On optimal input design for networked systems

Abstract

The topic of this paper is optimal input signal design for identification of interconnected/networked dynamic systems. We consider the case when it is only possible to design some of the input signals, while the rest of the inputs are only measurable. This is most common in industrial applications, where external excitation can only be applied to some subsystems. One example is feed-forward control from measurable disturbances. The optimal input signal will be correlated with the measured signals. The main purpose of this paper is to reveal how to re-formulate the input design problem for networked systems as an input design problem for feedback control systems. We can then use the powerful partial correlation approach for optimal closed loop input design. This means that the corresponding networked optimal input design problem can be formulated as a semi-definite program, for which there are efficient numerical methods. We evaluate this approach using two numerical examples with important applications. The result reveals some non-trivial interesting properties of the optimal input signals.

Optimal identification experiment design for the interconnection of locally controlled systems

“…Using (17), we see also that the matrices P −1 θi that determines the size ρ i (ω) of the elements T i of T via the LMI (30) are all affine functions of the to-be-designed spectra and thus of the decisions variables σ j,l (j = 1...N mod , l = 0...M ).…”

“…To tackle this issue, we propose the following iterative algorithm inspired by the so called D-K iterations [28]. Before presenting the algorithm, we note that, if we arbitrarily choose spectra Φ ri (ω) (i = 1...N mod ), we can compute the corresponding P θi (i = 1...N mod ) via (17). With these P θi , we can compute P wc,ub (ω, T ) via Theorems 2 and 3 and we can therefore verify whether (35) holds at each ω ∈ Ω.…”

“…Note that the framework considered here is much different than the frameworks of [25,17] which is, to our knowledge, the only other papers treating the optimal experiment design problem in a network. In [25], the authors consider input design for nonparametric identification of static nonlinearities embedded in a network.…”

“…In [25], the authors consider input design for nonparametric identification of static nonlinearities embedded in a network. The main purpose of [17] lies in the use of measurable disturbances in optimal experiment design.…”

Optimal input design for uncertain max‐plus linear systems

“…For example, Keesman and Walter investigated the optimal input design for the model discrimination of nonlinear single‐state systems. H gg and Wahlberg studied the optimal input signal design for the identification of networked dynamic systems. Qian et al developed a closed‐loop online optimal identification approach for a class of nonlinear dynamic systems that optimises the economic cost function and maintains the closed‐loop asymptotic stability.…”