Naly Rakoto-Ravalontsalama

A polynomial approach for stability analysis of switched systems

A polynomial approach to deal with the stability analysis of switched non-linear systems under arbitrary switching using dissipation inequalities is presented. It is shown that a representation of the original switched problem into a continuous polynomial system allows us to use dissipation inequalities for the stability analysis of polynomial systems. With this method and from a theoretical point of view, we provide an alternative way to search for a common Lyapunov function for switched non-linear systems.

Optimal Control of Switched Systems: A Polynomial Approach

Abstract A polynomial approach to solve the optimal control problem of switched systems is presented. It is shown that the representation of the original switched problem into a continuous polynomial systems allow us to use the method of moments. With this method and from a theoretical point of view, we provide necessary and sufficient conditions for the existence of minimizer by using particular features of the minimizer of its relaxed, convex formulation. Even in the absence of classical minimizers of the switched system, the solution of its relaxed formulation provide minimizers.

MLD control of hybrid systems: application to the three tank benchmark problem

This paper presents a solution of the three tank benchmark problem modeled using the Mixed Logical and Dynamical (MLD) system framework and controlled using model predictive control (MPC). Compared to the existing works using the same approach, this work is different in the Mixed Integer Quadratic Programming, especially in the tuning method of the weighting matrices.

Supervision and optimal control of a class of industrial processes

This paper presents a methodological approach of supervision and optimal control of some industrial processes. The modeling formalism used mixed logical and dynamical (MLD) systems framework, and it is used for obtaining a model predictive control (MPC) scheme. The methodology is applied to a water treatment plant in Bogota, Columbia and some preliminary results are presented.

Distributed building temperature control with power constraints

Generally, heating, cooling and air conditioning (HVAC) systems are designed to handle worst case loads, and this over-design of HVAC equipment is one of the main reasons for building energy inefficiency. When the HVAC system is not over-designed, there exists a trade-off between the comfort of the buildings occupants and the available heating/cooling power at critical load hours. We propose a distributed approach that maximizes the comfort of the buildings occupants under several power constraints. We prove by means of graph theoretical tools and passivity analysis, that the proposed controller asymptotically reaches an optimal equilibrium without the need of full information. Finally, some simulations and comparisons are presented to illustrate the performance of our method.

Modeling and control of a water treatment plant

This work presents some results in hybrid modeling and control of a drinking water treatment plant. The work is focused in modeling of the filtering sub-process using the mixed logical and dynamical (MLD) systems, this framework that is able to represent continuous dynamics and discrete-event dynamics in an integrated form. The resultant system is well-posed for model predictive control (MPC) that is used as control strategy for the system.

An Evolutionary Game Theory Approach to Modeling VMI Policies

The strategy of integration known as VMI (Vendor-Managed Inventory) allows the coordination of inventory policies between producers and buyers in supply chains. Based on a new proposed model for the implementation of VMI in a chain of two links composed of a producer and a buyer, this paper studies the evolution of individual strategies of the producer and the buyer by a formalism derived from the theory of evolutionary games. The conditions that determine the stability of evolutionarily stable strategies are derived and analyzed. Work results specify analytical conditions that favor the implementation of VMI on traditional chains without VMI.

Stability analysis of switched polynomial systems using dissipation inequalities

A polynomial approach to deal with stability analysis of polynomial switched systems, i.e., polynomial continuous systems with switching signals, using dissipation inequalities under arbitrary switching is presented. It is shown that the representation of the original switched problem into a continuous polynomial systems allows us to use the dissipation inequality for polynomial systems. With this method and from a theoretical point of view, we provide an alternative way to search for a common Lyapunov function for switched systems.

Probing Control for PWL Approximation of Nonlinear Cellular Growth

In this paper we develop and improve a piecewise-linear approximations of nonlinear cellular growth using orthonormal canonical piecewise linear functions (Julian et al., 2000), and it is tested by a probing control strategy (Akesson et al.)for the feed rate. The work is with the mammalian cells BHK (baby hamster kidney) in bioreactor in batch, fed-batch and continuous mode operation. Preliminary results show that this piecewise linear approximation is well suited for modeling such nonlinear dynamics.

Distributed resource allocation over stochastic networks: An application in smart grids

This paper focuses on an important problem involving distributed decision making, the optimal resource allocation in a network of agents. To address this problem, we explore a consensus-based algorithm that does not require any centralized computation. We use stochastic semistability theory to analyze the case when the communication network used by the agents to coordinate their decisions is not completely reliable, i.e., communication links are subject to a random failure process that is modeled by a continuous-time Markov chain. Some results on fault tolerance and optimality of the considered algorithm are provided. Finally, we present an application of the method to the distributed management of the customers of an aggregating entity in a smart grid environment.