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

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

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

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

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.Comment: arXiv admin note: substantial text overlap with arXiv:1708.0479

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

Probing quantum transport by engineering correlations in a speckle potential

We develop a procedure to modify the correlations of a speckle potential. This procedure, that is suitable for spatial light modulator devices, allows one to increase the localization efficiency of the speckle in a narrow energy region whose position can be easily tuned. This peculiar energy-dependent localization behavior is explored by pulling the potential through a cigar-shaped Bose-Einstein condensate. We show that the percentage of dragged atoms as a function of the pulling velocity depends on the potential correlations below a threshold of the disorder strength. Above this threshold, interference effects are no longer clearly observable during the condensate drag.Comment: 8 pages, 8 figures, final versio