Linear functional observers with guaranteed ε-convergence for discrete time-delay systems with input/output disturbances

The problem of designing linear functional observers for discrete time-delay systems with unknown-but-bounded disturbances in both the plant and the output is considered for the first time in this paper. A novel approach to design a minimum-order observer is proposed to guarantee that the observer error is ϵ-convergent, which means that the estimate converges robustly within an ϵ-bound of the true state. Conditions for the existence of this observer are first derived. Then, by utilising an extended Lyapunov-Krasovskii functional and the free-weighting matrix technique, a sufficient condition for ϵ-convergence of the observer error system is given. This condition is presented in terms of linear matrix inequalities with two parameters needed to be tuned, so that it can be efficiently solved by incorporating a two-dimensional search method into convex optimisation algorithms to obtain the smallest possible value for ϵ. Three numerical examples, including the well-known single-link flexible joint robotic system, are given to illustrate the feasibility and effectiveness of our results.

Unknown input observer design for one-sided Lipschitz discrete-time systems subject to time-delay

In this paper, we address the problem of unknown input observer design, which simultaneously estimates state and unknown input, of a class of nonlinear discrete-time systems with time-delay. A novel approach to the state estimation problem of nonlinear systems where the nonlinearities satisfy the one-sided Lipschitz and quadratically inner-bounded conditions is proposed. This approach also allows us to reconstruct the unknown inputs of the systems. The nonlinear system is first transformed to a new system which can be decomposed into unknown-input-free and unknown-input-dependent subsystems. The estimation problem is then reduced to designing observer for the unknown-input-free subsystem. Rather than full-order observer design, in this paper, we propose observer design of reduced-order which is more practical and cost effective. By utilizing several mathematical techniques, the time-delay issue as well as the bilinear terms, which often emerge when designing observers for nonlinear discrete-time systems, are handled and less conservative observer synthesis conditions are derived in the linear matrix inequalities form. Two numerical examples are given to show the efficiency and high performance of our results.

New finite-sum inequalities with applications to stability of discrete time-delay systems

This paper is concerned with the problem of stability analysis of discrete time-delay systems. New finite-sum inequalities, which encompass the ones based on Abel lemma or Wirtinger type inequality, are first proposed. The potential capability of the newly derived inequalities is then demonstrated by establishing less conservative stability conditions for some classes of linear discrete-time systems with delay. The derived stability criteria are theoretically and numerically proved to be less conservative than existing results.

Observer design for one-sided Lipschitz discrete-time systems subject to delays and unknown inputs

In this paper, we address the problem of observer design for a class of nonlinear discrete-time systems in the presence of delays and unknown inputs. The nonlinearities studied in this work satisfy the one-sided Lipschitz and quadratically inner-bounded conditions which are more general than the traditional Lipschitz conditions. Both H∞ observer design and asymptotic observer design with reduced-order are considered. The designs are novel compared to other relevant nonlinear observer designs subject to time delays and disturbances in the literature. In order to deal with the time-delay issue as well as the bilinear terms which usually appear in the problem of designing observers for discrete-time systems, several mathematical techniques are utilized to deduce observer synthesis conditions in the linear matrix inequalities form. A numerical example is given to demonstrate the effectiveness and high performance of our results.

Componentwise ultimate bounds for positive discrete time-delay systems perturbed by interval disturbances

This paper presents a method to derive componentwise ultimate upper bounds and componentwise ultimate lower bounds for linear positive systems with time-varying delays and bounded disturbances. The disturbance vector is assumed to vary within a known interval whose lower bound may be different from zero. We first derive a sufficient condition for the existence of componentwise ultimate bounds. This condition is given in terms of the spectral radius of the system matrices which is easy to check and allows us to compute directly both the smallest componentwise ultimate upper bound and the largest componentwise ultimate lower bound. Then, by using the comparison method, we extend the obtained result to a class of nonlinear time-delay systems which has linear positive bounds. Two numerical examples are given to illustrate the effectiveness of the obtained results.

