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

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.Comment: Submitted to Journal of theoretical Biolog

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.Comment: Submitted to Automatic

Monitoring Control Updating Period In Fast Gradient Based NMPC

In this paper, a method is proposed for on-line monitoring of the control updating period in fast-gradient-based Model Predictive Control (MPC) schemes. Such schemes are currently under intense investigation as a way to accommodate for real-time requirements when dealing with systems showing fast dynamics. The method needs cheap computations that use the algorithm on-line behavior in order to recover the optimal updating period in terms of cost function decrease. A simple example of constrained triple integrator is used to illustrate the proposed method and to assess its efficiency.Comment: 6 pages, 8 Figure

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.Comment: accepted in short version IFAC Nolcos 2016. submitted to Automatica as a technical communiqu

The effect of debt on corporate profitability : Evidence from French service sector

Current study aims to provide new empirical evidence on the impact of debt on corporate profitability. This impact can be explained by three essential theories: signaling theory, tax theory and the agency cost theory. Using panel data sample of 2240 French non listed companies of service sector during 1999-2006. By utilizing generalized method of moments (GMM) econometric technique on three measures of profitability ratio (PROF1, PROF2 and ROA), we show that debt ratio has no effect on corporate profitability, regardless of the size of company (VSEs, SMEs or LEs

On Adaptive Measurement Inclusion Rate In Real-Time Moving-Horizon Observers

This paper investigates a self adaptation mechanism regarding the rate with which new measurements have to be incorporated in Moving-Horizon state estimation algorithms. This investigation can be viewed as the dual of the one proposed by the author in the context of real-time model predictive control. An illustrative example is provided in order to assess the relevance of the proposed updating rule.Comment: 6 pages. 4 Figure