Controllability-observability of expanded composite systems

The relation between original and expanded systems within the Inclusion Principle from the point of view of controllability–observability of both subsystems and composite systems is studied. It is proved that complementary matrices always exist ensuring that the subsystems and the overall expanded system are simultaneously controllable–observable. Two practically important large classes of complementary matrices are identified to offer results computationally attractive. First, the existence of complementary matrices ensuring controllability–observability of decoupled subsystems is proved. Then, using this result, the same property is proved for the composite expanded system.Peer ReviewedPostprint (published version

Overlapping guaranteed cost control for uncertain continuous-time delayed systems

Overlapping guaranteed cost control design problem is solved for a class of linear continuous-time uncertain systems with state as well as control delays. Unknown arbitrarily time-varying uncertainties with known bounds are considered. A point delay is supposed. Conditions preserving closed-loop systems expansion-contraction relations including the identical bounds of performance indices are proved. A linear matrix inequality (LMI) delay independent procedure is used for control design in the expanded space. The results are specialized on the overlapping decentralized control design. A numerical illustrative example is supplied.Peer ReviewedPostprint (published version

Legal instruments for protection of soils

1 Legal instruments for protection of soils Abstract Diploma thesis analyses the topic of legal instruments for soil protection. Significance of soil, as one of the components of environment, lies especially in securing livelihood for the inhabitants of our planet, water circulation and retention, and in the fact that soil provides living space for a substantial portion of living organisms. In this context the legal instruments represent means by which we can successfully protect soil from its degradation. Considering that soil degradation is rapidly increasing in the last couple of decades, the topic of this diploma thesis becomes more and more pressing, though sometimes overlooked by general public. Thesis primarily analyses legal instruments which exist in the Czech legislation and are most significant for the state of soil in the Czech Republic. The objective of this thesis is particularly to analyse individual legal instruments, to critically evaluate them and suggest possible improvements to the current state of soil protection in the Czech Republic. The first chapter highlights the enviromental importance of soil and characterizes its specificities as one of the components of environment. Subsequently current soil degradation processes are presented. In the end of the chapter the thesis summarizes...Právní nástroje ochrany půdy Abstrakt Diplomová práce se zabývá problematikou právních nástrojů ochrany půdy. Význam půdy, jakožto složky životního prostředí, spočívá především v zajišťování výživy obyvatel planety, koloběhu a retenci vod a poskytování životního prostoru pro velkou část živých organismů. Právní nástroje v tomto kontextu představují prostředky, které jsou významnou měrou způsobilé půdu chránit před její degradací. Vzhledem k prokázané zvyšující se degradaci půdy v posledních desetiletích a její rychlosti se jedná o téma vysoce aktuální, ač často širokou veřejností přehlížené. Analyzovány jsou přitom primárně právní nástroje existující v podmínkách ČR, jejichž podoba a nastavení má největší dopad na stav půd v ČR. Cílem práce je zejména provést rozbor jednotlivých právních nástrojů, pokusit se je kriticky zhodnotit a v některých případech také předložit návrhy ke zlepšení současného stavu ochrany půdy v ČR. V první kapitole je nejprve pojednáno o významu půdy pro životní prostředí a její charakteristice coby složky životního prostředí. Následně jsou objasňovány jednotlivé degradační procesy, které ohrožují současný stav půdy. Ke konci dochází ke shrnutí pramenů právní úpravy ochrany půdy jak na úrovni mezinárodní, evropské, tak i vnitrostátní. Druhá a třetí kapitola se věnují právním...Katedra práva životního prostředíDepartment of Environmental LawPrávnická fakultaFaculty of La

Preservation of controllability-observability in expanded systems

The result contributed by the article is that controllability-observability of an original continuous-time LTI dynamic system can always be simultaneously preserved in expanded systems within the inclusion principle when using block structured complementary matrices. This new structure offers more degrees of freedom for the selection of specific complementary matrices than well known used cases, such as aggregations and restrictions, which enable such preservation only in certain special cases. A complete unrestricted transmission of these qualitative properties from the original controllable-observable system to its expansion is a basic requirement on the expansion/contraction process, mainly when controllers/observers are designed in expanded systems to be consequently contracted for implementation in initially given systems. An original system composed of two overlapped subsystems is adopted as a general prototype ease. A numerical example is suppliedPeer ReviewedPostprint (published version

