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Mazen Alamir

Publications and source records attributed to Mazen Alamir.

At least 37 records · Page 2Linked to original sources
arXiv2020

A new formulation of Economic Model Predictive Control without terminal constraint

In this paper, it is shown that a simple formulation of Economic Model Predictive Control can be used which possesses two features that are generally viewed as mutually exclusive, namely, a rather short prediction horizon (reachability-compatible) on one side, and the absence of final constraint on the other side. The result holds for discrete-time models that are originated from continuous-time models by means of discretization. Practical stability at a small neighborhood of the optimal unknown steady-state pair is shown when some parameters increase and sampling time decreases. A commonly used example is given to illustrate the result.

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arXiv2020

Explicit approximation of stochastic optimal feedback control for combined therapy of cancer

In this paper, a tractable methodology is proposed to approximate stochastic optimal feedback treatment in the context of mixed immuno-chemo therapy of cancer. The method uses a fixed-point value iteration that approximately solves a stochastic dynamic programming-like equation. It is in particular shown that the introduction of a variance-related penalty in the latter induces better results that cope with the consequences of softening the health safety constraints in the cost function. The convergence of the value function iteration is revisited in the presence of the variance related term. The implementation involves some Machine Learning tools in order to represent the optimal function and to perform complexity reduction by clustering. Quantitative illustration is given using a commonly used model of combined therapy involving twelve highly uncertain parameters.

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arXiv2020

The Ockham's razor applied to COVID-19 model fitting French data

This paper presents a data-based simple model for fitting the available data of the Covid-19 pandemic evolution in France. The time series concerning the 13 regions of mainland France have been considered for fitting and validating the model. An extremely simple, two-dimensional model with only two parameters demonstrated to be able to reproduce the time series concerning the number of daily demises caused by Covid-19, the hospitalizations, intensive care and emergency accesses, the daily number of positive test and other indicators, for the different French regions. These results might contribute to stimulate a debate on the suitability of much more complex models for reproducing and forecasting the pandemic evolution since, although relevant from a mechanistic point of view, they could lead to nonidentifiability issues.

stat.AP↗
arXiv2020

On the use of Data-Driven Cost Function Identification in Parametrized NMPC

In this paper, a framework with complete numerical investigation is proposed regarding the feasibility of constrained Nonlinear Model Predictive Control (NMPC) design using Data-Driven model of the cost function. Although the idea is very much in the air, this paper proposes a complete implementation using python modules that are made freely available on a GitHub repository. Moreover, a discussion regarding the different ways of deriving control via data-driven modeling is proposed that can be of interest to practitioners.

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arXiv2020

Probabilistically Certified Region of Attraction of a Tumor Growth Model with Combined Chemo- and Immunotherapy

This paper deals with the estimation of regions of attraction (RoAs) under parametric uncertainties for a cancer growth model with combined therapies. We propose a framework of probabilistic certification, based on the randomized methods, in order to derive probabilistically certified RoAs of a cancer growth model. The model that we consider in this paper describes the interaction between tumor and immune system in presence of a combined chemo- and immunotherapy. Furthermore, we model the concentration of the chemotherapy agent in the body via a pharmacokinetic equation.

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arXiv2018

On the use of supervised clustering in stochastic NMPC design

In this paper, a supervised clustering based-heuristic is proposed for the real-time implementation of approximate solutions to stochastic nonlinear model predictive control frameworks. The key idea is to update on-line a low cardinality set of uncertainty vectors to be used in the expression of the stochastic cost and constraints. These vectors are the centers of uncertainty clusters that are built using the optimal control sequences, cost and constraints indicators as supervision labels. The use of a moving clustering data buffer which accumulates recent past computations enables to reduce the computational burden per sampling period while making available at each period a relevant amount of samples for the clustering task. A relevant example is given to illustrate the contribution and the associated algorithms.

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arXiv2018

Computing control invariant sets in high dimension is easy

In this paper we consider the problem of computing control invariant sets for linear controlled high-dimensional systems with constraints on the input and on the states. Set inclusions conditions for control invariance are presented that involve the N-step sets and are posed in form of linear programming problems. Such conditions allow to overcome the complexity limitation inherent to the set addition and vertices enumeration and can be applied also to high dimensional systems. The efficiency and scalability of the method are illustrated by computing approximations of the maximal control invariant set, based on the 10-step operator, for a system whose state and input dimensions are 30 and 15, respectively.

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arXiv2017

Computing control invariant sets is easy

In this paper we consider the problem of computing control invariant sets for linear controlled systems with constraints on the input and on the states. We focus in particular on the complexity of the computation of the N-step operator, given by the Minkowski addition of sets, that is the basis of many of the iterative procedures for obtaining control invariant sets. Set inclusions conditions for control invariance are presented that involve the N-step sets and are posed in form of linear programming problems. Such conditions are employed in algorithms based on LP problems that allow to overcome the complexity limitation inherent to the set addition and can be applied also to high dimensional systems. The efficiency and scalability of the method are illustrated by computing in less than two seconds an approximation of the maximal control invariant set, based on the 15-step operator, for a system whose state and input dimensions are 20 and 10 respectively.

