AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This paper deals with the long run average continuous control problem of piecewise deterministic Markov processes (PDMPs) taking values in a general Borel space and with compact action space depending on the state variable. The control variable acts on the jump rate and transition measure of the PDMP, and the running and boundary costs are assumed to be positive but not necessarily bounded. Our first main result is to obtain an optimality equation for the long run average cost in terms of a discrete-time optimality equation related to the embedded Markov chain given by the postjump location of the PDMP. Our second main result guarantees the existence of a feedback measurable selector for the discrete-time optimality equation by establishing a connection between this equation and an integro-differential equation. Our final main result is to obtain some sufficient conditions for the existence of a solution for a discrete-time optimality inequality and an ordinary optimal feedback control for the long run average cost using the so-called vanishing discount approach. Two examples are presented illustrating the possible applications of the results developed in the paper.

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.

Generalized Coupled Algebraic Riccati Equations for Discrete-time Markov Jump with Multiplicative Noise Systems

In this paper we consider the existence of the maximal and mean square stabilizing solutions for a set of generalized coupled algebraic Riccati equations (GCARE for short) associated to the infinite-horizon stochastic optimal control problem of discrete-time Markov jump with multiplicative noise linear systems. The weighting matrices of the state and control for the quadratic part are allowed to be indefinite. We present a sufficient condition, based only on some positive semi-definite and kernel restrictions on some matrices, under which there exists the maximal solution and a necessary and sufficient condition under which there exists the mean square stabilizing solution fir the GCARE. We also present a solution for the discounted and long run average cost problems when the performance criterion is assumed be composed by a linear combination of an indefinite quadratic part and a linear part in the state and control variables. The paper is concluded with a numerical example for pension fund with regime switching.

Influence of insulin treatment on the lacrimal gland and ocular surface of diabetic rats

Previous studies have observed changes in the lacrimal gland and ocular surface related to diabetes mellitus and related it to insulin resistance or insufficiency and oxidative damage. The aim of this study was to evaluate whether insulin treatment inhibits those changes. Diabetes was induced in male Wistar rats with a single intravenous injection of streptozotocin and a subgroup was treated with insulin. After 5 and 10 weeks, the three groups (n = 5-10/group/experimental procedure) were compared for biochemical, functional, and histological parameters. After 5 weeks, changes in morphology and increased numbers of lipofucsin-like inclusions were observed in lacrimal glands of diabetic but not insulin-treated rats. After 5 weeks, malonaldehyde and total peroxidase activity were significantly higher in diabetic rats, but similar to control in insulin-treated diabetic rats (P = 0.03, P = 0.02, respectively). Our data indicate that diabetes induces histological alterations in lacrimal gland and suggests that hyperglycemia-related oxidative stress may participate in diabetic dry eye syndrome. Prevention by insulin replacement suggests direct hormone action and/or benefit by early sub optimal metabolic control.

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.

An approach of optimal sensitivity applied in the tertiary loop of the automatic generation control

This paper proposes an approach of optimal sensitivity applied in the tertiary loop of the automatic generation control. The approach is based on the theorem of non-linear perturbation. From an optimal operation point obtained by an optimal power flow a new optimal operation point is directly determined after a perturbation, i.e., without the necessity of an iterative process. This new optimal operation point satisfies the constraints of the problem for small perturbation in the loads. The participation factors and the voltage set point of the automatic voltage regulators (AVR) of the generators are determined by the technique of optimal sensitivity, considering the effects of the active power losses minimization and the network constraints. The participation factors and voltage set point of the generators are supplied directly to a computational program of dynamic simulation of the automatic generation control, named by power sensitivity mode. Test results are presented to show the good performance of this approach. (C) 2008 Elsevier B.V. All rights reserved.

Allosteric Control of Gating Mechanisms Revisited: The Large Conductance Ca(2+)-Activated K(+) Channel

Large-conductance Ca(2+)-activated K(+) channels (BK) play a fundamental role in modulating membrane potential in many cell types. The gating of BK channels and its modulation by Ca(2+) and voltage has been the subject of intensive research over almost three decades, yielding several of the most complicated kinetic mechanisms ever proposed. A large number of open and closed states disposed, respectively, in two planes, named tiers, characterize these mechanisms. Transitions between states in the same plane are cooperative and modulated by Ca(2+). Transitions across planes are highly concerted and voltage-dependent. Here we reexamine the validity of the two-tiered hypothesis by restricting attention to the modulation by Ca(2+). Large single channel data sets at five Ca(2+) concentrations were simultaneously analyzed from a Bayesian perspective by using hidden Markov models and Markov-chain Monte Carlo stochastic integration techniques. Our results support a dramatic reduction in model complexity, favoring a simple mechanism derived from the Monod-Wyman-Changeux allosteric model for homotetramers, able to explain the Ca(2+) modulation of the gating process. This model differs from the standard Monod-Wyman-Changeux scheme in that one distinguishes when two Ca(2+) ions are bound to adjacent or diagonal subunits of the tetramer.

