Theory of nonlinear feedback under uncertainty

AbstractOur main purpose here is to demonstrate the potential of a new approach which is an important expansion of the feedback concept: we have chosen what seemed a natural way of tackling some traditional problems of the control theory and of comparing the results against those offered by conventional methods.The main problem considered is the output stabilization for uncertain plants. Using structural transformations, uncertain systems can change to the form convenient for output feedback design. Synthesis of observer-based control for asymptotical stabilization or uniform ultimate boundedness of the closed-loop system is provided.We consider the notions of asymptotic and exponential invariance of a control system implies its suboptimality.A method is described for stabilization of uncertain discrete-time plants of which only compact sets are known to which plants parameters and exogenous signals belong. New approaches for solving some central problems of mathematical control theory are considered for nonlinear dynamical systems. New criterious of local and global controllability and stabilizability are indicated and some synthesis procedures are suggested

Approximating of unstable cycle in nonlinear autonomous systems

Numerical procedures for approximate construction of cycles in nonlinear systems are studied. The procedures are based on functional parameter methods combined with mechanical quadratures, Newton's, and gradient methods. The convergence rate of the procedures is studied, as well as their range of applicability, and their stability with respect to small perturbations of the parameters. The results obtained can be applied to nonlinear problems described by ordinary differential equations, to the systems with delay, and to distributed systems.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Finding Loop Invariants for Programs over Arrays Using a Theorem Prover

Abstract. We present a new method for automatic generation of loop invariants for programs containing arrays. Unlike all previously known methods, our method allows one to generate first-order invariants containing alternations of quantifiers. The method is based on the automatic analysis of the so-called update predicates of loops. An update predicate for an array A expresses updates made to A. We observe that many properties of update predicates can be extracted automatically from the loop description and loop properties obtained by other methods such as a simple analysis of counters occurring in the loop, recurrence solving and quantifier elimination over loop variables. We run the theorem prover Vampire on some examples and show that non-trivial loop invariants can be generated.

Barley starch

This thesis examined barley amylopectin structure and looked for correlations between the structure and physical properties of starch. The structure of amylopectin and gelatinisation and retrogradation of starch were studied in 10 different barley cultivars/breeding lines with differing genetic background. Amylopectin is built up of thousands of chains of glucose monomers, organised into clusters. The detailed fine structure of amylopectin was studied by isolating clusters of amylopectin and their building blocks, which are the tightly branched units building up the clusters. Barley cultivars/breeding lines possessing the amo1 mutation had fewer long chains of DP≥38 in amylopectin and more large building blocks. The structure of building blocks was rather conserved between the different barley cultivars/breeding lines studied and was categorized into different size groups. These different building blocks were shown to be randomly distributed in the amylopectin molecule. The C-chains in amylopectin can be of any length and are a category of chains different from the B-chains. The backbone in amylopectin consists of a special type of B-chains which, when cleaved by α-amylase, become chains of a similar type to C-chains. Gelatinisation and retrogradation (recrystallisation of gelatinised starch) of barley starch was studied by differential scanning calorimetry. The amo1 mutation resulted in a broader gelatinisation temperature range and a higher enthalpy of retrogradation. Other structural features were also found to influence the physical properties of starch. Small clusters and denser structure of the building blocks resulted in higher gelatinisation temperature. Fast retrogradation was observed in barley which had amylopectin with shorter chains and many large building blocks consisting of many chains. Amylopectin structure was also studied in developing barley kernels. Three barley cultivars/breeding lines were grown in a phytotron and kernels were harvested at 9, 12 and 24 days after flowering. The results showed that amylopectin synthesized at later stages of development had a more tightly branched structure. Expression of the enzymes involved in starch biosynthesis is also known to change during endosperm development