Browsing by Author "Kerrigan, Eric C."

Now showing 1 - 7 of 7
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    Constrained LQR for Low-Precision Data Representation
    (Elsevier Science B.V., Amsterdam., 2014-01-24T00:00:00Z) Longo, Stefano; Kerrigan, Eric C.; Constantinides, George A.
    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.
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    Energy-aware MPC co-design for DC-DC converters
    (Institute of Electrical and Electronics Engineers, 2013-07-22) Suardi, Andrea; Longo, Stefano; Kerrigan, Eric C.; Constantinides, George A.
    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.
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    Nonlinear predictive control of autonomous soaring UAVs using 3DOF models
    (Institute of Electrical and Electronics Engineers, 2013-07-22) Liu, Yuyi; Longo, Stefano; Kerrigan, Eric C.
    We design a nonlinear model predictive control (NMPC) system for a soaring UAV in order to harvest the energy from the atmospheric updrafts. Our control framework combines an online estimation with a heuristic search method to obtain the UAV optimal trajectory. To allow for real-time computation of the control commands we solve the optimal control problem using a 3 degrees-of-freedom (DOF) model but apply the inputs to a more realistic 6DOF model. Hence, we design a 3DOF-6DOF model interaction strategy. Simulations show how the control system succeeds in energy extraction in a challenging dynamic atmospheric environment while satisfying its real-time contraints.
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    Number representation in predictive control
    (Elsevier, 2012-09-30) Kerrigan, Eric C.; Jerez, Juan L.; Longo, Stefano; Constantinides, George A.
    In predictive control a nonlinear optimization problem has to be solved at each sample instant. Solving this optimization problem in a computationally efficient and numerically reliable fashion on an embedded system is a challenging task. This paper presents results to reduce the computational requirements for solving fundamental problems that arise when implementing predictive controllers in finite precision arithmetic. By employing novel formulations and tailor-made optimization algorithms, this paper shows that computational resources can be reduced using very low precision arithmetic. We also present new mathematical results that enable computational savings to be made in the most numerically critical part of an optimization solver, namely the linear algebra kernel, using fixed-point arithmetic. Our theoretical results are supported by numerical results from implementations on a Field Programmable Gate Array (FPGA).
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    Predictive control for soaring of unpowered autonomous UAVs
    (Elsevier, 2012-08-27) Lee, Darren; Longo, Stefano; Kerrigan, Eric C.
    In this paper we propose an energy-harvesting controller design for a 3 degree-of-freedom glider in a nonlinear MPC framework. The glider is simulated within a generic atmospheric updraft environment with the aim of extracting the maximum amount of energy from the environment. We focus on conceptual feasibility at this stage and we take the realistic assumption that the glider is able to obtain updraft information only along the flight trajectory. The surrounding updraft distribution is then recursively estimated (online) by combining the measurements from the optimal trajectory with a heuristic search, if necessary. A variation of the standard grid search is used such that the grid spacing is altered depending on the updraft information along the glider’s flight path. Results from both standard and adaptive grid search approaches are presented. In abstract terms, this work can be viewed as finding optimal paths in uncertain vector fields.
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    A predictive control solver for low-precision data representation
    (Institute of Electrical and Electronics Engineers, 2013-07-22) Longo, Stefano; Kerrigan, Eric C.; Constantinides, George A.
    We propose a method to efficiently exploit the non- standard number representation of some embedded computer architectures for the solution of constrained LQR problems. The resulting quadratic programming problem is formulated to include auxiliary decision variables as well as the inputs and states. The new formulation introduces smaller roundoff errors in the optimization solver, hence allowing one to trade off the number of bits used for data representation against speed and/or hardware resources. Interestingly, because of the data dependencies of the operations, the algorithm complexity (in terms of computation time and hardware resources) does not increase despite the larger number of decision variables.
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    Robust explicit MPC design under finite precision arithmetic
    (Elsevier, 2014-08-29) Suardi, Andrea; Longo, Stefano; Kerrigan, Eric C.; Constantinides, George A.
    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.