking and billing customer journeys. In many schemes, a customer can start and end a journey at different docking stations and is billed according to a set fee structure. However, a given system generally becomes imbalanced due to asymmetry of demand for such “one-way” services across the system and throughout the day, and the resulting cost of employing staff to redistribute the system's vehicles is significant. This paper describes how dynamic customer prices, varying geographically as a function of the current and expected future state of the system, could be used as control signals to improve service rates. Such signals could be communicated to customers using existing ICT infrastructure. We show, using an agent-based model parameterized with historical data from London's Barclays Cycle Hire scheme, that simple proportional price control rules can improve service rates without the need to resort to conventional bike redistribution staff. In addition we analyze the performance obtained and discuss system design issues.
[Show abstract][Hide abstract] ABSTRACT: While rule based control (RBC) is current practice in most building automation systems that issue discrete control signals, recent simulation studies suggest that advanced, optimization based control methods such as hybrid model predictive control (HMPC) can potentially outperform RBC in terms of energy efficiency and occupancy comfort. However, HMPC requires a more complex IT infrastructure and numerical optimization in the loop, which makes commissioning, operation of the building, and error handling significantly more involved than in the rule based setting. In this paper, we suggest an automated RBC synthesis procedure for binary decisions that extracts prevalent information from simulation data with HMPC controllers. The result is a set of simple decision rules that preserves much of the control performance of HMPC. The methods are based on standard machine learning algorithms, in particular support vector machines (SVMs) and adaptive boosting (AdaBoost). We consider also the ranking and selection of measurements which are used for a decision and show that this feature selection is useful in both complexity reduction and reduction of investment costs by pruning unnecessary sensors. The suggested methods are evaluated in simulation for six different case studies and shown to maintain the performance of HMPC despite a tremendous reduction in complexity.
Journal of Process Control 06/2014; · 2.18 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Model predictive control (MPC) is a promising alternative in building control with the potential to improve energy efficiency and comfort and to enable demand response capabilities. Creating an accurate building model that is simple enough to allow the resulting MPC problem to be tractable is a challenging but crucial task in the control development. In this paper we introduce the Building Resistance-Capacitance Modeling (BRCM) Matlab Toolbox that facilitates the physical modeling of buildings for MPC. The Toolbox provides a means for the fast generation of (bi-)linear resistance-capacitance type models from basic building geometry, construction and systems data. Moreover, it supports the generation of the corresponding potentially time-varying costs and constraints. The Toolbox is based on previously validated modeling principles. In a case study a BRCM model was automatically generated from an EnergyPlus input data file and its predictive capabilities were compared to the EnergyPlus model. The Toolbox itself, the details of the modeling and the documentation can be found at www.brcm.ethz.ch.
2014 American Control Conference - ACC 2014; 06/2014
[Show abstract][Hide abstract] ABSTRACT: This paper considers model predictive control (MPC) of switched mode power converters and uses a hybrid prediction model that represents the switching ripple of the converter state. The goal of the approach is to achieve both high dynamic performance and low harmonic distortion of the output at steady state. It is argued that the previously published approaches to hybrid MPC of power converters are sensitive to plant/model mismatch, and an alternative problem formulation is suggested. The new formulation describes the converter state in terms of dynamic Fourier coefficients. This allows to quantify and feed back more information about the switched converter waveform, and can thus reduce the dependence on the system model. The suggested approach is evaluated in both simulation and experiment, and it is shown to be less sensitive to plant/model mismatch than approaches from the literature. Index Terms— Dynamic phasor, LCL filter, model predictive control (MPC), optimal pulsewidth modulation (PWM), switched mode power converter, voltage source inverter.
Control Systems Technology, IEEE Transactions on 05/2014; 1. · 1.86 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Soft constrained model predictive control (MPC) is frequently applied in practice in order to ensure feasibility of the optimization during online operation. Standard techniques offer global feasibility by relaxing state or output constraints, but cannot ensure closed-loop stability. This paper presents a new soft constrained MPC approach for tracking that provides stability guarantees even for unstable systems. Two types of soft constraints and slack variables are proposed to enlarge the terminal constraint and relax the state constraints. The approach ensures feasibility of the MPC problem in a large region of the state space, depending on the imposed hard constraints, and stability is guaranteed by design. The optimal performance of the MPC control law is preserved whenever all state constraints can be enforced. Asymptotic stability of all feasible reference steady-states under the proposed control law is shown, as well as input-to-state stability for the system under additive disturbances. The soft constrained method can be combined with a robust MPC approach, in order to exploit the benefits of both techniques. The properties of the proposed methods are illustrated by numerical examples.
IEEE Transactions on Automatic Control 02/2014; 59(5):1190 - 1202. · 2.72 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A hierarchical and decentralized model predictive control scheme is proposed for the fast tracking of active and reactive power references of HVDC systems. The objective is to exploit optimally the system actuation and dynamics to improve power quality, provide voltage support and stabilize the grid. The system constraints are incorporated into the formulation to keep the system within its admissible operating range during all transients. At the high level, two HVDC line model predictive controllers deal with the dc system objectives by manipulating the power references that are given to two low-level ac current model predictive controllers that manipulate the voltage-source-inverter duty cycles. The proposed formulation is suitable for fast implementation and its performance is verified in simulation.
IEEE Transactions on Power Delivery 02/2014; 29(1):462-471. · 1.52 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A novel stereoscopic image acquisition setup and a procedure for measuring multidimensional particle size distributions (nD PSDs) during crystallization based on image analysis are presented. Images of crystals in suspension passing a flow through cell are generated by two cameras which are arranged in an orthogonal manner. Particles are conveyed to the flow through cell using a sampling loop, thus allowing for online monitoring. Automated image analysis provides contour data which can be used to classify crystals into different generic particle model classes. For each type of particle size data is calculated and stored. Finally, time resolved nD PSD data can be calculated. The accuracy of this novel size measurement was confirmed by comparison to measurements obtained with a Coulter Multisizer. The non-invasive nature and repeatability of experiments are shown by monitoring populations of sodium chloride and of the β polymorph of l-glutamic acid under different conditions. Finally, crystal growth of acetaminophen during cooling crystallization is shown. In addition, a virtual test bench is used to study the measurement method in silico.
Chemical Engineering Science 02/2014; 105:155–168. · 2.61 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: High-speed applications impose a hard real-time constraint on the solution of a model predictive control (MPC) problem, which generally prevents the computation of the optimal control input. As a result, in most MPC implementations guarantees on feasibility and stability are sacrificed in order to achieve a real-time setting. In this paper we develop a real-time MPC approach for linear systems that provides these guarantees for arbitrary time constraints, allowing one to trade off computation time vs. performance. Stability is guaranteed by means of a constraint, enforcing that the resulting suboptimal MPC cost is a Lyapunov function. The key is then to guarantee feasibility in real-time, which is achieved by the proposed algorithm through a warm-starting technique in combination with robust MPC design. We address both regulation and tracking of piecewise constant references. As a main contribution of this paper, a new warm-start procedure together with a Lyapunov function for real-time tracking is presented. In addition to providing strong theoretical guarantees, the proposed method can be implemented at high sampling rates. Simulation examples demonstrate the effectiveness of the real-time scheme and show that computation times in the millisecond range can be achieved.