Quantum kernels for unattributed graphs using discrete-time quantum walks

In this paper, we develop a new family of graph kernels where the graph structure is probed by means of a discrete-time quantum walk. Given a pair of graphs, we let a quantum walk evolve on each graph and compute a density matrix with each walk. With the density matrices for the pair of graphs to hand, the kernel between the graphs is defined as the negative exponential of the quantum Jensen–Shannon divergence between their density matrices. In order to cope with large graph structures, we propose to construct a sparser version of the original graphs using the simplification method introduced in Qiu and Hancock (2007). To this end, we compute the minimum spanning tree over the commute time matrix of a graph. This spanning tree representation minimizes the number of edges of the original graph while preserving most of its structural information. The kernel between two graphs is then computed on their respective minimum spanning trees. We evaluate the performance of the proposed kernels on several standard graph datasets and we demonstrate their effectiveness and efficiency.

A Scheduling Algorithm for Flexible Manufacturing Cell

In this paper, a new scheduling algorithm for the flexible manufacturing cell is presented, which is a discrete time control method with fixed length control period combining with event interruption. At the flow control level we determine simultaneously the production mix and the proportion of parts to be processed through each route. The simulation results for a hypothetical manufacturing cell are presented.

Optimal controllers with complex order derivatives

This paper studies the optimization of complex-order algorithms for the discrete-time control of linear and nonlinear systems. The fundamentals of fractional systems and genetic algorithms are introduced. Based on these concepts, complexorder control schemes and their implementation are evaluated in the perspective of evolutionary optimization. The results demonstrate not only that complex-order derivatives constitute a valuable alternative for deriving control algorithms, but also the feasibility of the adopted optimization strategy.

Fractional order modelling of fractional-order holds

Discrete time control systems require sample- and-hold circuits to perform the conversion from digital to analog. Fractional-Order Holds (FROHs) are an interpolation between the classical zero and first order holds and can be tuned to produce better system performance. However, the model of the FROH is somewhat hermetic and the design of the system becomes unnecessarily complicated. This paper addresses the modelling of the FROHs using the concepts of Fractional Calculus (FC). For this purpose, two simple fractional-order approximations are proposed whose parameters are estimated by a genetic algorithm. The results are simple to interpret, demonstrating that FC is a useful tool for the analysis of these devices.

Optimal tuning of fractional controllers using genetic algorithms

This study addresses the optimization of fractional algorithms for the discrete-time control of linear and non-linear systems. The paper starts by analyzing the fundamentals of fractional control systems and genetic algorithms. In a second phase the paper evaluates the problem in an optimization perspective. The results demonstrate the feasibility of the evolutionary strategy and the adaptability to distinct types of systems.

Novos resultados sobre a estabilidade e controle de sistemas nao-lineares utilizando modelos fuzzy e LMI

Relaxed conditions for the stability study of nonlinear, continuous and discrete-time systems given by fuzzy models are presented. A theoretical analysis shows that the proposed method provides better or at least the same results of the methods presented in the literature. Digital simulations exemplify this fact. These results are also used for the fuzzy regulators design. The nonlinear systems are represented by the fuzzy models proposed by Takagi and Sugeno. The stability analysis and the design of controllers are described by LMIs (Linear Matrix Inequalities), that can be solved efficiently by convex programming techniques. The specification of the decay rate, constraints on control input and output are also described by LMIs. Finally, the proposed design method is applied in the control of an inverted pendulum.

Stochastic Stability for Markovian Jump Linear Systems Subject to a Crucial Failure Event

This paper is concerned with the stability of discrete-time linear systems subject to random jumps in the parameters, described by an underlying finite-state Markov chain. In the model studied, a stopping time τ Δ is associated with the occurrence of a crucial failure after which the system is brought to a halt for maintenance. The usual stochastic stability concepts and associated results are not indicated, since they are tailored to pure infinite horizon problems. Using the concept named stochastic τ-stability, equivalent conditions to ensure the stochastic stability of the system until the occurrence of τ Δ is obtained. In addition, an intermediary and mixed case for which τ represents the minimum between the occurrence of a fix number N of failures and the occurrence of a crucial failure τ Δ is also considered. Necessary and sufficient conditions to ensure the stochastic τ-stability are provided in this setting that are auxiliary to the main result.

Modos deslizantes discretos em sistemas incertos com atraso na computação do sinal de controle

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Projetos de controle discreto com modos deslizantes para sistemas sujeitos a atraso no controle

Pós-graduação em Engenharia Elétrica - FEIS

Controle discreto com modos deslizantes em sistemas incertos com atraso no sinal de controle

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)