Galerkin Method and Weighting Functions Applied to Nonlinear H(infinity) Control with Output Feedback

This paper considers two aspects of the nonlinear H(infinity) control problem: the use of weighting functions for performance and robustness improvement, as in the linear case, and the development of a successive Galerkin approximation method for the solution of the Hamilton-Jacobi-Isaacs equation that arises in the output-feedback case. Design of nonlinear H(infinity) controllers obtained by the well-established Taylor approximation and by the proposed Galerkin approximation method applied to a magnetic levitation system are presented for comparison purposes.

Sampled Control for Mean-Variance Hedging in a Jump Diffusion Financial Market

In this technical note we consider the mean-variance hedging problem of a jump diffusion continuous state space financial model with the re-balancing strategies for the hedging portfolio taken at discrete times, a situation that more closely reflects real market conditions. A direct expression based on some change of measures, not depending on any recursions, is derived for the optimal hedging strategy as well as for the ""fair hedging price"" considering any given payoff. For the case of a European call option these expressions can be evaluated in a closed form.

On the convergence of successive Galerkin approximation for nonlinear output feedback H(infinity) control

Although the formulation of the nonlinear theory of H(infinity) control has been well developed, solving the Hamilton-Jacobi-Isaacs equation remains a challenge and is the major bottleneck for practical application of the theory. Several numerical methods have been proposed for its solution. In this paper, results on convergence and stability for a successive Galerkin approximation approach for nonlinear H(infinity) control via output feedback are presented. An example is presented illustrating the application of the algorithm.

THE VANISHING DISCOUNT APPROACH FOR THE AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This work is concerned with the existence of an optimal control strategy for the long-run average continuous control problem of piecewise-deterministic Markov processes (PDMPs). In Costa and Dufour (2008), sufficient conditions were derived to ensure the existence of an optimal control by using the vanishing discount approach. These conditions were mainly expressed in terms of the relative difference of the alpha-discount value functions. The main goal of this paper is to derive tractable conditions directly related to the primitive data of the PDMP to ensure the existence of an optimal control. The present work can be seen as a continuation of the results derived in Costa and Dufour (2008). Our main assumptions are written in terms of some integro-differential inequalities related to the so-called expected growth condition, and geometric convergence of the post-jump location kernel associated to the PDMP. An example based on the capacity expansion problem is presented, illustrating the possible applications of the results developed in the paper.

Using bifurcations in the determination of lock-in ranges for third-order phase-locked loops

Transmission and switching in digital telecommunication networks require distribution of precise time signals among the nodes. Commercial systems usually adopt a master-slave (MS) clock distribution strategy building slave nodes with phase-locked loop (PLL) circuits. PLLs are responsible for synchronizing their local oscillations with signals from master nodes, providing reliable clocks in all nodes. The dynamics of a PLL is described by an ordinary nonlinear differential equation, with order one plus the order of its internal linear low-pass filter. Second-order loops are commonly used because their synchronous state is asymptotically stable and the lock-in range and design parameters are expressed by a linear equivalent system [Gardner FM. Phaselock techniques. New York: John Wiley & Sons: 1979]. In spite of being simple and robust, second-order PLLs frequently present double-frequency terms in PD output and it is very difficult to adapt a first-order filter in order to cut off these components [Piqueira JRC, Monteiro LHA. Considering second-harmonic terms in the operation of the phase detector for second order phase-locked loop. IEEE Trans Circuits Syst [2003;50(6):805-9; Piqueira JRC, Monteiro LHA. All-pole phase-locked loops: calculating lock-in range by using Evan`s root-locus. Int J Control 2006;79(7):822-9]. Consequently, higher-order filters are used, resulting in nonlinear loops with order greater than 2. Such systems, due to high order and nonlinear terms, depending on parameters combinations, can present some undesirable behaviors, resulting from bifurcations, as error oscillation and chaos, decreasing synchronization ranges. In this work, we consider a second-order Sallen-Key loop filter [van Valkenburg ME. Analog filter design. New York: Holt, Rinehart & Winston; 1982] implying a third order PLL The resulting lock-in range of the third-order PLL is determined by two bifurcation conditions: a saddle-node and a Hopf. (C) 2008 Elsevier B.V. All rights reserved.

