Grégory François

Optimal Service Pricing for a Cloud Cache

Cloud applications that offer data management services are emerging. Such clouds support caching of data in order to provide quality query services. The users can query the cloud data, paying the price for the infrastructure they use. Cloud management necessitates an economy that manages the service of multiple users in an efficient, but also, resource-economic way that allows for cloud profit. Naturally, the maximization of cloud profit given some guarantees for user satisfaction presumes an appropriate price-demand model that enables optimal pricing of query services. The model should be plausible in that it reflects the correlation of cache structures involved in the queries. Optimal pricing is achieved based on a dynamic pricing scheme that adapts to time changes. This paper proposes a novel price-demand model designed for a cloud cache and a dynamic pricing scheme for queries executed in the cloud cache. The pricing solution employs a novel method that estimates the correlations of the cache services in an time-efficient manner. The experimental study shows the efficiency of the solution.

Comparison of Gradient Estimation Methods for Real-time Optimization

Various real-time optimization techniques proceed by controlling the gradient to zero. These methods primarily differ in the way the gradient is estimated. This paper compares various gradient estimation methods. It is argued that methods with model-based gradient estimation converge faster but can be inaccurate in the presence of plant-model mismatch. In contrast, model-free methods are accurate but typically take longer to converge.

Real-Time Optimization for Kites

Over the past decade, a large number of academics and start-ups have devoted them- selves to developing kites, or airplanes on tethers, as a renewable energy source. Determining the trajectories the kite should follow is a modeling and optimization challenge. We present a dynamic model and analyse how uncertainty affects the resulting optimization problem. We show how measurements can be used to rapidly correct the model-based optimal trajectories in real time. This novel real-time optimization approach does not rely on intensive online computation. Rather, it uses knowledge of the structure of the optimal solution, which can be studied offline.

Measurement-Based Real-Time Optimization of Chemical Processes

This chapter presents recent developments in the field of process optimization. In the presence of uncertainty in the form of plant-model mismatch and process disturbances, the standard model-based optimization techniques might not achieve optimality for the real process or, worse, they might violate some of the process constraints. To avoid constraints violations, a potentially large amount of conservatism is generally introduced, thus leading to sub-optimal performance. Fortunately, process measurements can be used to reduce this sub-optimality, while guaranteeing satisfaction of process constraints. Measurement-based optimization schemes can be classified depending on the way measurements are used to compensate the effect of uncertainty. Three classes of measurement-based real-time optimization methods are discussed and compared. Finally, four representative application problems are presented and solved using some of the proposed real-time optimization schemes.

Convergence analysis of run-to-run control for a class of nonlinear systems

In run-to-run control, measurements from previous runs are used to push the outputs of the current run towards desired set points. From a run-to-run perspective, the classical dynamics get integrated by each run, thereby leading to static nonlinear input-output map. This paper shows that, when successive linearization of this nonlinear map is used to adapt the run-to-run controller, convergence may not be achieved. However, convergence can be guaranteed of the controller is based on a linear approximation for which the outputs are in-phase (i.e., within 90/spl deg/) with the true outputs. A convergence proof based on Lyapunov approach is provided. The theoretical aspects are illustrated through the simulated meal-to-meal control of blood glucose concentration in diabetic patients.

Input Filter Design for Feasibility in Constraint-Adaptation Schemes

The subject of real-time, steady-state optimization under significant uncertainty is addressed in this paper. Specifically, the use of constraint-adaptation schemes is reviewed, and it is shown that, in general, such schemes cannot guarantee process feasibility over the relevant input space during the iterative process. This issue is addressed via the design of a feasibility-guaranteeing input filter, which is easily derived through the use of a Lipschitz bound on the plant behavior.While the proposed approach works to guarantee feasibility for the single-constraint case, early sub-optimal convergence is noted for cases with multiple constraints. In this latter scenario, some constraint violations must be accepted if convergence to the optimum is desired. An illustrative example is given to demonstrate these points.

Run-to-Run MPC Tuning via Gradient Descent

A gradient-descent method for the run-to-run tuning of MPC controllers is proposed. It is shown that, with an assumption on process repeatability, the MPC tuning parameters may be brought to a locally optimal set. SISO and MIMO examples illustrate the characteristics of the proposed approach.

Exploiting local quasiconvexity for gradient estimation in modifier-adaptation schemes

A new approach for gradient estimation in the context of real-time optimization under uncertainty is proposed in this paper. While this estimation problem is often a difficult one, it is shown that it can be simplified significantly if an assumption on the local quasiconvexity of the process is made and the resulting constraints on the gradient are exploited. To do this, the estimation problem is formulated as a constrained weighted least-squares problem with appropriate choice of the weights. Two numerical examples illustrate the effectiveness of the proposed method in converging to the true process optimum, even in the case of significant measurement noise.

A therapy parameter-based model for predicting blood glucose concentrations in patients with type 1 diabetes

In this paper, the problem of predicting blood glucose concentrations (BG) for the treatment of patients with type 1 diabetes, is addressed. Predicting BG is of very high importance as most treatments, which consist in exogenous insulin injections, rely on the availability of BG predictions. Many models that can be used for predicting BG are available in the literature. However, it is widely admitted that it is almost impossible to perfectly model blood glucose dynamics while still being able to identify model parameters using only blood glucose measurements. The main contribution of this work is to propose a simple and identifiable linear dynamical model, which is based on the static prediction model of standard therapy. It is shown that the model parameters are intrinsically correlated with physician-set therapy parameters and that the reduction of the number of model parameters to identify leads to inferior data fits but to equivalent or slightly improved prediction capabilities compared to state-of-the-art models: a sign of an appropriate model structure and superior reliability. The validation of the proposed dynamic model is performed using data from the UVa simulator and real clinical data, and potential uses of the proposed model for state estimation and BG control are discussed.

Directional real-time optimization applied to a kite-control simulation benchmark

This paper applies a novel two-layer optimizing control scheme to a kite-control benchmark problem. The upper layer is a recent real-time optimization algorithm, called Directional Modifier Adaptation, which represents a variation of the popular Modifier Adaptation algorithm. The lower layer consists of a path-following controller that can follow arbitrary paths. Application to a challenging benchmark scenario in simulation shows that this two-layer scheme is capable of substantially improving the performance of a complex system affected by significant stochastic disturbances, measurement noise and plant-model mismatch, while respecting operational constraints.