Constrained LQR for Low-Precision Data Representation

Performing computations with a low-bit number representation results in a faster implementation that uses less silicon, and hence allows an algorithm to be implemented in smaller and cheaper processors without loss of performance. We propose a novel formulation to efficiently exploit the low (or non-standard) precision number representation of some computer architectures when computing the solution to constrained LQR problems, such as those that arise in predictive control. The main idea is to include suitably-defined decision variables in the quadratic program, in addition to the states and the inputs, to allow for smaller roundoff errors in the solver. This enables one to trade off the number of bits used for data representation against speed and/or hardware resources, so that smaller numerical errors can be achieved for the same number of bits (same silicon area). Because of data dependencies, the algorithm complexity, in terms of computation time and hardware resources, does not necessarily increase despite the larger number of decision variables. Examples show that a 10-fold reduction in hardware resources is possible compared to using double precision floating point, without loss of closed-loop performance

Energy-aware MPC co-design for DC-DC converters

In this paper, we propose an integrated controller design methodology for the implementation of an energy-aware explicit model predictive control (MPC) algorithms, illustrat- ing the method on a DC-DC converter model. The power consumption of control algorithms is becoming increasingly important for low-power embedded systems, especially where complex digital control techniques, like MPC, are used. For DC-DC converters, digital control provides better regulation, but also higher energy consumption compared to standard analog methods. To overcome the limitation in energy efficiency, instead of addressing the problem by implementing sub-optimal MPC schemes, the closed-loop performance and the control algorithm power consumption are minimized in a joint cost function, allowing us to keep the controller power efficiency closer to an analog approach while maintaining closed-loop op- timality. A case study for an implementation in reconfigurable hardware shows how a designer can optimally trade closed-loop performance with hardware implementation performance

Provision of education in the middle school years in Cyprus

The aim of this study is to examine the type of education offered during the middle school years in Cyprus. At first an attempt is made to define middle school years and relate this concept to the educational system of Cyprus and other countries. The History of Education in Cyprus is briefly surveyed to set the background against which the Gymnasium, a distinct educational unit catering for the middle school years, has evolved and reached its present form. The aims, objectives, structure and content of the Gymnasium are examined in detail. Qualitative and quantitative measures are employed to investigate the role of the Gymnasium within the educational system and the degree to which this role is successfully accomplished. The results reveal that on the whole, content and time span of the Gymnasium are satisfactory. There is, however, a strong feeling that there is scope for improvement in the content of the curriculum in order to make it more effective. On the basis of the findings of the present survey a model of a new educational unit is presented which intends to bridge the gap between the primary and secondary education at its lower end and pave the way to the smooth transition from the free compulsory to the upper secondary level of education. The programme of the new unit is hoped to serve more effectively the primary aim of the concept of the democratisation of education, namely the provision of equal educational opportunities to all according to individualised goals, needs, abilities and talents. Finally certain recent developments in the educational system of Cyprus and their implications for the future of the Gymnasium are discussed. A proposal for the reorganisation of secondary education is developed and its merits are presented

Robust explicit MPC design under finite precision arithmetic

We propose a design methodology for explicit Model Predictive Control (MPC) that guarantees hard constraint satisfaction in the presence of finite precision arithmetic errors. The implementation of complex digital control techniques, like MPC, is becoming increasingly adopted in embedded systems, where reduced precision computation techniques are embraced to achieve fast execution and low power consumption. However, in a low precision implementation, constraint satisfaction is not guaranteed if infinite precision is assumed during the algorithm design. To enforce constraint satisfaction under numerical errors, we use forward error analysis to compute an error bound on the output of the embedded controller. We treat this error as a state disturbance and use this to inform the design of a constraint-tightening robust controller. Benchmarks with a classical control problem, namely an inverted pendulum, show how it is possible to guarantee, by design, constraint satisfaction for embedded systems featuring low precision, fixed-point computations

The Frescoes of the Church of the Holy Archangels at Zemo-Krichi, Rača (Georgia) and the Contemporary Monuments on Mani in Southern Greece

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The Tetraevangelion, Manuscript 93 of the Athens National Library (pls 61-86)

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Optimal combined word-length allocation and architectural synthesis of digital signal processing circuits

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