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arXiv2017

Useful redundancy in parameter and time delay estimation for continuous-time models

This paper proposes an algorithm to estimate the parameters, including time delay, of continuous time systems based on instrumental variable identification methods. To overcome the multiple local minima of the cost function associated with the estimation of a time delay system, we utilise the useful redundancy technique. Specifically, the cost function is filtered through a set of low-pass filters to improve convexity with the useful redundancy technique exploited to achieve convergence to the global minimum of the optimization problem. Numerical examples are presented to demonstrate the effectiveness of the proposed algorithm.

math.ST↗
arXiv2017

Stability proof for nonlinear MPC design using monotonically increasing weighting profiles without terminal constraints

In this note, a new formulation of Model Predictive Control (MPC) framework with no stability-related terminal constraint is proposed and its stability is proved under mild standard assumptions. The novelty in the formulation lies in the use of time-varying monotonically increasing stage cost penalty. The main result is that the $0$-reachability prediction horizon can always be made stabilizing provided that the increasing rate of the penalty is made sufficiently high.

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arXiv2017

Approximate explicit model predictive control via piecewise nonlinear system identification

This article presents an identification methodology to capture general relationships, with application to piecewise nonlinear approximations of model predictive control for constrained (non)linear systems. The mathematical formulation takes, at each iteration, the form of a constrained linear (or quadratic) optimization problem that is mathematically feasible as well as numerically tractable. The efficiency of the devised methodology is demonstrated via two industrial applications. Results suggest the possibility to achieve high approximate precision with limited number of regions, leading to a significant reduction in computation time when compared to the state-of-the-art implicit model predictive control solvers.

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arXiv2016

Output Feedback Control of a Class of Uncertain Systems Under Control-derivative dependent disturbances

This paper addresses the design of robust dynamic output feedback control for highly uncertain systems in which the unknown disturbance might be excited by the derivative of the control input. This context appears in many industrial problems such as the speed control of the hydraulic turbines and the frequency stabilization in micro grids to cite but few examples. A key feature that has to be carefully addressed in this context is that too agressive feedback might lead to the loss of controllability and/or a significant drop in the closed-loop performance. The paper formulates the problem, underlines its relevance and gives a rigorous solution in which a dynamic output feedback is given together with a realistic set of sufficient conditions on the controller's parameters that enable to assess the behavior of the closed-loop under different circumstances. A numerical example is given to illustrate the relevance of the proposed successful design characterization.

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arXiv2016

A New Contraction-Based NMPC Formulation Without Stability-Related terminal Constraints

Contraction-Based Nonlinear Model Predictive Control (NMPC) formulations are attractive because of the generally short prediction horizons they require and the needless use of terminal set computation that are commonly necessary to guarantee stability. However, the inclusion of the contraction constraint in the definition of the underlying optimization problem often leads to non standard features such as the need for multi-step open-loop application of control sequences or the use of multi-step memorization of the contraction level that may induce unfeasibility in presence of unexpected disturbance. This paper proposes a new formulation of contraction-based NMPC in which no contraction constraint is explicitly involved. Convergence of the resulting closed-loop behavior is proved under mild assumptions.

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arXiv2015

A State-Dependent Updating Period For Certified Real-Time Model Predictive Control

In this paper, a state-dependent control updating period framework is proposed that leads to real-time implementable Model Predictive Control with certified practical stability results and constraints satisfaction. The scheme is illustrated and validated using new certification bound that is derived in the case where the Fast Gradient iteration is used through a penalty method to solve generally constrained convex optimization problems. Both the certification bound computation and its use in the state-dependent updating period framework are illustrated in the particular case of linear MPC. An illustrative example involving a chain of four integrators is used to show the explicit computation of the state-dependent control updating scheme.

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arXiv2015

On Probabilistic Certification of Combined Cancer Therapies Using Strongly Uncertain Models

This paper proposes a general framework for probabilistic certification of cancer therapies. The certification is defined in terms of two key issues which are the tumor contraction and the lower admissible bound on the circulating lymphocytes which is viewed as indicator of the patient health. The certification is viewed as the ability to guarantee with a predefined high probability the success of the therapy over a finite horizon despite of the unavoidable high uncertainties affecting the dynamic model that is used to compute the optimal scheduling of drugs injection. The certification paradigm can be viewed as a tool for tuning the treatment parameters and protocols as well as for getting a rational use of limited or expensive drugs. The proposed framework is illustrated using the specific problem of combined immunotherapy/chemotherapy of cancer.

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arXiv2015

NLP Solutions as Asymptotic Values of ODE Trajectories

In this paper, it is shown that the solutions of general differentiable constrained optimization problems can be viewed as asymptotic solutions to sets of Ordinary Differential Equations (ODEs). The construction of the ODE associated to the optimization problem is based on an exact penalty formulation in which the weighting parameter dynamics is coordinated with that of the decision variable so that there is no need to solve a sequence of optimization problems, instead, a single ODE has to be solved using available efficient methods. Examples are given in order to illustrate the results. This includes a novel systematic approach to solve combinatoric optimization problems as well as fast computation of a class of optimization problems using analogic circuits leading to fast, parallel and highly scalable solutions.

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arXiv2014

Experimental Investigation of Control Updating Period Monitoring In Industrial PLC-based Fast MPC: Application to The Constrained Control of a Cryogenic Refrigerator

In this paper, a complete industrial validation of a recently published scheme for on-line adaptation of the control updating period in Model Predictive Control is proposed. The industrial process that serves in the validation is a cryogenic refrigerator that is used to cool the supra-conductors involved in particle accelerators or experimental nuclear reactors. Two recently predicted features are validated: the first states that it is sometimes better to use less efficient (per iteration) optimizer if the lack of efficiency is over-compensated by an increase in the updating control frequency. The second is that for a given solver, it is worth monitoring the control updating period based on the on-line measured behavior of the cost function.

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