Christophe Fiter

A state dependent sampling for linear state feedback

In this work, a new state-dependent sampling control enlarges the sampling intervals of state feedback control. We consider the case of linear time invariant systems and guarantee the exponential stability of the system origin for a chosen decay rate. The approach is based on LMIs obtained thanks to sufficient Lyapunov-Razumikhin stability conditions and follows two steps. In the first step, we compute a Lyapunov-Razumikhin function that guarantees exponential stability for all time-varying sampling intervals up to some given bound. This value can be used as a lower-bound of the state-dependent sampling function. In a second step, an off-line computation provides a mapping from the state-space into the set of sampling intervals: the state is divided into a finite number of regions, and to each of these regions is associated an allowable upper-bound of the sampling intervals that will guarantee the global (exponential or asymptotic) stability of the system. The results are based on sufficient conditions obtained using convex polytopes. Therefore, they involve some conservatism with respect to necessary and sufficient conditions. However, at each of the two steps, an optimization on the sampling upper-bounds is proposed. The approach is illustrated with numerical examples from the literature for which the number of actuations is shown to be reduced with respect to the periodic sampling case.

Adding expert knowledge and exploration in monte-carlo tree search

We present a new exploration term, more efficient than classical UCT-like exploration terms. It combines efficiently expert rules, patterns extracted from datasets, All-Moves-As-First values, and classical online values. As this improved bandit formula does not solve several important situations (semeais, nakade) in computer Go, we present three other important improvements which are central in the recent progress of our program MoGo. We show an expert-based improvement of Monte-Carlo simulations for nakade situations; we also emphasize some limitations of this modification. We show a technique which preserves diversity in the Monte-Carlo simulation, which greatly improves the results in 19x19. Whereas the UCB-based exploration term is not efficient in MoGo, we show a new exploration term which is highly efficient in MoGo. MoGo recently won a game with handicap 7 against a 9Dan Pro player, Zhou JunXun, winner of the LG Cup 2007, and a game with handicap 6 against a 1Dan pro player, Li-Chen Chien.

Recent developments on the stability of systems with aperiodic sampling: An overview ☆

This article presents basic concepts and recent research directions about the stability of sampled-data systems with aperiodic sampling. We focus mainly on the stability problem for systems with arbitrary time-varying sampling intervals which has been addressed in several areas of research in Control Theory. Systems with aperiodic sampling can be seen as time-delay systems, hybrid systems, Input/Output interconnections, discrete-time systems with time-varying parameters, etc. The goal of the article is to provide a structural overview of the progress made on the stability analysis problem. Without being exhaustive, which would be neither possible nor useful, we try to bring together results from diverse communities and present them in a unified manner. For each of the existing approaches, the basic concepts, fundamental results, converse stability theorems (when available), and relations with the other approaches are discussed in detail. Results concerning extensions of Lyapunov and frequency domain methods for systems with aperiodic sampling are recalled, as they allow to derive constructive stability conditions. Furthermore, numerical criteria are presented while indicating the sources of conservatism, the problems that remain open and the possible directions of improvement. At last, some emerging research directions, such as the design of stabilizing sampling sequences, are briefly discussed.

State Dependent Sampling: an LMI Based Mapping Approach ⋆,⋆⋆

Abstract The uprising use of embedded systems and Networked Control Systems (NCS) requires reductions of the use of processor and network loads. In this work, we present a state dependent sampling control that maximizes the sampling intervals of state feedback control. We consider linear time invariant systems and guarantee the exponential stability of the system origin for a chosen decay rate α. The proof of the α-stability is based on a quadratic Lyapunov function which is computed, thanks to LMIs, so as to optimize some performance criterion on the sampling intervals. A mapping of the state space is then designed offline: it computes for each state of the state space the maximum allowable sampling interval, which makes it possible to reduce the number of actuations during the real-time control of the system.

State-dependent sampling for perturbed time-delay systems

In this work we present a state-dependent sampling control that allows for enlarging the sampling intervals of state-feedback control. We consider the case of perturbed linear time-invariant systems with input-delay and guarantee their ℒ2-stability. The approach is based on a novel class of switched Lyapunov-Krasovskii functionals with state-dependent matrices. It results in an LMI problem that allows for enlarging the sampling interval according to the system state. Then, a mapping of the state space is designed offline: it computes for each state of the state space a lower-bound estimation of the maximum allowable sampling interval, which makes it possible to reduce the number of actuations during the real-time control of the system.

A robust stability framework for LTI systems with time-varying sampling

This work aims at enlarging the sampling intervals in several state feedback control situations by designing a sampling map in the state space. We consider the case of linear time invariant (LTI) systems with state-bounded perturbations, and guarantee their exponential stability for a chosen decay-rate. The approach is based on linear matrix inequalities (LMIs) obtained thanks to Lyapunov-Razumikhin stability conditions and convexification arguments. First, it enables to optimize the lower-bound of the sampling maps by computing the adequate Lyapunov-Razumikhin function. This result can be interpreted as a robust stability analysis with respect to arbitrary time-varying sampling intervals, which may be useful in the case of uncontrolled sampling, or in the presence of phenomenon such as sampling jitter. Then, the obtained results are extended to design the sampling map in three dynamic sampling control situations: event-triggered control, self-triggered control, and state-dependent sampling. The results are illustrated with a numerical example from the literature.

State-dependent sampling for Linear Time Invariant systems: A discrete time analysis

This work concerns the adaptation of sampling times for Linear Time Invariant (LTI) systems controlled by state feedback. Complementary to various works that guarantee stabilization independently of changes in the sampling rate, here we provide conditions to design stabilizing sequences of sampling instants. In order to reduce the number of these sampling instants, a dynamic scheduling algorithm optimizes, over a given sampling horizon, a sampling sequence depending on the system state value. Our proofs are inspired by switched system techniques combining Lyapunov functions and LMI optimization. To show the applicability of the technique, the theoretical study is illustrated by an implementation in Matlab/TRUE TIME.

Tutorial on arbitrary and state-dependent sampling

This tutorial, presents basic concepts and recent research directions about sampled-data systems. We focus mainly on the stability of systems with time-varying sampling intervals. Without being exhaustive, which would be neither possible nor useful, we try to give a structural survey of what we think to be the main results and issues in this domain.

Sensorless Control of a Stepper Motor Based on Higher Order Sliding Modes

A robust control for a stepper motor with no position nor velocity sensors and only needing current and voltage measurements is designed. Second order sliding mode based observers are realized to estimate both rotor angular position and velocity. Moreover, a robust control law, which is also based on second order sliding modes and which uses the estimates of the observer, is designed. The stability of the observer based control loop is discussed. The results obtained in simulations indicate the usefulness and the robustness of the method.

Stability of piecewise affine systems with state-dependent delay, and application to congestion control

In this work, we consider the exponential stability of piecewise affine systems with time- and state-dependent delay, and delayed-state-dependent switching. The stability analysis is based on the use of Lyapunov-Krasovskii functionals, and is divided into two parts. First, global stability conditions are proposed in the case of systems with (state-independent) time-varying delay. Then, local stability conditions are derived in the case of systems with time- and state-dependent delay. In the latter case, estimations of the domain of attraction are also proposed. The theoretical results are applied to the congestion control problem, which can be modelled by such systems.