LMI relaxation to Riccati equations in structured ℋ<inf>2</inf> control

In this paper we discuss structured [image omitted] control methods for large-scale interconnected systems. Based on a relaxation of Riccati equations, we derive some linear matrix inequality (LMI) conditions for sub-optimal controllers in which information structure can be imposed. In particular, we derive controllers by solving low-dimensional LMIs, which are decentralized except for the sharing information between neighbours, as determined by the plant interconnection; also we optimize a performance bound for each of the derived controllers

ROS programski paket za distribuirano upravljanje mrežama dinamičkih sustava

Prateći brzi razvoj komunikacijskih i informacijskih tehnologija, the razvoj novih generacija senzora i aktuatora, počeo se pojavljivati skup novih sustava, čije ostvarenje donedavno nije bilo moguće. Riječ je o mrežama dinamičkih sustava, koje se javljaju u grupama mobilnih robota koji surađuju na ostvarivanju zajedničkog cilja; kolonama autonomnih vozila na automatiziranim autocestama; električnim mrežama nove generacije; adaptivnoj optici; pametnim konstrukcijama, na koje je ugrađen velik broj senzora i aktuatora, sa ciljem prigušenja neželjenih vibracija, ili upravljanja protokom fluida. Zajednička je karakteristika takvih sustava da se sastoje od relativno velikog broja prostorno distribuiranih dinamičkih podsustava, koji međusobno interagiraju fizičkim vezama i/ili komunikacijskim kanalima. Takvi se sustavi nazivaju mrežama dinamičkih sustava, ili kraće, dinamičkim mrežama. Glavni je fokus današnjeg istraživanja u ovom području razvoj metoda sinteze upravljačkih zakona. Izazov je projektiranje lokalnih upravljačkih zakona koji će garantirati ostvarivanje globalnih ciljeva na razini cijele mreže. Trenutno, međutim, još uvijek ne postoji univerzalno primjenjiva teorija koja nudi fleksibilno i robusno riješenje. Osim teorije, trenutno nedostaje i programski okvir koji bi omogućavao razvoj, simulaciju, testiranje, i praktičnu implementaciju upravljačkih algoritama za takve sustave. U sklopu ovog rada razvijen je i predstavljen jedan takav programski okvir, koji omogućuje modeliranje velikog broja različitih vrsta dinamičkih mreža u Python programskom jeziku, a koji se izvršava unutar Robot Operating Systema (ROS)

Convex modeling with priors

Thesis (Ph. D.)--Massachusetts Institute of Technology, School of Architecture and Planning, Program in Media Arts and Sciences, 2006.Includes bibliographical references (leaves 159-169).As the study of complex interconnected networks becomes widespread across disciplines, modeling the large-scale behavior of these systems becomes both increasingly important and increasingly difficult. In particular, it is of tantamount importance to utilize available prior information about the system's structure when building data-driven models of complex behavior. This thesis provides a framework for building models that incorporate domain specific knowledge and glean information from unlabeled data points. I present a methodology to augment standard methods in statistical regression with priors. These priors might include how the output series should behave or the specifics of the functional form relating inputs to outputs. My approach is optimization driven: by formulating a concise set of goals and constraints, approximate models may be systematically derived. The resulting approximations are convex and thus have only global minima and can be solved efficiently. The functional relationships amongst data are given as sums of nonlinear kernels that are expressive enough to approximate any mapping. Depending on the specifics of the prior, different estimation algorithms can be derived, and relationships between various types of data can be discovered using surprisingly few examples.(cont.) The utility of this approach is demonstrated through three exemplary embodiments. When the output is constrained to be discrete, a powerful set of algorithms for semi-supervised classification and segmentation result. When the output is constrained to follow Markovian dynamics, techniques for nonlinear dimensionality reduction and system identification are derived. Finally, when the output is constrained to be zero on a given set and non-zero everywhere else, a new algorithm for learning latent constraints in high-dimensional data is recovered. I apply the algorithms derived from this framework to a varied set of domains. The dissertation provides a new interpretation of the so-called Spectral Clustering algorithms for data segmentation and suggests how they may be improved. I demonstrate the tasks of tracking RFID tags from signal strength measurements, recovering the pose of rigid objects, deformable bodies, and articulated bodies from video sequences. Lastly, I discuss empirical methods to detect conserved quantities and learn constraints defining data sets.by Benjamin Recht.Ph.D