Unexpected Diversity of Cellular Immune Responses against Nef and Vif in HIV-1-Infected Patients Who Spontaneously Control Viral Replication

Background: HIV-1-infected individuals who spontaneously control viral replication represent an example of successful containment of the AIDS virus. Understanding the anti-viral immune responses in these individuals may help in vaccine design. However, immune responses against HIV-1 are normally analyzed using HIV-1 consensus B 15-mers that overlap by 11 amino acids. Unfortunately, this method may underestimate the real breadth of the cellular immune responses against the autologous sequence of the infecting virus. Methodology and Principal Findings: Here we compared cellular immune responses against nef and vif-encoded consensus B 15-mer peptides to responses against HLA class I-predicted minimal optimal epitopes from consensus B and autologous sequences in six patients who have controlled HIV-1 replication. Interestingly, our analysis revealed that three of our patients had broader cellular immune responses against HLA class I-predicted minimal optimal epitopes from either autologous viruses or from the HIV-1 consensus B sequence, when compared to responses against the 15-mer HIV-1 type B consensus peptides. Conclusion and Significance: This suggests that the cellular immune responses against HIV-1 in controller patients may be broader than we had previously anticipated.

Cost effectiveness of OptiMal (R) rapid diagnostic test for malaria in remote areas of the Amazon Region, Brazil

Background: In areas with limited structure in place for microscopy diagnosis, rapid diagnostic tests (RDT) have been demonstrated to be effective. Method: The cost-effectiveness of the Optimal (R) and thick smear microscopy was estimated and compared. Data were collected on remote areas of 12 municipalities in the Brazilian Amazon. Data sources included the National Malaria Control Programme of the Ministry of Health, the National Healthcare System reimbursement table, hospitalization records, primary data collected from the municipalities, and scientific literature. The perspective was that of the Brazilian public health system, the analytical horizon was from the start of fever until the diagnostic results provided to patient and the temporal reference was that of year 2006. The results were expressed in costs per adequately diagnosed cases in 2006 U. S. dollars. Sensitivity analysis was performed considering key model parameters. Results: In the case base scenario, considering 92% and 95% sensitivity for thick smear microscopy to Plasmodium falciparum and Plasmodium vivax, respectively, and 100% specificity for both species, thick smear microscopy is more costly and more effective, with an incremental cost estimated at US$ 549.9 per adequately diagnosed case. In sensitivity analysis, when sensitivity and specificity of microscopy for P. vivax were 0.90 and 0.98, respectively, and when its sensitivity for P. falciparum was 0.83, the RDT was more cost-effective than microscopy. Conclusion: Microscopy is more cost-effective than OptiMal (R) in these remote areas if high accuracy of microscopy is maintained in the field. Decision regarding use of rapid tests for diagnosis of malaria in these areas depends on current microscopy accuracy in the field.

Transmission loss allocation based on optimal power flow and sensitivity analysis

This paper presents a new approach to the transmission loss allocation problem in a deregulated system. This approach belongs to the set of incremental methods. It treats all the constraints of the network, i.e. control, state and functional constraints. The approach is based on the perturbation of optimum theorem. From a given optimal operating point obtained by the optimal power flow the loads are perturbed and a new optimal operating point that satisfies the constraints is determined by the sensibility analysis. This solution is used to obtain the allocation coefficients of the losses for the generators and loads of the network. Numerical results show the proposed approach in comparison to other methods obtained with well-known transmission networks, IEEE 14-bus. Other test emphasizes the importance of considering the operational constraints of the network. And finally the approach is applied to an actual Brazilian equivalent network composed of 787 buses, and it is compared with the technique used nowadays by the Brazilian Control Center. (c) 2007 Elsevier Ltd. All rights reserved.

