Control of structured populations by harvest

It has long been recognized that demographic structure within a population can significantly affect the likely outcomes of harvest. Many studies have focussed on equilibrium dynamics and maximization of the value of the harvest taken. However, in some cases the management objective is to maintain the population at a abundance that is significantly below the carrying capacity. Achieving such an objective by harvest can be complicated by the presence of significant structure (age or stage) in the target population. in such cases, optimal harvest strategies must account for differences among age- or stage-classes of individuals in their relative contribution to the demography of the population. In addition, structured populations are also characterized by transient non-linear dynamics following perturbation, such that even under an equilibrium harvest, the population may exhibit significant momentum, increasing or decreasing before cessation of growth. Using simple linear time-invariant models, we show that if harvest levels are set dynamically (e.g., annually) then transient effects can be as or more important than equilibrium outcomes. We show that appropriate harvest rates can be complicated by uncertainty about the demographic structure of the population, or limited control over the structure of the harvest taken. (c) 2006 Elsevier B.V. All rights reserved.

Mathematical modelling and control of agitated extraction columns

Liquid-liquid extraction has long been known as a unit operation that plays an important role in industry. This process is well known for its complexity and sensitivity to operation conditions. This thesis presents an attempt to explore the dynamics and control of this process using a systematic approach and state of the art control system design techniques. The process was studied first experimentally under carefully selected. operation conditions, which resembles the ranges employed practically under stable and efficient conditions. Data were collected at steady state conditions using adequate sampling techniques for the dispersed and continuous phases as well as during the transients of the column with the aid of a computer-based online data logging system and online concentration analysis. A stagewise single stage backflow model was improved to mimic the dynamic operation of the column. The developed model accounts for the variation in hydrodynamics, mass transfer, and physical properties throughout the length of the column. End effects were treated by addition of stages at the column entrances. Two parameters were incorporated in the model namely; mass transfer weight factor to correct for the assumption of no mass transfer in the. settling zones at each stage and the backmixing coefficients to handle the axial dispersion phenomena encountered in the course of column operation. The parameters were estimated by minimizing the differences between the experimental and the model predicted concentration profiles at steady state conditions using non-linear optimisation technique. The estimated values were then correlated as functions of operating parameters and were incorporated in·the model equations. The model equations comprise a stiff differential~algebraic system. This system was solved using the GEAR ODE solver. The calculated concentration profiles were compared to those experimentally measured. A very good agreement of the two profiles was achieved within a percent relative error of ±2.S%. The developed rigorous dynamic model of the extraction column was used to derive linear time-invariant reduced-order models that relate the input variables (agitator speed, solvent feed flowrate and concentration, feed concentration and flowrate) to the output variables (raffinate concentration and extract concentration) using the asymptotic method of system identification. The reduced-order models were shown to be accurate in capturing the dynamic behaviour of the process with a maximum modelling prediction error of I %. The simplicity and accuracy of the derived reduced-order models allow for control system design and analysis of such complicated processes. The extraction column is a typical multivariable process with agitator speed and solvent feed flowrate considered as manipulative variables; raffinate concentration and extract concentration as controlled variables and the feeds concentration and feed flowrate as disturbance variables. The control system design of the extraction process was tackled as multi-loop decentralised SISO (Single Input Single Output) as well as centralised MIMO (Multi-Input Multi-Output) system using both conventional and model-based control techniques such as IMC (Internal Model Control) and MPC (Model Predictive Control). Control performance of each control scheme was. studied in terms of stability, speed of response, sensitivity to modelling errors (robustness), setpoint tracking capabilities and load rejection. For decentralised control, multiple loops were assigned to pair.each manipulated variable with each controlled variable according to the interaction analysis and other pairing criteria such as relative gain array (RGA), singular value analysis (SVD). Loops namely Rotor speed-Raffinate concentration and Solvent flowrate Extract concentration showed weak interaction. Multivariable MPC has shown more effective performance compared to other conventional techniques since it accounts for loops interaction, time delays, and input-output variables constraints.

