Electrical and Electronic Engineering - Research Publications
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ItemPWM hybrid control systems: averaging tools for analysis and design(IEEE, 2010)We consider averaging for a class of hybrid systems that are motivated by Pulse Width Modulated (PWM) implementation of hybrid control laws for general nonlinear plants. Rapid time variations in the flow map of a hybrid system generate solutions that are also solutions of a time-invariant average hybrid system that is slightly perturbed. Results relating solutions of the time-varying system to solutions of the average system ensue. In the absence of finite escape times for the average system, on compact time domains each solution of the time-varying system is close to a solution of the average system. In the presence of asymptotic stability for the average system, the time-varying system exhibits semi-global, practical asymptotic stability. These results rely on mild regularity properties for the average system. In particular, the average system is not required to exhibit unique solutions. Both periodic and non-periodic flow maps are considered.
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ItemIdle speed control using linear time varying model predictive control and discrete time approximations(IEEE, 2010-01-01)This paper addresses the problem of idle speed control of hydrogen fueled internal combustion engine (H2ICE) using model predictive control (MPC) and sampled data control (SDC) theories. In the first step, results from SDC theory and a version of MPC are collectively employed to obtain a rigorously developed new generic control strategy. Here, a controller, based on a family of approximate discrete time models, is designed within a previously proposed framework to have guaranteed practical asymptotic stability of the exact (unknown) discrete time model. Controller design, accomplished using MPC theory, is facilitated by successive online linearizations of the nonlinear discrete time model at each sampling instant. In the second step, the technique is implemented in the idle speed control of hydrogen internal combustion engine (H2ICE). Various conditions under which this theory can be implemented are presented and their validity for idle speed control problem are discussed. Simulations are presented to illustrate the effectiveness of the control scheme.
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ItemExtremum Seeking From 1922 To 2010(IEEE, 2010-01-01)Extremum seeking is a form of adaptive control where the steady-state input-output characteristic is optimized, without requiring any explicit knowledge about this input-output characteristic other than that it exists and that it has an extremum. Because extremum seeking is model free, it has proven to be both robust and effective in many different application domains. Equally being model free, there are clear limitations to what can be achieved. Perhaps paradoxically, although being model free, extremum seeking is a gradient based optimization technique. Extremum seeking relies on an appropriate exploration of the process to be optimized to provide the user with an approximate gradient, and hence the means to locate an extremum. These observations are elucidated in the paper. Using averaging and time-scale separation ideas more generally, the main behavioral characteristics of the simplest (model free) extremum seeking algorithm are established.
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ItemA Unifying Approach to Extremum Seeking: Adaptive Schemes Based on Estimation of Derivatives(IEEE, 2010-01-01)A unifying, prescriptive framework is presented for the design of a family of adaptive extremum seeking controllers. It is shown how extremum seeking can be achieved by combining an arbitrary continuous optimization method (such as gradient descent or continuous Newton) with an estimator for the derivatives of the unknown steady-state reference-to-output map. A tuning strategy is presented for the controller parameters that ensures non-local convergence of all trajectories to the vicinity of the extremum. It is shown that this tuning strategy leads to multiple time scales in the closed-loop dynamics, and that the slowest time scale dynamics approximate the chosen continuous optimization method. Results are given for both static and dynamic plants. For simplicity, only single-input-single-output (SISO) plants are considered.
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ItemOn emulation-based observer design for networked control systems(IEEE, 2010)We extend our recent framework developed for the emulation-based observer design for networked control systems (NCS) to larger classes of systems and scheduling protocols. Consider a continuous-time observer that satisfies some input-to-state / input-to-output stability properties with respect to measurement errors, we prove that the observation error converges semiglobally and practically with the maximum allowable transmission interval (MATI) as parameter, when it is implemented via a network governed by a Lyapunov uniformly globally asymptotically stable (UGAS) protocol. We show that our results can be used to build various observers for NCS such as circle criterion observers. The stability analyses rely on trajectory based small gain theorems for parametrized systems.
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ItemTrajectory based small gain theorems for parameterized systems(IEEE, 2010)In this paper, trajectory based small gain theorems are developed for parameterized families of continuous-time systems. We show that the interconnection of two input-to-state stable (ISS) parameterized systems is semiglobally and practically ISS, when ISS gain functions are appropriately parameterized, and we provide explicit sufficient conditions on the parameter. A small gain theorem is also presented for the case where two parameterized systems that satisfy some input-to-state and input-to-output stability properties are interconnected with a bounded-input-bounded-state system. Obtained results are applied to several stabilization and tracking problems.
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ItemA framework for the observer design for networked control systems(IEEE, 2010-01-01)This paper provides a general framework for the observer design for networked control systems (NCS) affected by disturbances, via an emulation-like approach. The proposed model formulation allows us to consider various static and dynamic time-scheduling protocols, in-network processing implementations and encompasses sampled-data systems as a particular case. Provided that the continuous-time observer is robust to measurement errors (in an appropriate sense) we derive bounds on the maximum allowable transmission interval (MATI) that ensure the convergence of observation errors under network-induced communication constraints. The stability analysis is trajectory-based and utilizes small-gain arguments. It has to be emphasized that this paper also furnishes new tools for the observer design for sampled-data systems. Various observers can be combined and used within our approach to obtain estimators for NCS.
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ItemOn stochastic stability of packetized predictive control of non-linear systems over erasure channels(IFAC, 2010-01-01)We study a predictive control formulation for discrete-time non-linear plant models where controller output data is transmitted over an unreliable communication channel. The channel is affected by random data-loss and does not provide acknowledgments of receipt. To achieve robustness with respect to dropouts, at every sampling instant the controller transmits packets of data. These contain possible control inputs for a finite number of future time instants, and minimize a finite horizon cost function. At the plant actuator side, received packets are buffered, providing the plant inputs. Within this context, we adopt a stochastic Lyapunov function approach to establish stability results of this networked control system.
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ItemResults on passification of nonlinear controllers via a suitable time-regular reset map(IFAC - International Federation of Automatic Control, 2010-01-01)For a class of square continuous time nonlinear controllers we design a suitable resetting rule inspired by the resetting rule for Clegg integrators and First Order Reset Elements (FORE). With this rule, we prove that the arising hybrid system with temporal regularization is passive in the conventional continuous time sense with a small shortage of input passivity decreasing with the temporal regularization constant. Based on the passivity property, we then investigate the finite gain stability of the interconnection between this passive controller and a passive nonlinear plant.
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ItemPiecewise quadratic lyapunov functions for linear control systems with first order reset elements(IFAC - International Federation of Automatic Control, 2010-01-01)For a class of reset control systems, we reconsider the piecewise quadratic Lyapunov function construction proposed in Zaccarian et al. [2005]. In particular, we propose an alternative construction that addresses an analysis subtlety overlooked in that preliminary result. An example illustrates the potential pitfalls of ignoring this analysis subtlety. Another example is used to show that the new statement leads to numerical results that are similar to the ones that come from Zaccarian et al. [2005].