Christos Yfoulis

Constrained switching stabilization of a dc-dc boost converter using piecewise-linear Lyapunov functions

This paper describes a new methodology for designing robust and efficient control laws for power converters. In addition to guaranteed closed-loop robust stability, the proposed design is capable of addressing a number of further key issues, i.e. low complexity of the implementation, accurate nonlinear dynamics incorporation, nonconservative handling of hard state and control constraints, and robustness to supply voltage variations and setpoint changes. The control design is of a set-theoretic nature. The iterative algorithms used for controller generation are based on the ray-gridding approach, that generates piecewise-linear Lyapunov functions and corresponding controlled invariant polytopes, induced by systematic conic decompositions of the state-space and state-dependent switching control actions. The proposed technique is evaluated on a boost converter case study. Simulation results in the MATLAB/SIMULINK™ environment are reported. The bifurcation behaviour of the system is further studied by numerical and analytical nonlinear stability analysis.

Efficient load balancing in partitioned queries under random perturbations

This work investigates a particular instance of the problem of designing efficient adaptive systems, under the condition that each adaptation decision incurs some nonnegligible cost when enacted. More specifically, we deal with the problem of dynamic, intraquery load balancing in parallel database queries across heterogeneous nodes in a way that takes into account the inherent cost of adaptations and thus avoids both overreacting and deciding when to adapt in a completely heuristic manner. The latter may lead to serious performance degradation in several cases, such as periodic and random imbalances. We follow a control theoretical approach to this problem; more specifically, we propose a multiple-input multiple-output feedback linear quadratic regulation (LQR) controller, which captures the tradeoff between reaching a balanced state and the cost inherent in such adaptations. Our approach, apart from benefitting from and being characterized by a solid theoretical foundation, exhibits better performance than state-of-the-art heuristics in realistic situations, as verified by thorough evaluation.

An efficient load balancing LQR controller in parallel database queries under random perturbations

This work investigates the problem of dynamic, intra-query load balancing in parallel database queries across heterogeneous nodes in a way that takes into account the inherent cost of adaptations and thus avoids both over-reacting and deciding when to adapt in a completely heuristic manner. The latter may lead to serious performance degradation in several cases, such as periodic and random imbalances. We follow a control theoretical approach to this problem; more specifically, we propose a multiple-input multiple-output feedback linear quadratic regulation (LQR) controller, which captures the tradeoff between reaching a balanced state and the cost inherent in such adaptations. Our approach, apart from benefitting from and being characterized by a solid theoretical foundation, exhibits better performance than state-of-the-art heuristics in realistic situations, as verified by thorough evaluation.

Robust constrained stabilization of a boost DC-DC converter with Lyapunov-based control and piecewise-linear Lyapunov functions

In this paper we describe a new methodology for designing robust and efficient state-feedback control laws for a switched-mode boost DC-DC power converter. The proposed design is adopting the so-called Lyapunov-based control law and attempts to solve the robust constrained stabilization problem under large parameter variations. With the methodology proposed static or switching state-feedback control laws are generated so that a number of further key issues are addressed, i.e. low complexity of the implementation, accurate nonlinear dynamics incorporation, nonconservative handling of hard state and control constraints, robustness to supply voltage variations, set-point and load changes. The control design procedure is based on the generation of controlled invariant polytopes (safety domains) using piecewise-linear Lyapunov functions. The proposed technique is numerically evaluated using the exact switched model of the converter.

A computational technique characterizing the asymptotic stabilizability of planar linear switched systems with unstable modes

In this paper a new computational technique for characterizing the asymptotic stabilizability of linear switched systems on the plane is presented. Switching between a finite number of unstable LTI systems is studied. A ray-gridding idea is used which allows the construction of sufficiently dense subdivisions of the state space into conic regions, whose boundaries are candidate switching domains. Progressive refinements of the partition add flexibility in the search for a solution. Necessary and sufficient conditions for the asymptotic stabilizability of linear switched systems are developed by constructing polyhedral Lyapunov-like functions (PLF) associated to the convergence of an iterative algorithm. Therefore, it is shown that the existence of a PLF is equivalent to the asymptotic stabilizability of linear switched systems with unstable modes. The extension of the results to higher dimensions and the computational complexity associated with their implementation is also discussed.