Optimally-designed single fiber Bragg grating filter scheme for RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK format conversion

We investigate return-to-zero (RZ) to non-return-to-zero (NRZ) format conversion by means of the linear time-invariant system theory. It is shown that the problem of converting random RZ stream to NRZ stream can be reduced to constructing an appropriate transfer function for the linear filter. This approach is then used to propose novel optimally-designed single fiber Bragg grating (FBG) filter scheme for RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK format conversion. The spectral response of the FBG is designed according to the optical spectra of the algebraic difference between isolated NRZ and RZ pulses, and the filter order is optimized for the maximum Q-factor of the output NRZ signals. Experimental results as well as simulations show that such an optimallydesigned FBG can successfully perform RZ-OOK/DPSK/DQPSK to NRZOOK/ DPSK/DQPSK format conversion.

An efficient, approximate path-following algorithm for elastic net based nonlinear spike enhancement

Unwanted spike noise in a digital signal is a common problem in digital filtering. However, sometimes the spikes are wanted and other, superimposed, signals are unwanted, and linear, time invariant (LTI) filtering is ineffective because the spikes are wideband - overlapping with independent noise in the frequency domain. So, no LTI filter can separate them, necessitating nonlinear filtering. However, there are applications in which the noise includes drift or smooth signals for which LTI filters are ideal. We describe a nonlinear filter formulated as the solution to an elastic net regularization problem, which attenuates band-limited signals and independent noise, while enhancing superimposed spikes. Making use of known analytic solutions a novel, approximate path-following algorithm is given that provides a good, filtered output with reduced computational effort by comparison to standard convex optimization methods. Accurate performance is shown on real, noisy electrophysiological recordings of neural spikes.

Modelagem da propagação sonora em dutos : abordagem matemática no domínio da frequência e do tempo utilizando transformada de laplace

Dissertação (mestrado)—Universidade de Brasília, Faculdade UnB Gama, Faculdade de Tecnologia, Programa de Pós-graduação em Integridade de Materiais da Engenharia, 2016.

Approximate Model Checking of Real-Time Systems for Linear Duration Invariants

Real-time systems are usually modelled with timed automata and real-time requirements relating to the state durations of the system are often specifiable using Linear Duration Invariants, which is a decidable subclass of Duration Calculus formulas. Various algorithms have been developed to check timed automata or real-time automata for linear duration invariants, but each needs complicated preprocessing and exponential calculation. To the best of our knowledge, these algorithms have not been implemented. In this paper, we present an approximate model checking technique based on a genetic algorithm to check real-time automata for linear durration invariants in reasonable times. Genetic algorithm is a good optimization method when a problem needs massive computation and it works particularly well in our case because the fitness function which is derived from the linear duration invariant is linear. ACM Computing Classification System (1998): D.2.4, C.3.

H-infinity control design for time-delay linear systems: a rational transfer function based approach

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Linear quadratic Gaussian control of discrete-time Markov jump linear systems with horizon defined by stopping times

The linear quadratic Gaussian control of discrete-time Markov jump linear systems is addressed in this paper, first for state feedback, and also for dynamic output feedback using state estimation. in the model studied, the problem horizon is defined by a stopping time τ which represents either, the occurrence of a fix number N of failures or repairs (T N), or the occurrence of a crucial failure event (τ δ), after which the system paralyzed. From the constructive method used here a separation principle holds, and the solutions are given in terms of a Kalman filter and a state feedback sequence of controls. The control gains are obtained by recursions from a set of algebraic Riccati equations for the former case or by a coupled set of algebraic Riccati equation for the latter case. Copyright © 2005 IFAC.

H ∞ state feedback control of discrete-time Markov jump linear systems through linear matrix inequalities

This paper addresses the H ∞ state-feedback control design problem of discretetime Markov jump linear systems. First, under the assumption that the Markov parameter is measured, the main contribution is on the LMI characterization of all linear feedback controllers such that the closed loop output remains bounded by a given norm level. This results allows the robust controller design to deal with convex bounded parameter uncertainty, probability uncertainty and cluster availability of the Markov mode. For partly unknown transition probabilities, the proposed design problem is proved to be less conservative than one available in the current literature. An example is solved for illustration and comparisons. © 2011 IFAC.