On the Filtering Problem for Continuous-Time Markov Jump Linear Systems with no Observation of the Markov Chain

We consider in this paper the optimal stationary dynamic linear filtering problem for continuous-time linear systems subject to Markovian jumps in the parameters (LSMJP) and additive noise (Wiener process). It is assumed that only an output of the system is available and therefore the values of the jump parameter are not accessible. It is a well known fact that in this setting the optimal nonlinear filter is infinite dimensional, which makes the linear filtering a natural numerically, treatable choice. The goal is to design a dynamic linear filter such that the closed loop system is mean square stable and minimizes the stationary expected value of the mean square estimation error. It is shown that an explicit analytical solution to this optimal filtering problem is obtained from the stationary solution associated to a certain Riccati equation. It is also shown that the problem can be formulated using a linear matrix inequalities (LMI) approach, which can be extended to consider convex polytopic uncertainties on the parameters of the possible modes of operation of the system and on the transition rate matrix of the Markov process. As far as the authors are aware of this is the first time that this stationary filtering problem (exact and robust versions) for LSMJP with no knowledge of the Markov jump parameters is considered in the literature. Finally, we illustrate the results with an example.

Discrete-time mean variance optimal control of linear systems with Markovian jumps and multiplicative noise

In this article, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noise under three kinds of performance criterions related to the final value of the expectation and variance of the output. In the first problem it is desired to minimise the final variance of the output subject to a restriction on its final expectation, in the second one it is desired to maximise the final expectation of the output subject to a restriction on its final variance, and in the third one it is considered a performance criterion composed by a linear combination of the final variance and expectation of the output of the system. We present explicit sufficient conditions for the existence of an optimal control strategy for these problems, generalising previous results in the literature. We conclude this article presenting a numerical example of an asset liabilities management model for pension funds with regime switching.

Comparison of friction models applied to a control valve

Eight different models to represent the effect of friction in control valves are presented: four models based on physical principles and four empirical ones. The physical models, both static and dynamic, have the same structure. The models are implemented in Simulink/Matlab (R) and compared, using different friction coefficients and input signals. Three of the models were able to reproduce the stick-slip phenomenon and passed all the tests, which were applied following ISA standards. (C) 2008 Elsevier Ltd. All rights reserved.

Postural control during kneeling

Postural control was studied when the subject was kneeling with erect trunk in a quiet posture and compared to that obtained during quiet standing. The analysis was based on the center of pressure motion in the sagittal plane (CPx), both in the time and in the frequency domains. One could assume that postural control during kneeling would be poorer than in standing because it is a less natural posture. This could cause a higher CPx variability. The power spectral density (PSD) of the CPx obtained from the experimental data in the kneeling position (KN) showed a significant decrease at frequencies below 0.3 Hz compared to upright (UP) (P < 0.01), which indicates less sway in KN. Conversely, there was an increase in fast postural oscillations (above 0.7 Hz) during KN compared to UP (P < 0.05). The root mean square (RMS) of the CPx was higher for UP (P < 0.01) while the mean velocity (MV) was higher during KN (P < 0.05). Lack of vision had a significant effect on the PSD and the parameters estimated from the CPx in both positions. We also sought to verify whether the changes in the PSD of the CPx found between the UP and KN positions were exclusively due to biomechanical factors (e.g., lowered center of gravity), or also reflected changes in the neural processes involved in the control of balance. To reach this goal, besides the experimental approach, a simple feedback model (a PID neural system, with added neural noise and controlling an inverted pendulum) was used to simulate postural sway in both conditions (in KN the pendulum was shortened, the mass and the moment of inertia were decreased). A parameter optimization method was used to fit the CPx power spectrum given by the model to that obtained experimentally. The results indicated that the changed anthropometric parameters in KN would indeed cause a large decrease in the power spectrum at low frequencies. However, the model fitting also showed that there were considerable changes also in the neural subsystem when the subject went from standing to kneeling. There was a lowering of the proportional and derivative gains and an increase in the neural noise power. Additional increases in the neural noise power were found also when the subject closed his eyes.

