Interval State Estimation and Observer Design in Uncertain Dynamical Systems

Interval state estimation and observer design address the challenge of determining the range within which the true state of a dynamical system evolves when model parameters, external inputs and measurements are subject to bounded uncertainties. Rather than yielding a single best estimate, interval methods compute upper and lower bounds that provably contain the actual state, thus offering guaranteed performance in the presence of noise, disturbances and parameter variations. Core techniques rely on set-membership theory to describe uncertainty sets and on interval arithmetic to propagate these sets through system dynamics. Observer designs aim to refine these bounds over successive updates, mitigating over-approximation and ensuring convergence of interval widths to acceptable levels. Recent advances encompass the use of polytopic and zonotopic representations to capture complex uncertainty geometries, the extension to time-varying and nonlinear systems via observability-based constructions, and the deployment of distributed and fractional-order observers for networked multi-agent architectures. The global significance of these methods spans aerospace navigation, robotic control, power systems monitoring and sensor fusion, where reliable performance under uncertainty is paramount.

Research from Nature Portfolio

No recent Nature Portfolio content available.

Research from all publishers

Recent work in nonlinear discrete-time systems has introduced an indirect polytopic set‐membership approach that preserves the exact polytopic description of feasible states. By representing the intersection of predicted and measurement‐consistent sets as zonotopic intersections, the method avoids repeated over‐approximation and delivers tighter bounds on the true state trajectory, as demonstrated in illustrative simulations.

For multiple-input multiple-output linear time-varying discrete-time systems, a new estimator design exploits the observability matrix together with past input/output records to construct interval enclosures. This scheme guarantees finite-time convergence of the interval width and computes a priori error bounds under unknown but bounded uncertainties, offering a systematic path to tight interval estimates.

In the context of fractional-order multi-agent nonlinear networks, a distributed interval observer framework has been developed. By leveraging monotone system theory, the design ensures that error dynamics remain positive so that the computed upper and lower bounds reliably trap the true state. A Lyapunov-based criterion in the fractional calculus setting provides sufficient conditions for boundedness, and the accompanying algorithm scales to large-scale networked systems.

Interval State Estimation and Observer Design in Uncertain Dynamical Systems publication trend

The graph below shows the total number of articles in interval state estimation and observer design in uncertain dynamical systems across all publications each year (not limited to Nature Index journals).

Technical terms

Interval state estimation: A methodology that computes lower and upper bounds on the system state under bounded uncertainties, ensuring the true state lies within these intervals.

Observer: An algorithmic construct that uses system inputs and outputs to estimate or bound the internal state of a dynamical system.

Set-membership: A theoretical framework in which uncertainties are described as sets, and state estimation seeks all states consistent with system equations and measurement bounds.

Zonotope: A convex set represented as the Minkowski sum of line segments, commonly used to approximate and propagate uncertainty in high-dimensional systems.

Polytopic set: A convex polyhedron defined by a finite number of linear inequalities, employed to model uncertainty regions in state-space.

References

1. Guaranteed State Estimation for Nonlinear Discrete-Time Systems via Indirectly Implemented Polytopic Set Computation. IEEE Transactions on Automatic Control (2018).
2. Interval State Estimator Design Using the Observability Matrix for Multiple Input Multiple Output Linear Time-Varying Discrete-Time Systems. IEEE Access (2019).
3. Fractional-Order Interval Observer for Multiagent Nonlinear Systems. Fractal and Fractional (2022).