Multimodal passive vibration control of sandwich beams with shunted shear piezoelectric materials

This work presents a performance analysis of multimodal passive vibration control of a sandwich beam using shear piezoelectric materials, embedded in a sandwich beam core, connected to independent resistive shunt circuits. Shear piezoelectric actuators were recently shown to be more interesting for higher frequencies and stiffer structures. In particular, for shunted damping, it was shown that equivalent material loss factors of up to 31% can be achieved by optimizing the shunt circuit. In the present work, special attention is given to the design of multimodal vibration control through independent shunted shear piezoelectric sensors. In particular, a parametric analysis is performed to evaluate optimal configurations for a set of modes to be damped. Then, a methodology to evaluate the modal damping resulting from each shunted piezoelectric sensor is presented using the modal strain energy method. Results show that modal damping factors of 1%-2% can be obtained for three selected vibration modes.

A safety assessment methodology applied to CNS/ATM-based air traffic control system

In the last decades, the air traffic system has been changing to adapt itself to new social demands, mainly the safe growth of worldwide traffic capacity. Those changes are ruled by the Communication, Navigation, Surveillance/Air Traffic Management (CNS/ATM) paradigm, based on digital communication technologies (mainly satellites) as a way of improving communication, surveillance, navigation and air traffic management services. However, CNS/ATM poses new challenges and needs, mainly related to the safety assessment process. In face of these new challenges, and considering the main characteristics of the CNS/ATM, a methodology is proposed at this work by combining ""absolute"" and ""relative"" safety assessment methods adopted by the International Civil Aviation Organization (ICAO) in ICAO Doc.9689 [14], using Fluid Stochastic Petri Nets (FSPN) as the modeling formalism, and compares the safety metrics estimated from the simulation of both the proposed (in analysis) and the legacy system models. To demonstrate its usefulness, the proposed methodology was applied to the ""Automatic Dependent Surveillance-Broadcasting"" (ADS-B) based air traffic control system. As conclusions, the proposed methodology assured to assess CNS/ATM system safety properties, in which FSPN formalism provides important modeling capabilities, and discrete event simulation allowing the estimation of the desired safety metric. (C) 2011 Elsevier Ltd. All rights reserved.

Real time optimization (RTO) with model predictive control (MPC)

This paper studies a simplified methodology to integrate the real time optimization (RTO) of a continuous system into the model predictive controller in the one layer strategy. The gradient of the economic objective function is included in the cost function of the controller. Optimal conditions of the process at steady state are searched through the use of a rigorous non-linear process model, while the trajectory to be followed is predicted with the use of a linear dynamic model, obtained through a plant step test. The main advantage of the proposed strategy is that the resulting control/optimization problem can still be solved with a quadratic programming routine at each sampling step. Simulation results show that the approach proposed may be comparable to the strategy that solves the full economic optimization problem inside the MPC controller where the resulting control problem becomes a non-linear programming problem with a much higher computer load. (C) 2010 Elsevier Ltd. All rights reserved.

Stable Model Predictive Control for Integrating Systems with Optimizing Targets

This paper concern the development of a stable model predictive controller (MPC) to be integrated with real time optimization (RTO) in the control structure of a process system with stable and integrating outputs. The real time process optimizer produces Optimal targets for the system inputs and for Outputs that Should be dynamically implemented by the MPC controller. This paper is based oil a previous work (Comput. Chem. Eng. 2005, 29, 1089) where a nominally stable MPC was proposed for systems with the conventional control approach where only the outputs have set points. This work is also based oil the work of Gonzalez et at. (J. Process Control 2009, 19, 110) where the zone control of stable systems is studied. The new control for is obtained by defining ail extended control objective that includes input targets and zone controller the outputs. Additional decision variables are also defined to increase the set of feasible solutions to the control problem. The hard constraints resulting from the cancellation of the integrating modes Lit the end of the control horizon are softened,, and the resulting control problem is made feasible to a large class of unknown disturbances and changes of the optimizing targets. The methods are illustrated with the simulated application of the proposed,approaches to a distillation column of the oil refining industry.

Robust model predictive control with zone control

Model predictive control (MPC) is usually implemented as a control strategy where the system outputs are controlled within specified zones, instead of fixed set points. One strategy to implement the zone control is by means of the selection of different weights for the output error in the control cost function. A disadvantage of this approach is that closed-loop stability cannot be guaranteed, as a different linear controller may be activated at each time step. A way to implement a stable zone control is by means of the use of an infinite horizon cost in which the set point is an additional variable of the control problem. In this case, the set point is restricted to remain inside the output zone and an appropriate output slack variable is included in the optimisation problem to assure the recursive feasibility of the control optimisation problem. Following this approach, a robust MPC is developed for the case of multi-model uncertainty of open-loop stable systems. The controller is devoted to maintain the outputs within their corresponding feasible zone, while reaching the desired optimal input target. Simulation of a process of the oil re. ning industry illustrates the performance of the proposed strategy.