Electrical and Electronic Engineering - Research Publications

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    Multi-agent source seeking via discrete-time extremum seeking control
    Khong, SZ ; Tan, Y ; Manzie, C ; Nesic, D (PERGAMON-ELSEVIER SCIENCE LTD, 2014-09)
    Recent developments in extremum seeking theory have established a general framework for the methodology, although the specific implementations, particularly in the context of multi-agent systems, have not been demonstrated. In this work, a group of sensor-enabled vehicles is used in the context of the extremum seeking problem using both local and global optimisation algorithms to locate the extremum of an unknown scalar field distribution. For the former, the extremum seeker exploits estimates of gradients of the field from local dithering sensor measurements collected by the mobile agents. It is assumed that a distributed coordination which ensures uniform asymptotic stability with respect to a prescribed formation of the agents is employed. An inherent advantage of the frameworks is that a broad range of nonlinear programming algorithms can be combined with a wide class of cooperative control laws to perform extreme source seeking. Semi-global practical asymptotically stable convergence to local extrema is established in the presence of field sampling noise. Subsequently, global extremum seeking with multiple agents is investigated and shown to give rise to robust practical convergence whose speed can be improved via computational parallelism. Nonconvex field distributions with local extrema can be accommodated within this global framework.
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    Unified frameworks for sampled-data extremum seeking control: Global optimisation and multi-unit systems
    Khong, SZ ; Nesic, D ; Tan, Y ; Manzie, C (PERGAMON-ELSEVIER SCIENCE LTD, 2013-09)
    Two frameworks are proposed for extremum seeking of general nonlinear plants based on a sampled-data control law, within which a broad class of nonlinear programming methods is accommodated. It is established that under some generic assumptions, semi-global practical convergence to a global extremum can be achieved. In the case where the extremum seeking algorithm satisfies a stronger asymptotic stability property, the converging sequence is also shown to be stable using a trajectory-based proof, as opposed to a Lyapunov-function- type approach. The former is more straightforward and insightful. This allows for more general optimisation algorithms than considered in existing literature, such as those which do not admit a state-update realisation and/or Lyapunov functions. Lying at the heart of the analysis throughout is robustness of the optimisation algorithms to additive perturbations of the objective function. Multi-unit extremum seeking is also investigated with the objective of accelerating the speed of convergence.
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    Multidimensional global extremum seeking via the DIRECT optimisation algorithm
    Khong, SZ ; Nesic, D ; Manzie, C ; Tan, Y (PERGAMON-ELSEVIER SCIENCE LTD, 2013-07-01)
    DIRECT is a sample-based global optimisation method for Lipschitz continuous functions defined over compact multidimensional domains. This paper adapts the DIRECT method with a modified termination criterion for global extremum seeking control of multivariable dynamical plants. Finite-time semi-global practical convergence is established based on a periodic sampled-data control law, whose sampling period is a parameter which determines the region and accuracy of convergence. A crucial part of the development is dedicated to a robustness analysis of the DIRECT method against bounded additive perturbations on the objective function. Extremum seeking involving multiple units is also considered within the same context as a means to increase the speed of convergence. Numerical examples of global extremum seeking based on DIRECT are presented at the end.
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    A non-gradient approach to global extremum seeking: An adaptation of the Shubert algorithm
    Nesic, D ; Thang, N ; Tan, Y ; Manzie, C (PERGAMON-ELSEVIER SCIENCE LTD, 2013-03-01)
    The main purpose of this paper is to adapt the so-called Shubert algorithm for extremum seeking control of general dynamic plants. This algorithm is a good representative of the "sampling optimization methods" that achieve global extremum seeking on compact sets in the presence of local extrema. The algorithm applies to Lipschitz mappings; the model of the system is assumed unknown but the knowledge of its Lipschitz constant is assumed. The controller depends on a design parameter, the "waiting time", and tuning guidelines that relate the design parameter and the region of convergence and accuracy of the algorithm are presented. The analysis shows that semi-global practical convergence (in the initial states) to the global extremum can be achieved in presence of local extrema if compact sets of inputs are considered. Numerical simulations for global optimization in the presence of local extrema are provided to demonstrate the proposed approach.
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    Extremum seeking of dynamical systems via gradient descent and stochastic approximation methods
    Khong, SZ ; Tan, Y ; Manzie, C ; Nesic, D (Elsevier, 2015-06)
    Abstract This paper examines the use of gradient based methods for extremum seeking control of possibly infinite-dimensional dynamic nonlinear systems with general attractors within a periodic sampled-data framework. First, discrete-time gradient descent method is considered and semi-global practical asymptotic stability with respect to an ultimate bound is shown. Next, under the more complicated setting where the sampled measurements of the plant’s output are corrupted by an additive noise, three basic stochastic approximation methods are analysed; namely finite-difference, random directions, and simultaneous perturbation. Semi-global convergence to an optimum with probability one is established. A tuning parameter within the sampled-data framework is the period of the synchronised sampler and hold device, which is also the waiting time during which the system dynamics settle to within a controllable neighbourhood of the steady-state input–output behaviour.