A single network adaptive critic (SNAC) architecture for optimal control synthesis for a class of nonlinear systems

Even though dynamic programming offers an optimal control solution in a state feedback form, the method is overwhelmed by computational and storage requirements. Approximate dynamic programming implemented with an Adaptive Critic (AC) neural network structure has evolved as a powerful alternative technique that obviates the need for excessive computations and storage requirements in solving optimal control problems. In this paper, an improvement to the AC architecture, called the �Single Network Adaptive Critic (SNAC)� is presented. This approach is applicable to a wide class of nonlinear systems where the optimal control (stationary) equation can be explicitly expressed in terms of the state and costate variables. The selection of this terminology is guided by the fact that it eliminates the use of one neural network (namely the action network) that is part of a typical dual network AC setup. As a consequence, the SNAC architecture offers three potential advantages: a simpler architecture, lesser computational load and elimination of the approximation error associated with the eliminated network. In order to demonstrate these benefits and the control synthesis technique using SNAC, two problems have been solved with the AC and SNAC approaches and their computational performances are compared. One of these problems is a real-life Micro-Electro-Mechanical-system (MEMS) problem, which demonstrates that the SNAC technique is applicable to complex engineering systems.

Constructions of 2D-Metallamacrocycles Using Half-Sandwich Ru-2(II) Precursors: Synthesis, Molecular Structures, and Self-Selection for a Single Linkage Isomer

Coordination-driven self-assembly of oxalato-bridged half-sandwich p-cymene ruthenium complex Ru-2(mu-eta(4)-C2O4)(MeOH)(2)(eta(6)-p-cymene)(2)] (O3SCF3)(2) (1a) with several ditopic donors (L-a-L-d) in methanol affords a series of bi- and tetranuclear metallamacrocycles (2a and 3-5). Similarly, the combination of 2,5-dihydroxy-1,4-benzoquinonato (dhbq)-bridged binuclear complex Ru-2(mu-eta(4)-C6H2O4)(MeOH)(2)(eta(6)-p-cymene)(2)](O3SCF3)(2) (1b) with a flexible bidentate amide linker (L-a) in 1:1 molar ratio gave the corresponding tetranuclear complex 2b. All the macrocycles were isolated as their triflate salts in high yields and were fully characterized by various spectroscopic techniques. Finally, the molecular structures of all the assemblies were determined unambiguously by single-crystal X-diffraction analysis. Interestingly, the combination of acceptor 1a or 1b with an unsymmetrical linear ditopic donor L-a results in a self-sorted linkage isomeric (head-to-tail) macrocycle (2a or 2b) despite the possibility of formation of two different isomeric macrocycles (head-to-head or head-to-tail) due to different connectivity of the donor. Molecular structures of the complexes 2a and 2b showed tetranuclear rectangular geometry with dimensions of 5.51 angstrom x 13.29 angstrom for 2a and 7.91 angstrom x 13.46 angstrom for 2b. In both cases, two binuclear Ru-2(II) building blocks are connected by a mu-N-(4-pyridyl)isonicotinamide donor in a head-to-tail fashion. Surprisingly, the macrocycle 2a loses one counteranion and cocrystallizes with monodeprotonated 1,3,5-trihydroxybenzene via strong intermolecular pi-pi stacking and hydrogen bonding. The tweezer complex 3 showed strong fluorescence in solution, and it showed fluorescence sensing toward nitroaromatic compounds. A fluorescence study demonstrated a marked quenching of the initial fluorescence intensity of the macrocycle 3 upon gradual addition of trinitrotoluene and exhibits significant fluorescence quenching response only for nitroaromatic compounds compared to various other aromatic compounds tested.

