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Lecture

Observability and Controllability

In course

EE-611: Linear system theory

The course covers control theory and design for linear time-invariant systems : (i) Mathematical descriptions of systems (ii) Multivariables realizations; (iii) Stability ; (iv) Controllability and Observability; (v) Minimal realizations and coprime fracti ...

Description

This lecture covers the concepts of observability and controllability in linear systems. It starts by defining the necessary and sufficient conditions for a system to be observable and controllable. The lecture then delves into the reachability of states and pseudo-state trajectories. It discusses the implications of coprimeness and the realization of systems from a state-space perspective. The importance of having no input decoupling for observability is highlighted.

Instructor

Philippe Müllhaupt

Official source

Ontological neighbourhood

Mathematics

Algebra: Linear algebra

Information engineering

Control theory and engineering: Control theory

Related concepts (32)

Observability

Observability is a measure of how well internal states of a system can be inferred from knowledge of its external outputs. In control theory, the observability and controllability of a linear system are mathematical duals. The concept of observability was introduced by the Hungarian-American engineer Rudolf E. Kálmán for linear dynamic systems. A dynamical system designed to estimate the state of a system from measurements of the outputs is called a state observer or simply an observer for that system.

State-space representation

In control engineering, model based fault detection and system identification a state-space representation is a mathematical model of a physical system specified as a set of input, output and variables related by first-order (not involving second derivatives) differential equations or difference equations. Such variables, called state variables, evolve over time in a way that depends on the values they have at any given instant and on the externally imposed values of input variables.

Controllability

Controllability is an important property of a control system and plays a crucial role in many control problems, such as stabilization of unstable systems by feedback, or optimal control. Controllability and observability are dual aspects of the same problem. Roughly, the concept of controllability denotes the ability to move a system around in its entire configuration space using only certain admissible manipulations. The exact definition varies slightly within the framework or the type of models applied.

Control theory

Control theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any delay, overshoot, or steady-state error and ensuring a level of control stability; often with the aim to achieve a degree of optimality. To do this, a controller with the requisite corrective behavior is required.

Hubble Space Telescope

The Hubble Space Telescope (often referred to as HST or Hubble) is a space telescope that was launched into low Earth orbit in 1990 and remains in operation. It was not the first space telescope, but it is one of the largest and most versatile, renowned both as a vital research tool and as a public relations boon for astronomy. The Hubble telescope is named after astronomer Edwin Hubble and is one of NASA's Great Observatories.

Related lectures (43)

State-Space Representation: Structure Theorem

Covers the structure theorem for state-space representations and companion forms.

State-Space Representation: Controllability and Observability

Explores state-space representation, controllability, observability, and regulator calculation using the Ackermann method.

Controllability and Observability

Covers controllability and observability in linear systems, discussing necessary conditions and implications of unimodular matrices.

Controllability and Reachability

Explores reachability and controllability in multivariable control systems, discussing tests, proofs, and their implications.

State-Space Representation: Basics & Transformations