 Mechanical Engineering  Research Publications
Mechanical Engineering  Research Publications
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ItemAveraging for nonlinear systems on Riemannian manifoldsTaringoo, F ; Nesic, D ; Tan, Y ; Dower, PM (IEEE, 2013)This paper provides a derivation of the averaging methods for nonlinear timevarying dynamical systems defined on Riemannian manifolds. We extend the results on ℝ n to Riemannian manifolds by employing the language of differential geometry.

ItemExtremum seeking control for nonlinear systems on compact Riemannian manifoldsTaringoo, F ; Nesic, D ; Tan, Y ; DOWER, PM (IEEE Press, 2014)This paper formulates the extremum seeking control problem for nonlinear dynamical systems which evolve on Riemannian manifolds and presents stability results for a class of numerical algorithms defined in this context. The results are obtained based upon an extension of extremum seeking algorithms in Euclidean spaces and a generalization of Lyapunov stability theory for dynamical systems defined on Rimannian manifolds. We employ local properties of Lyapunov functions to extend the singular perturbation analysis on Riemannian manifolds. Consequently, the results of the singular perturbation on manifolds are used to obtain the convergence of extremum seeking algorithms for dynamical systems on Riemannian manifolds.

ItemCloseness of solutions and averaging for nonlinear systems on Riemannian manifoldsTaringoo, F ; Nesic, D ; Tan, Y ; Dower, PM (IEEE, 2013)An averaging result for periodic dynamical systems evolving on Euclidean spaces is extended to those evolving on (differentiable) Riemannian manifolds. Using standard tools from differential geometry, a perturbation result for timevarying dynamical systems is developed that measures closeness of trajectories via a suitable metric on a finite time horizon. This perturbation result is then extended to bound excursions in the trajectories of periodic dynamical systems from those of their respective averages, on an infinite time horizon, yielding the specified averaging result. Some simple examples further illustrating this result are also presented.

ItemTrajectorybased proofs for sampleddata extremum seeking controlKHONG, S ; Nesic, D ; Tan, Y ; Manzie, CG (IEEE, 2013)Extremum seeking of nonlinear systems based on a sampleddata control law is revisited. It is established that under some generic assumptions, semiglobal practical asymptotically stable convergence to an extremum can be achieved. To this end, trajectorybased arguments are employed, by contrast with Lyapunovfunctiontype approaches in the existing literature. The proof is simpler and more straightforward; it is based on assumptions that are in general easier to verify. The proposed extremum seeking framework may encompass more general optimisation algorithms, such as those which do not admit a stateupdate realisation and/or Lyapunov functions. Multiunit extremum seeking is also investigated within the context of accelerating the speed of convergence.

ItemOn sampleddata extremum seeking control via stochastic approximation methodsKhong, SZ ; Tan, Y ; Nesic, D ; Manzie, C (IEEE, 20130101)This note establishes a link between stochastic approximation and extremum seeking of dynamical nonlinear systems. In particular, it is shown that by applying classes of stochastic approximation methods to dynamical systems via periodic sampleddata control, convergence analysis can be performed using standard tools in stochastic approximation. A tuning parameter within this 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 steadystate inputoutput behaviour. Semiglobal convergence with probability one is demonstrated for three basic classes of stochastic approximation methods: finitedifference, random directions, and simultaneous perturbation. The tradeoff between the speed of convergence and accuracy is also discussed within the context of asymptotic normality of the outputs of these optimisation algorithms.

ItemOpen Problems in Reset ControlZhao, G ; Nesic, D ; Tan, Y ; Wang, J (IEEE, 20130101)It is wellknown that there are fundamental performance limitations in the design of linear feedback control systems for singleinputsingleoutput (SISO) lineartimeinvariant (LTI) plants. These performance limitations sometimes include overshoot and rise time. This paper shows that for some examples of SISO LTI systems, it is possible to find suitable reset controllers that can overcome such performance limitations, though there are still some robust and implementable issues that need to be solved. This naturally leads to the formulation of several open research problems that we specify.

ItemExtremum Seeking Methods for Online Automotive CalibrationManzie, C ; Moase, W ; Shekhar, R ; Mohammadi, A ; Nesic, D ; Tan, Y ; Waschl, H ; Kolmanovsky, I ; Steinbuch, M ; del Re, L (Springer, 20140101)The automotive calibration process is becoming increasingly difficult as the degrees of freedom in modern engines rises with the number of actuators. This is coupled with the desire to utilise alternative fuels to gasoline and diesel for the promise of lower CO2 levels in transportation. However, the range of fuel blends also leads to variability in the combustion properties, requiring additional sensing and calibration effort for the engine control unit (ECU). Shifting some of the calibration effort online whereby the engine controller adjusts its operation to account for the current operating conditions may be an effective alternative if the performance of the controller can be guaranteed within some performance characteristics. This tutorial chapter summarises recent developments in extremum seeking control, and investigates the potential of these methods to address some of the complexity in developing fuelflexible controllers for automotive powertrains.

ItemMultiagent gradient climbing via extremum seeking controlKong, SZ ; Manzie, CG ; Tan, Y ; Nesic, D (IFAC  International Federation of Automatic Control, 2014)A unified framework based on discretetime gradientbased extremum seeking control is proposed to localise an extremum of an unknown scalar field distribution using a group of equipped with sensors. The controller utilises estimates of gradients of the field from local dithering sensor measurements collected by the mobile agents. It is assumed that distributed coordination which ensures uniform asymptotic stability with respect to a prescribed formation of the agents is employed. The framework is useful in that a broad range of nonlinear programming algorithms can be combined with a wide class of cooperative control laws to perform extreme source seeking. Semiglobal practical asymptotically stable convergence to local extrema is established in the presence of bounded field sampling noise.

ItemImproving L₂ Gain Performance of Linear Systems by Reset ControlZhao, G ; NESIC, D ; Tan, Y ; Wang, J ; Boje, E ; Xia, X (IFAC  International Federation of Automatic Control, 2014)In this paper, new Lyapunovbased reset rules are constructed to improve C2 gain performance of lineartimeinvariant (LTI) systems. By using the hybrid system framework, sufficient conditions for exponential and finite gain C2 stability are presented. It is shown that the C2 gain of the closed loop system with resets can be improved compared with the base system. Numerical example supports our results.

ItemMultiagent source seeking via discretetime extremum seeking controlKhong, SZ ; Tan, Y ; Manzie, C ; Nesic, D (PERGAMONELSEVIER SCIENCE LTD, 20140901)Recent developments in extremum seeking theory have established a general framework for the methodology, although the specific implementations, particularly in the context of multiagent systems, have not been demonstrated. In this work, a group of sensorenabled 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. Semiglobal 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.