3 sampled-data control of nonlinear systems

This chapter provides some of the main ideas resulting from recent developments in sampled-data control of nonlinear systems. We have tried to bring the basic parts of the new developments within the comfortable grasp of graduate students. Instead of presenting the more general results that are available in the literature, we opted to present their less general versions that are easier to understand and whose proofs are easier to follow. We note that some of the proofs we present have not appeared in the literature in this simplified form. Hence, we believe that this chapter will serve as an important reference for students and researchers that are willing to learn about this area of research

Families of moment matching based, structure preserving approximations for linear port Hamiltonian systems

In this paper we propose a solution to the problem of moment matching with preservation of the port Hamiltonian structure, in the framework of time-domain moment matching. We characterize several families of parameterized port Hamiltonian models that match the moments of a given port Hamiltonian system, at a set of finite interpolation points. We also discuss the problem of Markov parameters matching for linear systems as a moment matching problem for descriptor representations associated to the given system, at zero interpolation points. Solving this problem yields families of parameterized reduced order models that achieve Markov parameter matching. Finally, we apply these results to the port Hamiltonian case, resulting in families of parameterized reduced order port Hamiltonian approximations.Comment: 27 pages, 8 figures, Automatica journa

Homogeneity in the bi-limit as a tool for observer and feedback design

International audienceWe introduce an extension of the notion of homogeneous approximation to make it valid both at the origin and at infinity (homogeneity in the bi-limit). Exploiting this extension, we give several results concerning stability, robustness and uniform (in the initial condition) finite time convergence for a homogeneous in the bi-limit vector field. We then introduce a homogeneous in the bi-limit observer and state-feedback for a chain of integrators. Combining these two tools we establish a global asymptotic stabilization result by output feedback for feedback and feedforward systems. We obtain also a finite time observer for globally Lipschitz system

Dynamic vs static scaling: an existence result

International audienceThe relation between static and dynamic control Lyapunov functions scaling is discussed. It is shown that, under some technical assumptions, stabilizability by means of static scaling implies stabilizability by means of dynamic scaling. A motivating example and a worked out design example complement the theoretical part

Shared-control for the kinematic model of a mobile robot

This paper presents a shared-control algorithm for the kinematic model of a mobile robot. The set of feasible position of the robot is defined by a group of linear inequalities. The shared-control strategy is based on a hysteresis switch and its properties are established by a Lyapunov-like analysis. Simulation results illustrate the effectiveness of the algorithm

Shared-control for typical driving scenarios

A shared-control algorithm for the kinematic model of a rear-wheel driving car is presented. The design of the shared-controller is based on a hysteresis switch and its properties are established by a Lyapunov-like analysis. The shared-controller guarantees the safety of the car in both predefined, static environments and time-varying environments. The effectiveness of the controller is verified by two studies

Shared-control for the kinematic model of a mobile robot

This paper presents a shared-control algorithm for the kinematic model of a mobile robot. The set of feasible position of the robot is defined by a group of linear inequalities. The shared-control strategy is based on a hysteresis switch and its properties are established by a Lyapunov-like analysis. Simulation results illustrate the effectiveness of the algorithm

Output-feedback shared-control for fully actuated linear mechanical systems

This paper presents an output feedback shared-control algorithm for fully-actuated, linear, mechanical systems. The feasible configurations of the system are described by a group of linear inequalities which characterize a convex admissible set. The properties of the shared-control algorithm are established with a Lyapunov-like analysis. Simple numerical examples demonstrate the effectiveness of the strategy

Shared-control for a UAV operating in the 3D space

This paper presents a shared-control scheme for a UAV moving in a 3D space while its feasible Cartesian position set is defined by a group of linear inequalities. A hysteresis switch is used to combine the human input and the feedback control input based on the definitions of a safe set, a hysteresis set and a “dangerous” set. Case studies given in the paper show the effectiveness of the shared-control algorithm