Analysis of a sub-optimal scheme of drug dosage in the AIDS treatment

Here the results for CD4+T cells count and the viral load obtained from HIV sero-positive patients are compared with results from numerical simulations by computer. Also, the standard scheme of administration of drugs anti HIV (HAART schemes) which uses constant doses is compared with an alternative sub-optimal teatment scheme which uses variable drug dosage according to the evolution of a quantitative measure of the side effects. The quantitative analysis done here shows that it is possible to obtain, using the alternative scheme, the same performance of actual data but using variable dosage and having fewer side effects. Optimal control theory is used to solve and also to provide a prognosis related to the strategies for control of viraemia.

The LQ control problem for Markovian jumps linear systems with horizon defined by stopping times

This paper deals with a stochastic optimal control problem involving discrete-time jump Markov linear systems. The jumps or changes between the system operation modes evolve according to an underlying Markov chain. 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 (TN), or the occurrence of a crucial failure event (τΔ), after which the system is brought to a halt for maintenance. In addition, an intermediary mixed case for which T represents the minimum between TN and τΔ is also considered. These stopping times coincide with some of the jump times of the Markov state and the information available allows the reconfiguration of the control action at each jump time, in the form of a linear feedback gain. The solution for the linear quadratic problem with complete Markov state observation is presented. The solution is given in terms of recursions of a set of algebraic Riccati equations (ARE) or a coupled set of algebraic Riccati equation (CARE).

A maximum principle for infinite time asymptotically stable impulsive dynamic control systems

We consider an infinite horizon optimal impulsive control problems for which a given cost function is minimized by choosing control strategies driving the state to a point in a given closed set C ∞. We present necessary conditions of optimality in the form of a maximum principle for which the boundary condition of the adjoint variable is such that non-degeneracy due to the fact that the time horizon is infinite is ensured. These conditions are given for conventional systems in a first instance and then for impulsive control problems. They are proved by considering a family of approximating auxiliary interval conventional (without impulses) optimal control problems defined on an increasing sequence of finite time intervals. As far as we know, results of this kind have not been derived previously. © 2010 IFAC.

A maximum principle for constrained infinite horizon dynamic control systems

This article presents and discusses a maximum principle for infinite horizon constrained optimal control problems with a cost functional depending on the state at the final time. The main feature of these optimality conditions is that, under reasonably weak assumptions, the multiplier is shown to satisfy a novel transversality condition at infinite time. It is also shown that these conditions can also be obtained for impulsive control problems whose dynamics are given by measure driven differential equations. © 2011 IFAC.

New optimality conditions for nonsmooth control problems

This work considers nonsmooth optimal control problems and provides two new sufficient conditions of optimality. The first condition involves the Lagrange multipliers while the second does not. We show that under the first new condition all processes satisfying the Pontryagin Maximum Principle (called MP-processes) are optimal. Conversely, we prove that optimal control problems in which every MP-process is optimal necessarily obey our first optimality condition. The second condition is more natural, but it is only applicable to normal problems and the converse holds just for smooth problems. Nevertheless, it is proved that for the class of normal smooth optimal control problems the two conditions are equivalent. Some examples illustrating the features of these sufficient concepts are presented. © 2012 Springer Science+Business Media New York.

Chaos suppression in NEMs resonators by using nonlinear control design

In this work the chaotic behavior of a micro-mechanical resonator with electrostatic forces on both sides is suppressed. The aim is to control the system in an orbit of the analytical solution obtained by the Method of Multiple Scales. Two control strategies are used for controlling the trajectory of the system, namely: State Dependent Riccati Equation (SDRE) Control and Optimal Linear Feedback Control (OLFC). The controls proved effectiveness in controlling the trajectory of the system. Additionally, the robustness of each strategy is tested considering the presence of parametric errors and measurement noise in control. © 2012 American Institute of Physics.

