Identification of Systems With Regime Switching and Unmodeled Dynamics

Abstract

Abstract-This paper is concerned with persistent identification of systems that involve deterministic unmodeled dynamics and stochastic observation disturbances, and whose unknown parameters switch values (possibly large jumps) that can be represented by a Markov chain. Two classes of problems are considered. In the first class, the switching parameters are stochastic processes modeled by irreducible and aperiodic Markov chains with transition rates sufficiently faster than adaptation rates of the identification algorithms. In this case, tracking real-time parameters by output observations becomes impossible and we show that an averaged behavior of the parameter process can be derived from the stationary measure of the Markov chain and can be estimated with periodic inputs and least-squares type algorithms. Upper and lower error bounds are established that explicitly show impact of unmodeled dynamics. In contrast, the second class of problems represents systems whose state transitions occur infrequently. An adaptive algorithm with variable step sizes is introduced for tracking the time-varying parameters. Convergence and error bounds are derived. Numerical results are presented to illustrate the performance of the algorithm.

Adaptive Tracking Control of Linear Systems With Binary-Valued Observations and Periodic Target

“…By (20) and Assumption 2.1, it can be seen that which together with (19) implies that Thus, the theorem is true by Theorem 2.…”

“…This technical note considers the case where the noise distribution is known and other constrains required in Assumption 2.1. It should be pointed out that this methodology still works for the case of unknown distributions ( [18]) and more general noises such as mixing noises ( [20]). …”

Time-Variant Frequency Response Function Measurements on Weakly Nonlinear, Arbitrarily Time-Varying Systems Excited by Periodic Inputs

“…In some applications the time-variation originates from the switching between a finite number of linear time-invariant systems and, hence, is non-smooth. Examples of non-smooth time-variant dynamics can be found in power electronics [8], econometrics [9], and control applications [10]; and more general, in hybrid systems (see [11] and the references therein). In this paper we explicitly exclude non-smooth time-variations.…”

Razumikhin-type theorems on moment exponential stability of functional differential equations involving two-time-scale Markovian switching

“…Introduction. Recently, Markovian switching systems driven by continuoustime Markovian chains have drawn growing attention in biological sciences [1,22,35], financial engineering [3, 5-7, 31, 39], communications and manufacturing [32,38], among others. Such systems have been used to model many practical scenarios in which abrupt changes are experienced in the structure and parameters caused by phenomena such as component failures, communication link interruption, packet loss, and power line contingency.…”