Nonlinear Estimation and Stochastic Modeling

Session Chair: Patrick Dewilde, TU Delft  (The Netherlands), TU Munich (Germany)
Session Organizer: Jan Zarzycki, Wroclaw University of Technology (Poland)
Keynote Speakers:
  • Prof. Patrick Dewilde (TU Delft The Netherlands, TU Munich Germany)
  • Prof. Sankar Basu (National Science Foundation, Washington DC. USA)
  • Prof. John Baras (Univ. of Maryland USA, TU Munich, KTH Stockholm)
  • Prof. Karl Johansson (Royal Institute of Technology Stockholm, Sweden)

Stochastic Modeling is the art of producing an adequate reduced model for a dynamical system driven by one or more stochastic processes.
It is an essential step not only in understanding the behavior of such a system, but also in producing an essential component for `model based control’,
whereby the control law is derived from a good estimate of the system’ structure. In the case of linear (time variant or time invariant)
systems driven by a zero-mean Gaussian process, the problem of stochastic modeling has found some very elegant solutions,
depending on the kind of data available for the identification. The data could e.g., consist of correlations or partial parametrized models.
The problem becomes much more challenging in the case of non-linear systems driven by stochastic processes of general type,
and one may doubt that there would ever be a generally applicable methodology. However, there are interesting classes of systems
for which one can derive and identify adequate (reduced) models.
The session aims at reporting recent activities and new insights in the whole area of stochastic modeling in a non-conventional context.

Abstracts
Cyber security and privacy in networked control systems
Karl H. Johansson, KTH Royal Institute of Technology, Sweden

Security and privacy is of growing concern in many control systems. Cyber attacks are frequently reported for a variety of industrial and infrastructure systems. For more than a decade the control community has developed techniques for how to design control systems resilient to cyber-physical attacks. In  this talk, we will review recent advances in control systems security and privacy. In particular, as cyber and physical components of networked control systems are tightly interconnected, it is be argued that traditional IT security focusing only on the cyber part does not provide appropriate solutions. Modeling the objectives and resources of the adversary together with the plant and control dynamics is shown to be essential. The consequences of common attack scenarios, such  denial-of-service, replay, and bias injection attacks, can be analyzed using the presented framework. It is also shown how to strengthen the control loops by deriving security and
privacy aware estimation and control schemes. Applications in building automation, power networks, and automotive systems will be used to
motivate and illustrate the results. The presentation is based on joint work with several students and colleagues at KTH and elsewehere.

Toeplitz vs. Hankel
Patrick Dewilde, Institute of Advanced Study, TU Munich

Non-linear stochastic estimation and modeling problems generate equations that may be of the `Toeplitz type’, of the `Hankel type’ or even a mixture. The talk treats a number of issues concerning them: when does which type of equations occur?, how can one or the other be solved?, what can one do when both occur at the same time? It appears that both types have very strong but very different properties, and their conjunction gets especially tricky. Although solutions in elementary cases is classical (Schur-Levinson algorithm, Hamburger theorem), the generalization to the non-linear moment matching problem for a non-linear stochastic process is still a great challenge, but a new approach will be presented. The new theory is at the same time exhilarating, but contains also a collection of challenging unsolved questions—a fertile ground for new research.

Synthesis of passive multidimensional scattering matrices: a survey
Sankar Basu, National Science Foundation, Arlington, Virginia

The goal of this exposition is twofold. The first is to survey the sta-tus of synthesizability of multivariable (n-dimensional) passive linearshift invariant bounded (or positive) transfer functions as the scat-tering (or immittance) matrices of networks consisting ofndifferenttypes of inductances/capacitances and memoryless reciprocal or non-reciprocal elements such as the transformers, gyrators etc. The theorythus attempts to extend the classical network synthesis from univari-ate (i.e., 1-D) case to the multidimensional (n-D) case. It is knownthat the main bottleneck in pursuing this goal of multivariable circuitsynthesis is Hilbert’s 17-th problem on expressibility of positive poly-nomials as a sum of squares, which is an active problem area in realalgebraic geometry much studied for more than last hundred years.The interplay between these two closely related topics, each impor-tant in their own right, is the main topic of this survey. Synthesis ofboth lossless and lossy (i.e., dissipative) transfer functions are consid-ered. While a 2-D lossless transfer function can be shown to be syn-thesizable, it turns out that the technique of embedding a dissipativetransfer function within a lossless transfer function with a larger num-ber of ports, which is equivalent to a certain matrix dilation problem,can be carried out by means of spectral factorization only partially in 2-D, but completely fails in higher dimensions (i.e., forn >2).The fundamental reason for this breakdown is the unavailability of anadequate sum of squares representation of multivariable positive poly-nomials. In higher dimensions (i.e., forn >2) even lossless transferfunctions cannot in general be synthesized except for certain stableall-pass functions of low degree. Once again, this failure can be at-tributed to unavailability of sum of squares representation mentionedabove. Failure of other 1-D synthesis procedures, e.g., via matrix fac-torizations of various types are also briefly discussed in the interest of a complete status report on the multidimensional synthesis problem.Depending on the convenience of exposition, our mode of presentationtoggles between continuous time systems and discrete time systems.From a conceptual point of view this strategy is believed not to causeany loss of generality at least for the linear shift invariant systemsunder consideration.