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Manfred Morari

Publications and source records attributed to Manfred Morari.

50 records · Page 3Linked to original sources
arXiv2016

A Projected Gradient and Constraint Linearization Method for Nonlinear Model Predictive Control

Projected Gradient Descent denotes a class of iterative methods for solving optimization programs. Its applicability to convex optimization programs has gained significant popularity for its intuitive implementation that involves only simple algebraic operations. In fact, if the projection onto the feasible set is easy to compute, then the method has low complexity. On the other hand, when the problem is nonconvex, e.g. because of nonlinear equality constraints, the projection becomes hard and thus impractical. In this paper, we propose a projected gradient method for Nonlinear Programs (NLPs) that only requires projections onto the linearization of the nonlinear constraints around the current iterate, similarly to Sequential Quadratic Programming (SQP). Although the projection is easier to compute, it makes the intermediate steps unfeasible for the original problem. As a result, the gradient method does not fall either into the projected gradient descent approaches, because the projection is not performed onto the original nonlinear manifold, or into the standard SQP, since second-order information is not used. For nonlinear smooth optimization problems, we analyze the similarities of the proposed method with SQP and assess its local and global convergence to a Karush-Kuhn-Tucker (KKT) point of the original problem. Further, we show that nonlinear Model Predictive Control (MPC) is a promising application of the proposed method, due to the sparsity of the resulting optimization problem. We illustrate the computational efficiency of the proposed method in a numerical example with box constraints on the control input and a quadratic terminal constraint on the state variable.

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arXiv2016

Fast AC Power Flow Optimization using Difference of Convex Functions Programming

An effective means for analyzing the impact of novel operating schemes on power systems is time domain simulation, for example for investigating optimization-based curtailment of renewables to alleviate voltage violations. Traditionally, interior-point methods are used for solving the non-convex AC optimal power flow (OPF) problems arising in this type of simulation. This paper presents an alternative algorithm that better suits the simulation framework, because it can more effectively be warm-started, has linear computational and memory complexity in the problem size per iteration and globally converges to Karush-Kuhn-Tucker (KKT) points with a linear rate if they exist. The algorithm exploits a difference-of-convex-functions reformulation of the OPF problem, which can be performed effectively. Numerical results are presented comparing the method to state-of-the-art OPF solver implementations in MATPOWER, leading to significant speedups compared to the latter.

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arXiv2014

Linear Controller Design for Chance Constrained Systems

This paper is concerned with the design of a linear control law for linear systems 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 a long-run, rather than a finite-horizon operation. The controller synthesis 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, additionally to WSS, 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.

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arXiv2014

A Decomposition Method for Large Scale MILPs, with Performance Guarantees and a Power System Application

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.

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arXiv2014

Automatic Retraction and Full Cycle Operation for a Class of Airborne Wind Energy Generators

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.

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arXiv2014

Efficient evaluation of mp-MIQP solutions using lifting

This paper presents an efficient approach for the evaluation of multi-parametric mixed integer quadratic programming (mp-MIQP) solutions, occurring for instance in control problems involving discrete time hybrid systems with quadratic cost. Traditionally, the online evaluation requires a sequential comparison of piecewise quadratic value functions. As the main contribution, we introduce a lifted parameter space in which the piecewise quadratic value functions become piecewise affine and can be merged to a single value function defined over a single polyhedral partition without any overlaps. This enables efficient point location approaches using a single binary search tree. Numerical experiments include a power electronics application and demonstrate an online speedup up to an order of magnitude. We also show how the achievable online evaluation time can be traded off against the offline computational time.

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arXiv2013

The Scenario Approach for Stochastic Model Predictive Control with Bounds on Closed-Loop Constraint Violations

Many practical applications of control require that constraints on the inputs and states of the system be respected, while optimizing some performance criterion. In the presence of model uncertainties or disturbances, for many control applications it suffices to keep the state constraints at least for a prescribed share of the time, as e.g. in building climate control or load mitigation for wind turbines. For such systems, a new control method of Scenario-Based Model Predictive Control (SCMPC) is presented in this paper. It optimizes the control inputs over a finite horizon, subject to robust constraint satisfaction under a finite number of random scenarios of the uncertainty and/or disturbances. While previous approaches have shown to be conservative (i.e. to stay far below the specified rate of constraint violations), the new method is the first to account for the special structure of the MPC problem in order to significantly reduce the number of scenarios. In combination with a new framework for interpreting the probabilistic constraints as average-in-time, rather than pointwise-in-time, the conservatism is eliminated. The presented method retains the essential advantages of SCMPC, namely the reduced computational complexity and the handling of arbitrary probability distributions. It also allows for adopting sample-and-remove strategies, in order to trade performance against computational complexity.

