On some extension of optimal control theory

Some problems of Calculus of Variations do not have solutions in the class of classic continuous and smooth arcs. This suggests the need of a relaxation or extension of the problem ensuring the existence of a solution in some enlarged class of arcs. This work aims at the development of an extension for a more general optimal control problem with nonlinear control dynamics in which the control function takes values in some closed, but not necessarily bounded, set. To achieve this goal, we exploit the approach of R.V. Gamkrelidze based on the generalized controls, but related to discontinuous arcs. This leads to the notion of generalized impulsive control. The proposed extension links various approaches on the issue of extension found in the literature.

Optimal control strategy for fed-batch enzymatic hydrolysis of lignocellulosic biomass based on epidemic modeling

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Optimal Conditions for Biomass and Recombinant Glycerol Kinase Production Using the Yeast Pichia pastoris

The extracellular glycerol kinase gene from Saccharomyces cerevisiae (GUT]) was cloned into the expression vector pPICZ alpha. A and integrated into the genome of the methylotrophic yeast Pichia pastoris X-33. The presence of the GUT1 insert was confirmed by PCR analysis. Four clones were selected and the functionality of the recombinant enzyme was assayed. Among the tested clones, one exhibited glycerol kinase activity of 0.32 U/mL, with specific activity of 0.025 U/mg of protein. A medium optimized for maximum biomass production by recombinant Pichia pastoris in shaker cultures was initially explored, using 2.31 % (by volume) glycerol as the carbon source. Optimization was carried out by response surface methodology (RSM). In preliminary experiments, following a Plackett-Burman design, glycerol volume fraction (phi(Gly)) and growth time (t) were selected as the most important factors in biomass production. Therefore, subsequent experiments, carried out to optimize biomass production, followed a central composite rotatable design as a function of phi(Gly) and time. Glycerol volume fraction proved to have a significant positive linear effect on biomass production. Also, time was a significant factor (at linear positive and quadratic levels) in biomass production. Experimental data were well fitted by a convex surface representing a second order polynomial model, in which biomass is a function of both factors (R(2)=0.946). Yield and specific activity of glycerol kinase were mainly affected by the additions of glycerol and methanol to the medium. The optimized medium composition for enzyme production was: 1 % yeast extract, 1 % peptone, 100 mM potassium phosphate buffer, pH=6.0, 1.34 % yeast nitrogen base (YNB), 4.10(-5) % biotin, 1 %, methanol and 1 %, glycerol, reaching 0.89 U/mL of glycerol kinase activity and 14.55 g/L of total protein in the medium after 48 h of growth.

Influence of visual information on optimal obstacle crossing

Human motion seems to be guided by some optimal principles. In general, it is assumed that human walking is generated with minimal energy consumption. However, in the presence of disturbances during gait, there is a trade-off between stability (avoiding a fall) and energy-consumption. This work analyses the obstacle-crossing with the leading foot. It was hypothesized that energy-saving mechanisms during obstacle-crossing are modulated by the requirement to avoid a fall using the available sensory information, particularly, by vision. A total of fourteen subjects, seven with no visual impairment and seven blind, walked along a 5 meter flat pathway with an obstacle of 0.26 m height located at 3 m from the starting point. The seven subjects with normal vision crossed the obstacle successfully 30 times in two conditions: blindfolded and with normal vision. The seven blind subjects did the same 30 times. The motion of the leading limb was recorded by video at 60 Hz. There were markers placed on the subject's hip, knee, ankle, rear foot, and forefoot. The motion data were filtered with a fourth order Butterworth filter with a cut-off frequency of 4 Hz. The following variables were calculated: horizontal distance between the leading foot and the obstacle at toe-off prior to (DHPO) and after (DHOP) crossing, minimal vertical height from the foot to the obstacle (DVPO), average step velocity (VELOm). The segmental energies were also calculated and the work consumed by the leading limb during the crossing obstacle was computed for each trial. A statistical analysis repeated-measures ANOVA was conducted on these dependent variables revealing significant differences between the vision and non-vision conditions in healthy subjects. In addition, there were no significant differences between the blind and people with vision blindfolded. These results indicate that vision is crucial to determine the optimal trade-off between energy consumption and avoiding a trip during obstacle crossing.

Um método eficiente para resolução do problema de Despacho Ótimo de Reativos com controle discreto do TAP dos transformadores

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

Security constrained optimal active power flow via network model and interior point method

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

Performance Comparisons of EWMA Control Chart Schemes

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Mitigation of symmetry condition in positive realness for adaptive control

Feasibility of nonlinear and adaptive control methodologies in multivariable linear time-invariant systems with state-space realization (A, B, C) is apparently limited by the standard strictly positive realness conditions that imply that the product CB must be positive definite symmetric. This paper expands the applicability of the strictly positive realness conditions used for the proofs of stability of adaptive control or control with uncertainty by showing that the not necessarily symmetric CB is only required to have a diagonal Jordan form and positive eigenvalues. The paper also shows that under the new condition any minimum-phase systems can be made strictly positive real via constant output feedback. The paper illustrates the usefulness of these extended properties with an adaptive control example. (C) 2006 Elsevier Ltd. All rights reserved.

Design of fuzzy regulators with optimal initial conditions compensation

In almost all cases, the goal of the design of automatic control systems is to obtain the parameters of the controllers, which are described by differential equations. In general, the controller is artificially built and it is possible to update its initial conditions. In the design of optimal quadratic regulators, the initial conditions of the controller can be changed in an optimal way and they can improve the performance of the controlled system. Following this idea, a LNU-based design procedure to update the initial conditions of PI controllers, considering the nonlinear plant described by Takagi-Sugeno fuzzy models, is presented. The importance of the proposed method is that it also allows other specifications, such as, the decay rate and constraints on control input and output. The application in the control of an inverted pendulum illustrates the effectively of proposed method.

Metodologia para rastreamento com modificação dos zeros e rejeição de distúrbio aplicada a sistemas incertos

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

Controle ótimo H∞ de sistemas não-lineares com modelos fuzzy takagi-sugeno

Neste trabalho é proposta uma metodologia de rastreamento de sinais e rejeição de distúrbios aplicada a sistemas não-lineares. Para o projeto do sistema de rastreamento, projeta-se os controladores fuzzy M(a) e N(a) que minimizam o limitante superior da norma H∞ entre o sinal de referência r(t) e o sinal de erro de rastreamento e(t), sendo e(t) a diferença entre a entrada de referência e a saída do sistema z(t). No método de rejeição de distúrbio utiliza-se a realimentação dinâmica da saída através de um controlador fuzzy Kc(a) que minimiza o limitante superior da norma H∞ entre o sinal de entrada exógena w(t) e o sinal de saída z(t). O procedimento de projeto proposto considera as não-linearidades da planta através dos modelos fuzzy Takagi-Sugeno. Os métodos são equacionados utilizando-se inequações matriciais lineares (LMIs), que quando factíveis, podem ser facilmente solucionados por algoritmos de convergência polinomial. Por fim, um exemplo ilustra a viabilidade da metodologia proposta.

Controle ótimo H2 e H¥ com modificação de zeros para o problema de rastreamento usando LMI

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

Variable-Structure Control Design of Switched Systems With an Application to a DC-DC Power Converter

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

Reactive Control for Transmission Overload Relief Based on Sensitivity Analysis and Cooperative Game Theory

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Robust state-derivative pole placement LMI-based designs for linear systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)