Optimal switching Lyapunov-based control of a boost DC-DC converter

A new methodology for designing robust and efficient state-feedback control laws for a switched-mode boost DC-DC power converter has been recently proposed. This approach has adopted the so-called stabilizing or Lyapunov-based control paradigm which is well-known in the area of energy-based control of DC-DC converters, whereby the control law takes a state-feedback form parameterized by a positive scalar γ. Extension to state-dependent switching state-feedback control laws has been proposed, where the switching surfaces are parameterized by a number of positive scalars γ.i. In this paper this methodology is revisited by considering the problem of designing optimal switching state-feedback control laws, i.e. finding the optimal control parameters γ.i corresponding to the optimal position of the switching surfaces. This permits minimization of the number of switchings required for achieving an optimal performance and hence reduced complexity of the control law. Systematic derivation of gradient information to apply gradient-descent algorithms is provided. The proposed technique is numerically evaluated using the exact switched model of the converter.

Minimization of the response time in parallel database queries: An adaptive cost-aware MPC-based solution

Load balancing in partitioned database queries is a significant issue in efficient data management of large datasets. When such queries are processed in a volatile and unpredictable setting, as is the typical case today, continuous workload re-assignments need to take place to ensure that the workload allocated to each participating machine reflects its actual capabilities, so that the query response time is minimized. The main challenge is to continuously adapt the load balancing policy, while considering the inherent control cost. The problem is modeled as a constrained optimization problem and, in this work, we present an efficient and effective MPC-based solution, which improves upon previous work.

Optimal switching Lyapunov-based control of power electronic converters

This paper presents new ideas and insights towards a novel optimal control approach for power electronic converters. The so-called stabilizing or Lyapunov-based control paradigm is adopted, which is well known in the area of energy-based control of power electronic converters, in which the control law takes a nonlinear state-feedback form parameterized by a positive scalar λ. The first contribution is the extension to an optimal Lyapunov-based control paradigm involving the specification of the optimal value for the parameter λ in a typical optimal control setting. The second contribution is the extension to more flexible optimal switching-gain control laws, where the optimal switching surfaces are parameterized by a number of positive scalars λj. Systematic derivation of gradient information to apply gradient-descent algorithms is provided. The proposed techniques are numerically evaluated using the exact switched model of a DC-DC boost converter. Copyright

Stability analysis of digital state feedback controlled boost converters

In this paper we investigate the nonlinear dynamics of DC-DC boost converters under state feedback controllers. We demonstrate that it is possible to have multiple equilibria, which can further bifurcate and result in a torus or even chaos. More specifically, by changing the feedback gains we show that it is possible to have a saddle node and then a period 2 bifurcation. These are then followed by a slow scale bifurcation that results in a 2T torus. Also, the nominal or desired equilibrium hits a border in the state space that forces the steady state duty cycle to become 0. Obviously the occurrence of saturation in the duty cycle or the existence of instabilities can greatly decrease the converters performance. In this paper we study this behavior: we use semi-analytical methods to locate the stable and unstable period 1 and period 2 orbits, the unstable manifold of the period 1 orbit; and by using the theory of the monodromy matrix enhanced with the saltation matrix we determine the stability of the converter. The latter can be used for design purposes in order to guarantee a stable and satisfactory performance.

Self-optimizing block transfer in web service grids

Nowadays, Web Services (WSs) play an increasingly important role in Web data management solutions, since they offer a practical solution for accessing and manipulating data sources spanning administrative domains. Nevertheless, they are notoriously slow and transferring large data volumes across WSs becomes the main bottleneck in such WS-based applications. This paper deals with the problem of minimizing at runtime, in a self-managing way, the datatransfer cost of a WS encapsulating a data source. To reducethe transfer cost, the data volume is typically divided intoblocks. In this case, response time exhibits a quadratic-like, non-linear behavior with regards to the block size; as such, minimizing the transfer cost entails finding the optimum block size. This situation is encountered in several systems, such as WS Management Systems (WSMSs) for DBMS-like data management over wide area service-based networks, and WSs for accessing and integrating traditional DBMSs. The main challenges in this problem include (i) the unavailability of an analytical model; (ii) the presence of noise, which incurs local minima; (iii) the volatility of the environment, which results into a moving optimum operating point; and (iv) the requirements for fast convergence to the optimal size of the request from the side of the client rather than of the server, and for low overshooting. This paper presents two novel solutions for detecting the optimum block size during data transmission, thus yielding lower response times. The solutions are inspired by the broader areas of runtime optimization and switching extremum control. They incorporate heuristics to avoid local optimal points, and address all the afore-mentioned challenges. The effectiveness andeffciency of the solutions is verified through empirical evaluation in real cases.