Observer design for continuous-time dynamical systems

Abstract

We review the main design techniques of state observer design for continuous-time dynamical systems, namely algorithms which reconstruct online the full information of a dynamical process on the basis of partially measured data. Starting from necessary conditions for the existence of such asymptotic observers, we classify the available methods depending on the detectability/observability assumptions they require. We show how each class of observer relies on transforming the system dynamics in a particular normal form which allows the design of an observer, and how each observability condition guarantees the invertibility of its associated transformation and the convergence of the observer. Finally, some implementation aspects and open problems are briefly discussed.

Infinite gain margin, contraction and optimality: An LMI-based design

“…The problem that we aim to solve is to design an infinite gain margin control law α(•) that makes the closed-loop system to define a contraction according to Definition 2. In this paper, motivated by the system structure in (6), we focus on state-feedback controllers of the form…”

“…This notion is also denoted as contraction. In the last decades, contractivity properties attracted more and more attention because of their potential applications in many control problems such as observers design (see, e.g., [5], [6]), output regulation (see, e.g., [7]- [10]) and multi-agent synchronization (see, e. g, [11]- [13]). To this end, the design of controllers that make the closed-loop system to define a contraction is gathering more and more importance, see, e.g., [10], [14], [15].…”

Robust Flux and Speed State Observer Design for Sensorless Control of a Double Star Induction Motor

“…The electric equations are linear in the states but depend on the mechanical speed 𝜔 𝑚 , one can construct a reduced order state observer of the Luenberger type [12,17], obtained from the representation of the complete state of the DSIM in the frame (d, q) or (α, β). The complete state representation in the frame (d, q) which will be used to design our observers will therefore be the following:…”

“…These methods have proven particularly efficient and successful in decoupling torque and magnetic flux, which encouraged us to support them with control algorithms that do not rely on mechanical sensors in an attempt to completely abandon them for their multiple drawbacks that directly affect the efficiency of the control system as a whole. Unfortunately, the aforementioned controls require knowledge of one of the stator or rotor fluxes, but the latter is not measurable [15][16][17][18][19]. This raises in many papers the problem of estimating or observing these quantities.…”

Safe and Robust Observer-Controller Synthesis Using Control Barrier Functions

“…In most practical systems, the true state of the system is unknown and must be reconstructed using only (often noisy) measurements obtained from sensors. In such systems, it is common to design a full-state feedback controller, and then replace the state by an estimate provided by an observer [6,Sec. 8.7].…”