H-infinity control design for time-delay linear systems: a rational transfer function based approach

The aim of this paper is to present new results on H-infinity control synthesis for time-delay linear systems. We extend the use of a finite order LTI system, called comparison system to H-infinity analysis and design. Differently from what can be viewed as a common feature of other control design methods available in the literature to date, the one presented here treats time-delay systems control design with classical numeric routines based on Riccati equations arisen from H-infinity theory. The proposed algorithm is simple, efficient and easy to implement. Some examples illustrating state and output feedback design are solved and discussed in order to put in evidence the most relevant characteristic of the theoretical results. Moreover, a practical application involving a 3-DOF networked control system is presented.

A Separation Principle for the Continuous-Time LQ-Problem With Markovian Jump Parameters

In this paper, we devise a separation principle for the finite horizon quadratic optimal control problem of continuous-time Markovian jump linear systems driven by a Wiener process and with partial observations. We assume that the output variable and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time. As in the case with no jumps, we show that an optimal controller can be obtained from two coupled Riccati differential equations, one associated to the optimal control problem when the state variable is available, and the other one associated to the optimal filtering problem. This is a separation principle for the finite horizon quadratic optimal control problem for continuous-time Markovian jump linear systems. For the case in which the matrices are all time-invariant we analyze the asymptotic behavior of the solution of the derived interconnected Riccati differential equations to the solution of the associated set of coupled algebraic Riccati equations as well as the mean square stabilizing property of this limiting solution. When there is only one mode of operation our results coincide with the traditional ones for the LQG control of continuous-time linear systems.

Task partitioning and priority assignment for distributed hard real-time systems

In this paper, we propose the Distributed using Optimal Priority Assignment (DOPA) heuristic that finds a feasible partitioning and priority assignment for distributed applications based on the linear transactional model. DOPA partitions the tasks and messages in the distributed system, and makes use of the Optimal Priority Assignment (OPA) algorithm known as Audsley’s algorithm, to find the priorities for that partition. The experimental results show how the use of the OPA algorithm increases in average the number of schedulable tasks and messages in a distributed system when compared to the use of Deadline Monotonic (DM) usually favoured in other works. Afterwards, we extend these results to the assignment of Parallel/Distributed applications and present a second heuristic named Parallel-DOPA (P-DOPA). In that case, we show how the partitioning process can be simplified by using the Distributed Stretch Transformation (DST), a parallel transaction transformation algorithm introduced in [1].

Linear-quadratic optimal control of descriptor systems

In recent years the analysis and synthesis of (mechanical) control systems in descriptor form has been established. This general description of dynamical systems is important for many applications in mechanics and mechatronics, in electrical and electronic engineering, and in chemical engineering as well. This contribution deals with linear mechanical descriptor systems and its control design with respect to a quadratic performance criterion. Here, the notion of properness plays an important role whether the standard Riccati approach can be applied as usual or not. Properness and non-properness distinguish between the cases if the descriptor system is exclusively governed by the control input or by its higher-order time-derivatives additionally. In the unusual case of non-proper systems a quite different problem of optimal control design has to be considered. Both cases will be solved completely.

Robust pole assignment in systems subject to structured perturbations

The problem of robust pole assignment by feedback in a linear, multivariable, time-invariant system which is subject to structured perturbations is investigated. A measure of robustness, or sensitivity, of the poles to a given class of perturbations is derived, and a reliable and efficient computational algorithm is presented for constructing a feedback which assigns the prescribed poles and optimizes the robustness measure.

Regularization of Descriptor Systems by Derivative and Proportional State Feedback

For linear multivariable time-invariant continuous or discrete-time singular systems it is customary to use a proportional feedback control in order to achieve a desired closed loop behaviour. Derivative feedback is rarely considered. This paper examines how derivative feedback in descriptor systems can be used to alter the structure of the system pencil under various controllability conditions. It is shown that derivative and proportional feedback controls can be constructed such that the closed loop system has a given form and is also regular and has index at most 1. This property ensures the solvability of the resulting system of dynamic-algebraic equations. The construction procedures used to establish the theory are based only on orthogonal matrix decompositions and can therefore be implemented in a numerically stable way. The problem of pole placement with derivative feedback alone and in combination with proportional state feedback is also investigated. A computational algorithm for improving the “conditioning” of the regularized closed loop system is derived.