Differential Games Controllers That Confine a System to a Safe Region in the State Space, With Applications to Surge Tank Control

Surge tanks are units employed in chemical processing to regulate the flow of fluids between reactors. A notable feature of surge tank control is the need to constrain the magnitude of the Maximum Rate of Change (MROC) of the surge tank outflow, since excessive fluctuations in the rate of change of outflow can adversely affect down-stream processing (through disturbance of sediments, initiation of turbulence, etc.). Proportional + Integral controllers, traditionally employed in surge tank control, do not take direct account of the MROC. It is therefore of interest to explore alternative approaches. We show that the surge tank controller design problem naturally fits a differential games framework, proposed by Dupuis and McEneaney, for controlling a system to confine the state to a safe region of the state space. We show furthermore that the differential game arising in this way can be solved by decomposing it into a collection of (one player) optimal control problems. We discuss the implications of this decomposition technique, for the solution of other controller design problems possessing some features of the surge tank controller design problem

Minimax optimal control

Published versio

Decomposition of Differential Games with Multiple Targets

This paper provides a decomposition technique for the purpose of simplifying the solution of certain zero-sum differential games. The games considered terminate when the state reaches a target, which can be expressed as the union of a collection of target subsets considered as ‘multiple targets’; the decomposition consists in replacing the original target by each of the target subsets. The value of the original game is then obtained as the lower envelope of the values of the collection of games, resulting from the decomposition, which can be much easier to solve than the original game. Criteria are given for the validity of the decomposition. The paper includes examples, illustrating the application of the technique to pursuit/evasion games and to flow control

Optimal Control Problems with Mixed and Pure State Constraints

This paper provides necessary conditions of optimality for optimal control problems, in which the pathwise constraints comprise both ‘pure’ constraints on the state variable and also ‘mixed’ constraints on control and state variables. The proofs are along the lines of earlier analysis for mixed constraint problems, according to which Clarke’s theory of ‘stratified’ necessary conditions is applied to a modified optimal control problem resulting from absorbing the mixed constraint into the dynamics; the difference here is that necessary conditions which now take account of the presence of pure state constraints are applied to the modified problem. Necessary conditions are given for a rather general formulation of the problem containing both forms of the constraints, and then these are specialized to apply to problems having special structure. While combined pure state and mixed control/state problems have been previously treated in the literature, the necessary conditions in this paper are proved under less restrictive hypotheses and for novel formulations of the constraints

Regularity properties of optimal controls for problems with time-varying state and control constraints

Accepted versio

Just-In-Time Compilation of NumPy Vector Operations

In this paper, we introduce JIT compilation for thehigh-productivity framework Python/NumPy in order to boost theperformance significantly. The JIT compilation of Python/NumPyis completely transparent to the user – the runtime system willautomatically JIT compile and execute the NumPy instructionsencountered in a Python application. In other words, we introducea framework that provides the high-productivity from Pythonwhile maintaining the high-performance of a low-level, compiledlanguage.We transforms NumPy vector instruction into an AbstractSyntax Tree representation that creates the basis for furtheroptimizations. From the AST we auto-generate C code whichwe compile into computational kernels and execute. These incorporatetemporary array removal and loop-fusion which are mainbenefactors in the achieved speedups. In order to amortize theoverhead of creation, we also implement a cache for the compiledkernels.We evaluate the JIT compilation by executing several scientificcomputing benchmarks on an AMD. Compared to NumPy, weachieve speedups of a factor 4.72 for a N-Body application and7.51 for a Jacobi Stencil application executing on a single CPUcore

The Patient’s and the Therapist’s Evaluation of Bridges of Different Materials and Age

The aim of this study was to find out patients\u27 satisfaction with their bridges made of different materials (metal-ceramics, Au/resin, Ag-Pd/resin). One hundred and sixty four patients were examined at the Dental School, University of Zagreb, Croatia. They assessed their bridges – the overall quality, aesthetics, speech, chewing and the health of the gingiva by the scale from 1–5. The same categories were also assessed by a trained prosthodontist. The majority of the patients was really satisfied and gave the highest grades (quality, aesthetics, speech, etc.) and therefore the results were skewed and asymmetrical towards the biggest scores (biggest grades). The best gingival health was evaluated by the group of patients with ceramic crowns and bridges (p < 0.05) and the worst by the patients with Ag-Pd bridges. Speech was scored higher for the lateral than for the frontal bridges. Patients evaluated the health of the tissue surrounding their bridges, overall quality of fixed prosthodontic appliance and aesthetics with significantly higher scores than the prosthodontist (p < 0.01). The results point at a difference between the patient’s and the therapist\u27s evaluations and to the patient\u27s insufficient care about the gingiva around the bridge abutments

Towards two-dimensional metallic behavior at LaAlO3/SrTiO3 interfaces

Using a low-temperature conductive-tip atomic force microscope in cross-section geometry we have characterized the local transport properties of the metallic electron gas that forms at the interface between LaAlO3 and SrTiO3. At low temperature, we find that the carriers do not spread away from the interface but are confined within ~10 nm, just like at room temperature. Simulations taking into account both the large temperature and electric-field dependence of the permittivity of SrTiO3 predict a confinement over a few nm for sheet carrier densities larger than ~6 10^13 cm-2. We discuss the experimental and simulations results in terms of a multi-band carrier system. Remarkably, the Fermi wavelength estimated from Hall measurements is ~16 nm, indicating that the electron gas in on the verge of two-dimensionality.Comment: Accepted for publication in Physical Review Letter