Follow the bouncing ball: global results on tracking and state estimation with impacts

peer reviewedIn this paper we formulate tracking and state- estimation problems of a translating mass in a polyhedral billiard as a stabilization problem for a suitable set. Due to the discontinuous trajectories arising from the impacts, we use hybrid systems stability analysis tools to establish the results. Using a novel concept of mirrored images of the target mass we prove that 1) a tracking control algorithm, and 2) an observer algorithm guarantee global exponential stability results for specific classes of polyhedral billiards, including rectangles. Moreover, we combine these two algorithms within dynamic controllers that guarantee global output feedback tracking. The results are illustrated via simulations

Unsafe Point Avoidance in Linear State Feedback

International audienceWe propose a hybrid solution for the stabilization of the origin of a linear time-invariant stabilizable system with the property that a suitable neighborhood of a pre-defined unsafe point in the state space is avoided by the closed-loop solutions. Hybrid tools are motivated by the fact that the task at hand cannot be solved with continuous feedback, whereas the proposed hybrid solution induces nominal and robust asymptotic stability of the origin. More specifically, we formulate a semiglobal version of the problem at hand and describe a fully constructive approach under the assumption that the unsafe point to be avoided does not belong to the equilibrium subspace induced by the control input on the linear dynamics. The approach is illustrated on a numerical exampl

A hybrid dynamical systems approach to smart irrigation

We present a novel model for a drip irrigation system, using a hybrid dynamical systems paradigm to take into account the intrinsic binary nature of the control input. We consider an irrigation pipe with a generic number of drippers, analyzing the effect that the transients in the pipe have on the irrigation uniformity, and propose an intuitive irrigation strategy based on the one currently used by farmers. The model is presented together with simulations, whose parameters are based on real farm data

Distributed estimation based on multi-hop subspace decomposition

This paper deals with the problem of distributedly estimating the state of an LTI plant through an interconnected network of agents. The proposed approach results in an observer structure that incorporates consensus among the agents and that can be distributedly designed, achieving a robust solution with a good estimation performance. The developed solution is based on an iterative decomposition of the plant in the local observable staircase forms. The proposed observer has several positive features compared to recent results in the literature, which include milder assumptions on the network connectivity and the ability to set the convergence rate

Distributed implementation and design for state estimation

This paper presents an architecture for agent-based distributed state estimation of linear plants with distributed outputs. The estimation structure is based on an orthogonal decomposition of the local observable/unobservable subspaces associated to each set of locally accessible outputs. The design of the observers can be carried out in a distributed way, which might open the door to scalable designs when the number of agent grows. The proposed architecture is developed for a two-agents network, where we establish stability results for the error dynamics, but comments are given about the generalization to larger networks. Simulations are provided to illustrate the estimation scheme in such broader cases

Finite Gain L p Stability for Hybrid Dynamical Systems ⋆

Abstract We characterize finite gain Lp stability properties for hybrid dynamical systems. By defining a suitable concept of hybrid Lp norm, we introduce hybrid storage functions and provide sufficient Lyapunov conditions for Lp stability of hybrid systems, which cover the well-known continuous-time and discrete-time Lp stability notions as special cases. We then focus on homogeneous hybrid systems and prove a result stating the equivalence among local asymptotic stability of the origin, global exponential stability, existence of a homogeneous Lyapunov function with suitable properties for the hybrid system with no inputs, and input-to-state stability, and we show how these properties all imply Lp stability. Finally we characterize systems with direct and reverse average dwell time properties and establish parallel results for this class of systems. We also make several connections to the existing results on dissipativity properties of hybrid dynamical systems

Global tracking and state estimation with non- smooth impacts for a mass confined to an n-dimensional half-space

peer reviewedWe formulate tracking and state-estimation problems of a translating mass moving in an n-dimensional space and impacting on a hyperplane. Due to the discontinuous trajectories arising from the nonsmooth impacts, we use hybrid systems stability analysis tools to establish that 1) a tracking control algorithm and 2) an observer algorithm guarantee global exponential stability. Then, based on a separation principle, we combine the two constructions above to design a dynamic output feedback controller ensuring asymptotic tracking

Model recovery anti-windup for continuous-time rate and magnitude saturated linear plants

In this paper two approaches are given for anti-windup design for nonlinear control systems with linear plants subject to limitations both in the magnitude and the rate of variation of the control input. Both approaches are based on the so-called Model Recovery Anti-windup (MRAW) framework. The first approach is built by treating the rate+magnitude saturation as a single dynamic nonlinearity, while in the second one, the dynamic compensator dynamics is extended with extra states to treat the two saturations separately. Both approaches lead to global stability with exponentially stable plants and local stability in all other cases. For both approaches, stability and performance guarantees are proven, numerical recipes are given and the relative merits are comparatively highlighted on a simulation example.MIUR and PRIN project