observerbased

Observerbased, often written observer-based, refers to methods in control theory that rely on an observer to estimate the internal state of a dynamical system from external measurements and inputs. The estimated state, rather than the true state, is used for feedback control, enabling stabilization and regulation when some states are not directly measurable.

In the canonical continuous-time linear case, the system is x_dot = A x + B u, y = C x. An observer (for example, the Luenberger observer) has form x_hat_dot = A x_hat + B u + L(y - C x_hat). The estimation error e = x - x_hat evolves as e_dot = (A - L C) e. Choosing L so that A - L C is stable yields asymptotic convergence of the estimate. Similar discrete-time formulas apply.

For nonlinear or uncertain systems, variants include the extended Kalman filter (EKF) and unscented Kalman filter (UKF) as stochastic observers, high-gain observers for fast convergence, and sliding-mode observers for robustness to disturbances. In such contexts, the observer provides state estimates used in a separate or integrated controller, often respecting the separation principle under certain conditions.

Applications span aerospace, robotics, automotive systems (such as active suspensions and driver assistance), process control, and energy systems. Advantages include the ability to implement feedback with limited sensing and improved disturbance rejection; however, performance hinges on model fidelity, observer gain design, and noise characteristics. Computational complexity and robustness are important design considerations.

Historically, observer-based design traces to Luenberger’s work on state observers in the 1960s and to Kalman’s optimal estimation framework, which together underpin many modern control architectures.