Nonovershooting and nonundershooting exact output regulation

We consider the classic problem of exact output regulation for a linear time invariant plant. Under the assumption that either a state feedback or measurement feedback output regulator exists, we give design methods to obtain a regulator that avoids overshoot and undershoot in the transient response

Safe Adaptive Control of Hyperbolic PDE-ODE Cascades

Adaptive safe control employing conventional continuous infinite-time adaptation requires that the initial conditions be restricted to a subset of the safe set due to parametric uncertainty, where the safe set is shrunk in inverse proportion to the adaptation gain. The recent regulation-triggered adaptive control approach with batch least-squares identification (BaLSI, pronounced ``ballsy'') completes perfect parameter identification in finite time and offers a previously unforeseen advantage in adaptive safe control, which we elucidate in this paper. Since the true challenge of safe control is exhibited for CBF of a high relative degree, we undertake a safe BaLSI design in this paper for a class of systems that possess a particularly extreme relative degree: ODE-PDE-ODE sandwich systems. Such sandwich systems arise in various applications, including delivery UAV with a cable-suspended load. Collision avoidance of the payload with the surrounding environment is required. The considered class of plants is $2\times2$ hyperbolic PDEs sandwiched by a strict-feedback nonlinear ODE and a linear ODE, where the unknown coefficients, whose bounds are known and arbitrary, are associated with the PDE in-domain coupling terms that can cause instability and with the input signal of the distal ODE. This is the first safe adaptive control design for PDEs, where we introduce the concept of PDE CBF whose non-negativity as well as the ODE CBF's non-negativity are ensured with a backstepping-based safety filter. Our safe adaptive controller is explicit and operates in the entire original safe set

About stabilization of non-minimum phase systems by output feedback

This thesis work has been motivated by an internal benchmark dealing with the output regulation problem of a nonlinear non-minimum phase system in the case of full-state feedback. The system under consideration structurally suffers from finite escape time, and this condition makes the output regulation problem very hard even for very simple steady-state evolution or exosystem dynamics, such as a simple integrator. This situation leads to studying the approaches developed for controlling Non-minimum phase systems and how they affect feedback performances. Despite a lot of frequency domain results, only a few works have been proposed for describing the performance limitations in a state space system representation. In particular, in our opinion, the most relevant research thread exploits the so-called Inner-Outer Decomposition. Such decomposition allows splitting the Non-minimum phase system under consideration into a cascade of two subsystems: a minimum phase system (the outer) that contains all poles of the original system and an all-pass Non-minimum phase system (the inner) that contains all the unavoidable pathologies of the unstable zero dynamics. Such a cascade decomposition was inspiring to start working on functional observers for linear and nonlinear systems. In particular, the idea of a functional observer is to exploit only the measured signals from the system to asymptotically reconstruct a certain function of the system states, without necessarily reconstructing the whole state vector. The feature of asymptotically reconstructing a certain state functional plays an important role in the design of a feedback controller able to stabilize the Non-minimum phase system