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We propose an extended method for experiment design in nonlinear state space models. The proposed input design technique optimizes a scalar cost function of the information matrix, by computing the optimal stationary probability mass function (pmf) from which an input sequence is sampled. The feasible set of the stationary pmf is a polytope, allowing it to be expressed as a convex combination of its extreme points. The extreme points in the feasible set of pmf's can be computed using graph theory. Therefore, the final information matrix can be approximated as a convex combination of the information matrices associated with each extreme point. For nonlinear systems, the information matrices for each extreme point can be computed by using particle methods. Numerical examples show that the proposed technique can be successfully employed for experiment design in nonlinear systems., Comment: Accepted for publication in the 19th World Congress of the International Federation of Automatic Control, Cape Town, South Africa. Six pages, three figures

International audience; We derive in a straightforward way the null controllability of a 1-D heat equation with boundary control. We use the so-called {\em flatness approach}, which consists in parameterizing the solution and the control by the derivatives of a "flat output". This provides an explicit control law achieving the exact steering to zero. We also give accurate error estimates when the various series involved are replaced by their partial sums, which is paramount for an actual numerical scheme. Numerical experiments demonstrate the relevance of the approach.

International audience; This paper presents an energy estimate in terms of the total variation of the control for bilinear infinite dimensional quantum systems with unbounded potentials. These estimates allow a rigorous construction of propagators associated with controls of bounded variation. Moreover, upper bounds of the error made when replacing the infinite dimensional system by its finite dimensional Galerkin approximations is presented.

International audience; We consider the chemostat model with the substrate concentration as the single measurement. We propose a control strategy that drives the system at a steady state maximizing the gas production without the knowledge of the specific growth rate. Our approach separates the extremum seeking problem from the feedback control problem such that each of the two subproblems can be solved with relatively simple algorithms. We are then free to choose any numerical optimization algorithm. We give a demonstration for two choices: one is based on slow-fast dynamics and numerical continuation, the other is a combination of golden-section and Newton iteration. The method copes with non-monotonic growth functions.

Capturing disused satellites in orbit and their controlled reentry is the aim of the DEOS space mission. Satellites that ran out of fuel or got damaged pose a threat to working projects in orbit. Additionally, the reentry of such objects endangers the population as the place of impact cannot be controlled anymore. This paper demonstrates the modelling of a rendezvous szenario between a controlled service satellite and an uncontrolled target. The situation is modelled via first order ordinary differental equations where a stable target is considered. In order to prevent a collision of the two spacecrafts and to ensure both satellites are docked at the end of the maneuver, additional state constraints, box contraints for the control and a time dependent rendezvous condition for the final time are added. The problem is formulated as an optimal control problem with Bolza type cost functional and solved using a full discretization approach in AMPL/IpOpt. Last, simulation results for capturing a tumbling satellite are given., 6 pages, 4 figures

This paper presents an algorithm for computing inner estimates of the regions of attraction of limit cycles of a nonlinear hybrid system. The basic procedure is: (1) compute the dynamics of the system transverse to the limit cycle; (2) from the linearization of the transverse dynamics construct a quadratic candidate Lyapunov function; (3) search for a new Lyapunov function verifying maximal regions of orbital stability via iterated of sum-of-squares programs. The construction of the transverse dynamics is novel, and valid for a broad class of nonlinear hybrid systems. The problem of stabilization of unstable limit cycles will also be addressed, and a solution given based on stabilization of the transverse linearization.

This paper illustrates the application of recent research in region-of-attraction analysis for nonlinear hybrid limit cycles. Three example systems are analyzed in detail: the van der Pol oscillator, the “rimless wheel”, and the “compass gait”, the latter two being simplified models of underactuated walking robots. The method used involves decomposition of the dynamics about the target cycle into tangential and transverse components, and a search for a Lyapunov function in the transverse dynamics using sum-of-squares analysis (semidefinite programming). Each example illuminates different aspects of the procedure, including optimization of transversal surfaces, the handling of impact maps, optimization of the Lyapunov function, and orbitally-stabilizing control design.

The electrical power network is a critical infrastructure in today's society, so its safe and reliable operation is of major concern. State estimators are commonly used in power networks, for example, to detect faulty equipment and to optimally route power flows. The estimators are often located in control centers, to which large numbers of measurements are sent over unencrypted communication channels. Therefore cyber security for state estimators becomes an important issue. In this paper we analyze the cyber security of state estimators in supervisory control and data acquisition (SCADA) for energy management systems (EMS) operating the power network. Current EMS state estimation algorithms have bad data detection (BDD) schemes to detect outliers in the measurement data. Such schemes are based on high measurement redundancy. Although these methods may detect a set of basic cyber attacks, they may fail in the presence of an intelligent attacker. We explore the latter by considering scenarios where stealthy deception attacks are performed by sending false information to the control center. We begin by presenting a recent framework that characterizes the attack as an optimization problem with the objective specified through a security metric and constraints corresponding to the attack cost. The framework is used to conduct realistic experiments on a state-of-the-art SCADA EMS software for a power network example with 14 substations, 27 buses, and 40 branches. The results indicate how state estimators for power networks can be made more resilient to cyber security attacks., Comment: Modified version submitted to the 18th IFAC World Congress, 2011. The paper has 11 pages and 4 figures

In this paper we present an approach to control a vehicle in a hostile environment with static obstacles and moving adversaries. The vehicle is required to satisfy a mission objective expressed as a temporal logic specification over a set of properties satisfied at regions of a partitioned environment. We model the movements of adversaries in between regions of the environment as Poisson processes. Furthermore, we assume that the time it takes for the vehicle to traverse in between two facets of a region is exponentially distributed, and we obtain the rate of this exponential distribution from a simulator of the environment. We capture the motion of the vehicle and the vehicle updates of adversaries distributions as a Markov Decision Process. Using tools in Probabilistic Computational Tree Logic, we find a control strategy for the vehicle that maximizes the probability of accomplishing the mission objective. We demonstrate our approach with illustrative case studies.

We are introducing a model-free control and a control with a restricted model for finite-dimensional complex systems. This control design may be viewed as a contribution to "intelligent" PID controllers, the tuning of which becomes quite straightforward, even with highly nonlinear and/or time-varying systems. Our main tool is a newly developed numerical differentiation. Differential algebra provides the theoretical framework. Our approach is validated by several numerical experiments., This communication is a slightly modified and updated version of a paper by the same authors (Commande sans mod\`ele et commande \`a mod\`ele restreint, e-STA, vol. 5 (\degree 4), pp. 1-23, 2008. Available at http://hal.inria.fr/inria-00288107/en/), which is written in French