Daily biofilm control and oral health: Consensus on the epidemiological challenge-Latin American Advisory Panel

Our understanding of dental plaque biofilm has evolved since the nonspecific plaque hypothesis that considered plaque as a nonspecific mass of native microorganisms that, because of lack of oral hygiene, builds up in proportions great enough to overcome the host resistance threshold and affect the tooth structure and tooth supporting tissues. A great diversity of microorganisms-over 700 species-was detected in the oral cavity, and evidence shows that the investigation of specific microorganisms or associations of microorganisms as etiological agents for periodontal diseases and caries is not a simplistic approach. Although clinical evidence shows that oral mechanical hygiene is fundamental to prevent and control caries and periodontal disease, it is important to highlight that optimal control is not achieved by most individuals. Thus the complementary use of chemotherapeutic agents has been investigated as a way to overcome the deficiencies of mechanical oral hygiene habits, insofar as they reduce both plaque formation and gingival inflammation, and represent a valid strategy to change the biofilm and maintain dental and periodontal health. The role of the dental professional is to monitor patients and offer them the best recommendations to preserve oral health throughout their life. With this in mind, chemical control should be indicated as part of daily oral hygiene, together with mechanical procedures, for all individuals who present supragingival and/or subgingival biofilm, taking into account age, physical and/or psychological limitations, allergies, and other factors.

On the properness of an impulsive control extension of dynamic optimization problems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

NASH game and mixed H2/H∞ control

In this work a Nonzero-Sum NASH game related to the H2 and H∞ control problems is formulated in the context of convex optimization theory. The variables of the game are limiting bounds for the H2 and H∞ norms, and the final controller is obtained as an equilibrium solution, which minimizes the `sensitivity of each norm' with respect to the other. The state feedback problem is considered and illustrated by numerical examples.

Nonlinear state estimation and control for chaos suppression in MEMS resonator

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

SINGULARLY PERTURBED DISCOUNTED MARKOV CONTROL PROCESSES IN A GENERAL STATE SPACE

This paper studies the asymptotic optimality of discrete-time Markov decision processes (MDPs) with general state space and action space and having weak and strong interactions. By using a similar approach as developed by Liu, Zhang, and Yin [Appl. Math. Optim., 44 (2001), pp. 105-129], the idea in this paper is to consider an MDP with general state and action spaces and to reduce the dimension of the state space by considering an averaged model. This formulation is often described by introducing a small parameter epsilon > 0 in the definition of the transition kernel, leading to a singularly perturbed Markov model with two time scales. Our objective is twofold. First it is shown that the value function of the control problem for the perturbed system converges to the value function of a limit averaged control problem as epsilon goes to zero. In the second part of the paper, it is proved that a feedback control policy for the original control problem defined by using an optimal feedback policy for the limit problem is asymptotically optimal. Our work extends existing results of the literature in the following two directions: the underlying MDP is defined on general state and action spaces and we do not impose strong conditions on the recurrence structure of the MDP such as Doeblin's condition.

Model predictive control in thermal management of multiprocessor systems-on-chip

MultiProcessor Systems-on-Chip (MPSoC) are the core of nowadays and next generation computing platforms. Their relevance in the global market continuously increase, occupying an important role both in everydaylife products (e.g. smartphones, tablets, laptops, cars) and in strategical market sectors as aviation, defense, robotics, medicine. Despite of the incredible performance improvements in the recent years processors manufacturers have had to deal with issues, commonly called “Walls”, that have hindered the processors development. After the famous “Power Wall”, that limited the maximum frequency of a single core and marked the birth of the modern multiprocessors system-on-chip, the “Thermal Wall” and the “Utilization Wall” are the actual key limiter for performance improvements. The former concerns the damaging effects of the high temperature on the chip caused by the large power densities dissipation, whereas the second refers to the impossibility of fully exploiting the computing power of the processor due to the limitations on power and temperature budgets. In this thesis we faced these challenges by developing efficient and reliable solutions able to maximize performance while limiting the maximum temperature below a fixed critical threshold and saving energy. This has been possible by exploiting the Model Predictive Controller (MPC) paradigm that solves an optimization problem subject to constraints in order to find the optimal control decisions for the future interval. A fully-distributedMPC-based thermal controller with a far lower complexity respect to a centralized one has been developed. The control feasibility and interesting properties for the simplification of the control design has been proved by studying a partial differential equation thermal model. Finally, the controller has been efficiently included in more complex control schemes able to minimize energy consumption and deal with mixed-criticalities tasks