Flatness-based control of a single qubit gate

This work considers the open-loop control problem of steering a two-level quantum system from any initial to any final condition. The model of this system evolves on the state space X = SU(2), having two inputs that correspond to the complex amplitude of a resonant laser field. A symmetry preserving flat output is constructed using a fully geometric construction and quaternion computations. Simulation results of this flatness-based open-loop control are provided.

Adequacy of Cold Rolling Models to Upgrade Set-up Generation Systems

This paper presents two strategies for the upgrade of set-up generation systems for tandem cold mills. Even though these mills have been modernized mainly due to quality requests, their upgrades may be made intending to replace pre-calculated reference tables. In this case, Bryant and Osborn mill model without adaptive technique is proposed. As a more demanding modernization, Bland and Ford model including adaptation is recommended, although it requires a more complex computational hardware. Advantages and disadvantages of these two systems are compared and discussed and experimental results obtained from an industrial cold mill are shown.

Singular Perturbation for the Discounted Continuous Control of Piecewise Deterministic Markov Processes

This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP`s) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space a""e (n) . The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter epsilon > 0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as epsilon goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as epsilon goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.

A new technique to control brushless motor for blood pump application

This article presents a back-electromotive force (BEMF)-based technique of detection for sensorless brushless direct current motor (BLDCM) drivers. The BLDCM has been chosen as the energy converter in rotary or pulsatile blood pumps that use electrical motors for pumping. However, in order to operate properly, the BLDCM driver needs to know the shaft position. Usually, that information is obtained through a set of Hall sensors assembled close to the rotor and connected to the electronic controller by wires. Sometimes, a large distance between the motor and controller makes the system susceptible to interference on the sensor signal because of winding current switching. Thus, the goal of the sensorless technique presented in this study is to avoid this problem. First, the operation of BLDCM was evaluated on the electronic simulator PSpice. Then, a BEMF detector circuitry was assembled in our laboratories. For the tests, a sensor-dependent system was assembled where the direct comparison between the Hall sensors signals and the detected signals was performed. The obtained results showed that the output sensorless detector signals are very similar to the Hall signals at speeds of more than 2500 rpm. Therefore, the sensorless technique is recommended as a responsible or redundant system to be used in rotary blood pumps.

SKAN: Skin Scanner - System for Skin Cancer Detection Using Adaptive Techniques

SKAN: Skin Scanner - System for Skin Cancer Detection Using Adaptive Techniques - combines computer engineering concepts with areas like dermatology and oncology. Its objective is to discern images of skin cancer, specifically melanoma, from others that show only common spots or other types of skin diseases, using image recognition. This work makes use of the ABCDE visual rule, which is often used by dermatologists for melanoma identification, to define which characteristics are analyzed by the software. It then applies various algorithms and techniques, including an ellipse-fitting algorithm, to extract and measure these characteristics and decide whether the spot is a melanoma or not. The achieved results are presented with special focus on the adaptive decision-making and its effect on the diagnosis. Finally, other applications of the software and its algorithms are presented.

The AdapLib Library for Execution of Adaptive Devices: Architecture and Use

In this paper it is presented the theoretical background, the architecture (using the ""4+1"" model), and the use of the library for execution of adaptive devices, AdapLib. This library was created seeking to be accurate to the adaptive devices theory, and to allow its easy extension considering the specific details of solutions that employ this kind of device. As an example, it is presented a case study in which the library was used to create a proof of concept to monitor and diagnose problems in an online news portal.