Decentralised delay-dependent static output feedback variable structure control

In this paper, an output feedback stabilisation problem is considered for a class of large scale interconnected time delay systems with uncertainties. The uncertainties appear in both isolated subsystems and interconnections. The bounds on the uncertainties are nonlinear and time delayed. It is not required that either the known interconnections or the uncertain interconnections are matched. Then, a decentralised delay-dependant static output feedback variable structure control is synthesised to stabilise the system globally uniformly asymptotically using the Lyapunov Razumikhin approach. A case study relating to a river pollution control problem is presented to illustrate the proposed approach

Weak Interactions Based System Partitioning Using Integer Linear Programming

The partitioning of a system model will condition the structure of the controller as well as its design. In order to partition a system model, one has to know what states and inputs to group together to define subsystem models. For a given partitioning, the total magnitude of the interactions between subsystem models is evaluated. Therefore, the partitioning problem seeking for weak interactions can be posed as a minimization problem. Initially, the problem is formulated as a non-linear integer minimization that is then relaxed into a linear integer programming problem. It is shown within this paper that cuts can be applied to the initial search space in order to find the least interacting partitioning; only composed of controllable subsystems. Two examples are given to demonstrate the methodology

Decentralised Stabilisation of Nonlinear Time Delay Interconnected Systems

A decentralised state feedback control scheme is proposed to stabilise a class of nonlinear interconnected systems asymptotically based on the characteristics of the system structure. Under the condition that all the nominal isolated subsystems have uniform relative degree, the considered class of interconnected systems is transferred to a new interconnected system formed of single input systems, which facilitates the decentralised control design. A new term, weak mismatched uncertainty, is introduced for the first time to recognise a class of mismatched uncertainties in the isolated subsystems. The study shows that the effects of both matched and weak mismatched uncertainties in the isolated subsystems can be rejected completely by appropriate choice of control, and the effects of matched interconnections can be largely reduced if the control gain is sufficiently high

Lyapunov-Based Reinforcement Learning for Decentralized Multi-Agent Control

Decentralized multi-agent control has broad applications, ranging from multi-robot cooperation to distributed sensor networks. In decentralized multi-agent control, systems are complex with unknown or highly uncertain dynamics, where traditional model-based control methods can hardly be applied. Compared with model-based control in control theory, deep reinforcement learning (DRL) is promising to learn the controller/policy from data without the knowing system dynamics. However, to directly apply DRL to decentralized multi-agent control is challenging, as interactions among agents make the learning environment non-stationary. More importantly, the existing multi-agent reinforcement learning (MARL) algorithms cannot ensure the closed-loop stability of a multi-agent system from a control-theoretic perspective, so the learned control polices are highly possible to generate abnormal or dangerous behaviors in real applications. Hence, without stability guarantee, the application of the existing MARL algorithms to real multi-agent systems is of great concern, e.g., UAVs, robots, and power systems, etc. In this paper, we aim to propose a new MARL algorithm for decentralized multi-agent control with a stability guarantee. The new MARL algorithm, termed as a multi-agent soft-actor critic (MASAC), is proposed under the well-known framework of "centralized-training-with-decentralized-execution". The closed-loop stability is guaranteed by the introduction of a stability constraint during the policy improvement in our MASAC algorithm. The stability constraint is designed based on Lyapunov's method in control theory. To demonstrate the effectiveness, we present a multi-agent navigation example to show the efficiency of the proposed MASAC algorithm.Comment: Accepted to The 2nd International Conference on Distributed Artificial Intelligenc

MuSR method and tomographic probability representation of spin states

Muon spin rotation/relaxation/resonance (MuSR) technique for studying matter structures is considered by means of a recently introduced probability representation of quantum spin states. A relation between experimental MuSR histograms and muon spin tomograms is established. Time evolution of muonium, anomalous muonium, and a muonium-like system is studied in the tomographic representation. Entanglement phenomenon of a bipartite muon-electron system is investigated via tomographic analogues of Bell number and positive partial transpose (PPT) criterion. Reconstruction of the muon-electron spin state as well as the total spin tomography of composed system is discussed.Comment: 20 pages, 4 figures, LaTeX, submitted to Journal of Russian Laser Researc