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arXiv2013

Real-time Optimization and Adaptation of the Crosswind Flight of Tethered Wings for Airborne Wind Energy

Airborne wind energy systems aim to generate renewable energy by means of the aerodynamic lift produced by a wing tethered to the ground and controlled to fly crosswind paths. The problem of maximizing the average power developed by the generator, in presence of limited information on wind speed and direction, is considered. At constant tether speed operation, the power is related to the traction force generated by the wing. First, a study of the traction force is presented for a general path parametrization. In particular, the sensitivity of the traction force on the path parameters is analyzed. Then, the results of this analysis are exploited to design an algorithm to maximize the force, hence the power, in real-time. The algorithm uses only the measured traction force on the tether and it is able to adapt the system's operation to maximize the average force with uncertain and time-varying wind. The influence of inaccurate sensor readings and turbulent wind are also discussed. The presented algorithm is not dependent on a specific hardware setup and can act as an extension of existing control structures. Both numerical simulations and experimental results are presented to highlight the effectiveness of the approach.

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arXiv2013

Automatic crosswind flight of tethered wings for airborne wind energy: modeling, control design and experimental results

An approach to control tethered wings for airborne wind energy is proposed. A fixed length of the lines is considered, and the aim of the control system is to obtain figure-eight crosswind trajectories. The proposed technique is based on the notion of the wing's "velocity angle" and, in contrast with most existing approaches, it does not require a measurement of the wind speed or of the effective wind at the wing's location. Moreover, the proposed approach features few parameters, whose effects on the system's behavior are very intuitive, hence simplifying tuning procedures. A simplified model of the steering dynamics of the wing is derived from first-principle laws, compared with experimental data and used for the control design. The control algorithm is divided into a low-level loop for the velocity angle and a high-level guidance strategy to achieve the desired flight patterns. The robustness of the inner loop is verified analytically, and the overall control system is tested experimentally on a small-scale prototype, with varying wind conditions and using different wings.

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arXiv2013

Policy-based reserves for power systems

This paper introduces the concept of affine reserve policies for accommodating large, fluctuating renewable infeeds in power systems. The approach uses robust optimization with recourse to determine operating rules for power system entities such as generators and storage units. These rules, or policies, establish several hours in advance how these entities are to respond to errors in the prediction of loads and renewable infeeds once their values are discovered. Affine policies consist of a nominal power schedule plus a series of planned linear modifications that depend on the prediction errors that will become known at future times. We describe how to choose optimal affine policies that respect the power network constraints, namely matching supply and demand, respecting transmission line ratings, and the local operating limits of power system entities, for all realizations of the prediction errors. Crucially, these policies are time-coupled, exploiting the spatial and temporal correlation of these prediction errors. Affine policies are compared with existing reserve operation under standard modelling assumptions, and operating cost reductions are reported for a multi-day benchmark study featuring a poorly-predicted wind infeed. Efficient prices for such "policy-based reserves" are derived, and we propose new reserve products that could be traded on electricity markets.

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arXiv2013

Dynamic vehicle redistribution and online price incentives in shared mobility systems

This paper considers a combination of intelligent repositioning decisions and dynamic pricing for the improved operation of shared mobility systems. The approach is applied to London's Barclays Cycle Hire scheme, which the authors have simulated based on historical data. Using model-based predictive control principles, dynamically varying rewards are computed and offered to customers carrying out journeys. The aim is to encourage them to park bicycles at nearby under-used stations, thereby reducing the expected cost of repositioning them using dedicated staff. In parallel, the routes that repositioning staff should take are periodically recomputed using a model-based heuristic. It is shown that a trade-off between reward payouts to customers and the cost of hiring repositioning staff could be made, in order to minimize operating costs for a given desired service level.

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arXiv2013

Embedded Online Optimization for Model Predictive Control at Megahertz Rates

Faster, cheaper, and more power efficient optimization solvers than those currently offered by general-purpose solutions are required for extending the use of model predictive control (MPC) to resource-constrained embedded platforms. We propose several custom computational architectures for different first-order optimization methods that can handle linear-quadratic MPC problems with input, input-rate, and soft state constraints. We provide analysis ensuring the reliable operation of the resulting controller under reduced precision fixed-point arithmetic. Implementation of the proposed architectures in FPGAs shows that satisfactory control performance at a sample rate beyond 1 MHz is achievable even on low-end devices, opening up new possibilities for the application of MPC on embedded systems.

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arXiv2005

An algebraic geometry approach to nonlinear parametric optimization in control

We present a method for nonlinear parametric optimization based on algebraic geometry. The problem to be studied, which arises in optimal control, is to minimize a polynomial function with parameters subject to semialgebraic constraints. The method uses Groebner bases computation in conjunction with the eigenvalue method for solving systems of polynomial equations. In this way, certain companion matrices are constructed off-line. Then, given the parameter value, an on-line algorithm is used to efficiently obtain the optimizer of the original optimization problem in real time.

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