Optimal management of beaver population using a reduced-order distributed parameter model and single network adaptive critics

Beavers are often found to be in conflict with human interests by creating nuisances like building dams on flowing water (leading to flooding), blocking irrigation canals, cutting down timbers, etc. At the same time they contribute to raising water tables, increased vegetation, etc. Consequently, maintaining an optimal beaver population is beneficial. Because of their diffusion externality (due to migratory nature), strategies based on lumped parameter models are often ineffective. Using a distributed parameter model for beaver population that accounts for their spatial and temporal behavior, an optimal control (trapping) strategy is presented in this paper that leads to a desired distribution of the animal density in a region in the long run. The optimal control solution presented, imbeds the solution for a large number of initial conditions (i.e., it has a feedback form), which is otherwise nontrivial to obtain. The solution obtained can be used in real-time by a nonexpert in control theory since it involves only using the neural networks trained offline. Proper orthogonal decomposition-based basis function design followed by their use in a Galerkin projection has been incorporated in the solution process as a model reduction technique. Optimal solutions are obtained through a "single network adaptive critic" (SNAC) neural-network architecture.

Effect of thermal annealing on the dielectric properties of KTiOPO4 single crystals

Dielectric properties of potassium titanyl phosphate have been investigated as a function of thickness and frequency, as well as annealing treatment under various atmospheres. The low frequency dielectric constant of KTP crystals is shown to depend upon the sample thickness, and this feature is attributed to the existence of surface layers. The frequency-dependent dielectric response of KTP exhibits a non-Debye type relaxation, with a distribution of relaxation times. The dielectric behavior of KTP samples annealed in various atmospheres shows that the low frequency dielectric constant is influenced by the contribution from the space charge layers. Prolonged annealing of the samples leads to a surface degradation, resulting in the formation of a surface layer of lower dielectric constant. This surface degradation is least when annealed in the presence of dry oxygen. From the analysis of the dielectric data using complex electric modulus, alpha(m) has been evaluated for the virgin and annealed samples. (C) 1996 American Institute of Physics.

Optimal blood glucose regulation of diabetic patients using single network adaptive critics

Diabetes is a long-term disease during which the body's production and use of insulin are impaired, causing glucose concentration level to increase in the bloodstream. Regulating blood glucose levels as close to normal as possible leads to a substantial decrease in long-term complications of diabetes. In this paper, an intelligent online feedback-treatment strategy is presented for the control of blood glucose levels in diabetic patients using single network adaptive critic (SNAC) neural networks (which is based on nonlinear optimal control theory). A recently developed mathematical model of the nonlinear dynamics of glucose and insulin interaction in the blood system has been revised and considered for synthesizing the neural network for feedback control. The idea is to replicate the function of pancreatic insulin, i.e. to have a fairly continuous measurement of blood glucose and a situation-dependent insulin injection to the body using an external device. Detailed studies are carried out to analyze the effectiveness of this adaptive critic-based feedback medication strategy. A comparison study with linear quadratic regulator (LQR) theory shows that the proposed nonlinear approach offers some important advantages such as quicker response, avoidance of hypoglycemia problems, etc. Robustness of the proposed approach is also demonstrated from a large number of simulations considering random initial conditions and parametric uncertainties. Copyright (C) 2009 John Wiley & Sons, Ltd.

Single-molecule thermodynamics: the heat distribution function of a charged particle in a static magnetic field

Interest in the applicability of fluctuation theorems to the thermodynamics of single molecules in external potentials has recently led to calculations of the work and total entropy distributions of Brownian oscillators in static and time-dependent electromagnetic fields. These calculations, which are based on solutions to a Smoluchowski equation, are not easily extended to a consideration of the other thermodynamic quantity of interest in such systems-the heat exchanges of the particle alone-because of the nonlinear dependence of the heat on a particle's stochastic trajectory. In this paper, we show that a path integral approach provides an exact expression for the distribution of the heat fluctuations of a charged Brownian oscillator in a static magnetic field. This approach is an extension of a similar path integral approach applied earlier by our group to the calculation of the heat distribution function of a trapped Brownian particle, which was found, in the limit of long times, to be consistent with experimental data on the thermal interactions of single micron-sized colloids in a viscous solvent.