Estimation of hybrid systems using discrete sensors

Koutsoukos, Xenofon

doi:10.1109/cdc.2003.1272552

Cited by 28 publications

(21 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Some related results on identification, state estimation, and fault detection using binary or quantized outputs can be found in [17], [31], [33], [34], [35], [36]. In relation to the existing knowledge on observability of sampled systems, we refer the reader to standard textbooks on digital control systems; see, e.g., [7], [18], [24] for classical synchronized sampling schemes on linear systems, and [1], [11] on nonlinear systems.…”

mentioning

confidence: 99%

State Observability and Observers of Linear-Time-Invariant Systems Under Irregular Sampling and Sensor Limitations

Wang

Yin

et al. 2011

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

Abstract-State observability and observer designs are investigated for linear-time-invariant systems in continuous time when the outputs are measured only at a set of irregular sampling time sequences. The problem is primarily motivated by systems with limited sensor information in which sensor switching generates irregular sampling sequences. State observability may be lost and the traditional observers may fail in general, even if the system has a full-rank observability matrix. It demonstrates that if the original system is observable, the irregularly sampled system will be observable if the sampling density is higher than some critical frequency, independent of the actual time sequences. This result extends Shannon's sampling theorem for signal reconstruction under periodic sampling to system observability under arbitrary sampling sequences. State observers and recursive algorithms are developed whose convergence properties are derived under potentially dependent measurement noises. Persistent excitation conditions are validated by designing sampling time sequences. By generating suitable switching time sequences, the designed state observers are shown to be convergent in mean square, with probability one, and with exponential convergence rates. Schemes for generating desired sampling sequences are summarized.

show abstract

mentioning

confidence: 99%

State Observability and Observers of Linear-Time-Invariant Systems Under Irregular Sampling and Sensor Limitations

Wang

Yin

et al. 2011

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

show abstract

“…for j = 0, · · · , m i − 1 and i = 1, · · · , l. The coefficients c i (t), i = 1 · · · , n, depending on t, are uniquely determined by (14). r(z) is said to interpolate e z and its derivatives at the roots of c At (z).…”

Section: Frc152mentioning

confidence: 99%

“…(16) When the eigenvalues of A are all distinct, the method is called Sylvester interpolation. It should be pointed out that although determination of α(t) from (14) is unique, there may be other α(t) that satisfy (16) but not (14). In fact, in the proof of Theorem 6.2.9(a) of [8], r(z) is selected from interpolation of e z and its derivatives at the roots of the minimal polynomial of At.…”

Section: Frc152mentioning

confidence: 99%

Irregular sampling, active observability, and convergence rates of state observers for systems with binary-valued observations

Wang

Yin

et al. 2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

View full text Add to dashboard Cite

This paper is concerned with state observer design of systems with binary-valued output measurements. First, observability of sampled systems is obtained under noise-free observations and arbitrary sampling times. It demonstrates that if the original system is observable, the sampled system is always observable whenever sampling density is larger than some critical frequency, independent of the actual time sequences. This result is then used to design switching time sequences and deduce active observability for systems with binary-valued output observations. Convergence of state estimates relies on some persistent excitation conditions that are usually required to hold. When observations become noise corrupted it is shown that by designing suitable switching time sequences certain convergence rates can always be obtained, which are explicitly derived.

show abstract

“…In our final experiment, instead of considering arbitrarily chosen measurements, we assume to have one sensor in each tank that measures when a certain height is crossed. Following the idea presented by Koutsoukos (2003) for a similar model of two tanks, placing one of these sensors at the level of switching, i.e. in our case observing when x 2 (t) crosses k 3 , allows direct observation of the time of mode changes.…”

Section: Remarkmentioning

confidence: 99%

“…sensors that monitor only a single threshold value such as critical fluid level in chemical processes or proximity sensors in robotics applications. Discrete sensors are suitable for monitoring guard conditions that trigger discrete transitions in hybrid systems as emphasized by Koutsoukos (2003). Measurement noise is taken as a discrete time signal assumed additive and bounded with known bounds.…”

Section: Set-membership Estimation Of Hybrid Systemsmentioning

confidence: 99%