Automotive diesel engine transient operation: modeling, optimization and control

Traditionally, the study of internal combustion engines operation has focused on the steady-state performance. However, the daily driving schedule of automotive engines is inherently related to unsteady conditions. There are various operating conditions experienced by (diesel) engines that can be classified as transient. Besides the variation of the engine operating point, in terms of engine speed and torque, also the warm up phase can be considered as a transient condition. Chapter 2 has to do with this thermal transient condition; more precisely the main issue is the performance of a Selective Catalytic Reduction (SCR) system during cold start and warm up phases of the engine. The proposal of the underlying work is to investigate and identify optimal exhaust line heating strategies, to provide a fast activation of the catalytic reactions on SCR. Chapters 3 and 4 focus the attention on the dynamic behavior of the engine, when considering typical driving conditions. The common approach to dynamic optimization involves the solution of a single optimal-control problem. However, this approach requires the availability of models that are valid throughout the whole engine operating range and actuator ranges. In addition, the result of the optimization is meaningful only if the model is very accurate. Chapter 3 proposes a methodology to circumvent those demanding requirements: an iteration between transient measurements to refine a purpose-built model and a dynamic optimization which is constrained to the model validity region. Moreover all numerical methods required to implement this procedure are presented. Chapter 4 proposes an approach to derive a transient feedforward control system in an automated way. It relies on optimal control theory to solve a dynamic optimization problem for fast transients. From the optimal solutions, the relevant information is extracted and stored in maps spanned by the engine speed and the torque gradient.

LOCAL DIGITAL CONTROL OF POWER ELECTRONIC CONVERTERS IN A DC MICROGRID BASED ON A-PRIORI DERIVATION OF SWITCHING SURFACES

In power electronic basedmicrogrids, the computational requirements needed to implement an optimized online control strategy can be prohibitive. The work presented in this dissertation proposes a generalized method of derivation of geometric manifolds in a dc microgrid that is based on the a-priori computation of the optimal reactions and trajectories for classes of events in a dc microgrid. The proposed states are the stored energies in all the energy storage elements of the dc microgrid and power flowing into them. It is anticipated that calculating a large enough set of dissimilar transient scenarios will also span many scenarios not specifically used to develop the surface. These geometric manifolds will then be used as reference surfaces in any type of controller, such as a sliding mode hysteretic controller. The presence of switched power converters in microgrids involve different control actions for different system events. The control of the switch states of the converters is essential for steady state and transient operations. A digital memory look-up based controller that uses a hysteretic sliding mode control strategy is an effective technique to generate the proper switch states for the converters. An example dcmicrogrid with three dc-dc boost converters and resistive loads is considered for this work. The geometric manifolds are successfully generated for transient events, such as step changes in the loads and the sources. The surfaces corresponding to a specific case of step change in the loads are then used as reference surfaces in an EEPROM for experimentally validating the control strategy. The required switch states corresponding to this specific transient scenario are programmed in the EEPROM as a memory table. This controls the switching of the dc-dc boost converters and drives the system states to the reference manifold. In this work, it is shown that this strategy effectively controls the system for a transient condition such as step changes in the loads for the example case.

Solution of optimal continuous low-thrust transfer using Lie transforms

This paper addresses the problem of optimal constant continuous low-thrust transfer in the context of the restricted two-body problem (R2BP). Using the Pontryagin’s principle, the problem is formulated as a two point boundary value problem (TPBVP) for a Hamiltonian system. Lie transforms obtained through the Deprit method allow us to obtain the canonical mapping of the phase flow as a series in terms of the order of magnitude of the thrust applied. The reachable set of states starting from a given initial condition using optimal control policy is obtained analytically. In addition, a particular optimal transfer can be computed as the solution of a non-linear algebraic equation. Se investiga el uso de series y transformadas de Lie en problemas de optimización de trayectorias de satélites impulsados por motores de bajo empuje