Electrical and Electronic Engineering - Research Publications
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ItemInput-to-state stability analysis via averaging for parameterized discrete-time systems(Watam Press, 2010-12-15)The paper studies semi-global practical input-to-state stability (SGP-ISS) of a parameterized family of discrete-time systems that may arise when an approximate discrete-time model of a sampled-data system with disturbances is used for controller design. It is shown under appropriate conditions that if the solutions of the time varying family of discrete-time systems with disturbances converge uniformly on compact time intervals to the solutions of the average family of discrete-time systems, then ISS of the average family of systems implies SGP-ISS of the original family of systems. A trajectory based approach is utilized to establish the main result.
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ItemAveraging for a class of hybrid systems(Watam Press, 2010-12-15)Averaging theory for ordinary differential equations is extended to a class of hybrid systems. Rapid time variations in the flow map of a hybrid system generate solutions that are also solutions of a slightly perturbed time-invariant average hybrid system. 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. If the average system is asymptotically stable, 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. The results are partially motivated by the desire to justify a pulse-width modulated implementation of hybrid feedback control for nonlinear systems.
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ItemNetworked Control Systems With Communication Constraints: Tradeoffs Between Transmission Intervals, Delays and Performance(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2010-08-01)There are many communication imperfections in networked control systems (NCS) such as varying transmission delays, varying sampling/transmission intervals, packet loss, communication constraints and quantization effects. Most of the available literature on NCS focuses on only some of these aspects, while ignoring the others. In this paper we present a general framework that incorporates communication constraints, varying transmission intervals and varying delays. Based on a newly developed NCS model including all these network phenomena, we will provide an explicit construction of a continuum of Lyapunov functions. Based on this continuum of Lyapunov functions we will derive bounds on the maximally allowable transmission interval (MATI) and the maximally allowable delay (MAD) that guarantee stability of the NCS in the presence of communication constraints. The developed theory includes recently improved results for delay-free NCS as a special case. After considering stability, we also study semi-global practical stability (under weaker conditions) and performance of the NCS in terms of Lp gains from disturbance inputs to controlled outputs. The developed results lead to tradeoff curves between MATI, MAD and performance gains that depend on the used protocol. These tradeoff curves provide quantitative information that supports the network designer when selecting appropriate networks and protocols guaranteeing stability and a desirable level of performance, while being robust to specified variations in delays and transmission intervals. The complete design procedure will be illustrated using a benchmark example.
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ItemRobustness of nonlinear control systems with quantized feedback(ELSEVIER SCI LTD, 2010-05-01)This paper analyzes the stability of nonlinear systems with quantized feedback in the presence of exogenous disturbances. This paper is an extension of [D. Liberzon, D. Nešić, Input-to-state stabilization of linear systems with quantized state measurements, IEEE Trans. Automat. Control 52 (2007), 413-436] to nonlinear systems. Under appropriate assumptions using a nonlinear modification of the scheme proposed in [D. Liberzon, D. Nešić, Input-to-state stabilization of linear systems with quantized state measurements, IEEE Transactions on Automat. Control 52 (2007), 413-436], it is shown here that it is possible to achieve input-to-state and nonlinear gain l 2 stability for nonlinear systems with quantized feedback.
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ItemInput-to-State Stability and Averaging of Linear Fast Switching Systems(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2010-05-01)We consider the averaging method for stability of rapidly switching linear systems with disturbances. We show that the notions of strong and weak averages proposed in [1], with partial strong average defined in this note, play an important role in the context of switched systems. Using these notions of average, we show that exponential input-to-state stability (ISS) of the strong and the partial strong average system with linear gain imply exponential ISS with linear gain of the actual system. Similarly, exponential ISS of the weak average guarantees an appropriate exponential derivative ISS (DISS) property for the actual system. Moreover, using the Lyapunov method, we show that linear ISS gains of the actual system and its average converge to each other as the switching rate is increased.
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ItemSummability characterizations of uniform exponential and asymptotic stability of sets for difference inclusions(TAYLOR & FRANCIS LTD, 2010-01-01)We present several equivalent characterizations of uniform global exponential stability (UGES) and uniform global asymptotic stability (UGAS) of arbitrary closed (not necessarily compact) sets for non-linear difference inclusions. In particular, we provide several characterizations of these stability properties via summability criteria that do not require the knowledge of a Lyapunov function. We apply our results to prove novel-nested Matrosov theorems for UGES and UGAS of the origin for time-varying non-linear difference inclusions.
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ItemOn controller & capacity allocation co-design for networked control systems(ELSEVIER, 2009-09-01)This paper presents a framework for examining joint optimal channel-capacity allocation and controller design for networked control systems using store-and-forward networks in a discrete-time linear time-invariant setting. The resultant framework provides a synthesis procedure for designing distributed linear control laws for capacity-constrained networks taking the allocation of the capacity within the network into account.
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ItemOn Extremum Seeking in Bioprocesses with Multivalued Cost Functions(WILEY, 2009)Finding optimal operating modes for bioprocesses has been, for a long time, a relevant issue in bioengineering. The problem is of special interest when it implies the simultaneous optimization of competing objectives. In this paper, we address the problem of finding optimal steady states that achieve the best tradeoff between yield and productivity by using nonmodel-based extremum-seeking control with semiglobal practical stability and convergence properties. A special attention is paid to processes with multiple steady states and multivalued cost functions.
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ItemExtremum Seeking Control: Convergence Analysis(ELSEVIER, 2009-05-01)This paper summarizes our recent work on dynamical properties for a class of extremum seeking (ES) controllers that have attracted a great deal of research attention in the past decade. Their local stability properties were already investigated, see [2]. We first show that semi-global practical convergence is possible if the controller parameters are carefully tuned and the objective function has a unique (global) extremum. An interesting tradeoff between the convergence rate and the size of the domain of attraction of the scheme is uncovered: the larger the domain of attraction, the slower the convergence of the algorithm. The amplitude, frequency and shape of the dither signal are important design parameters in the extremum seeking controller. In particular, we show that changing the amplitude of the dither adaptively can be used to deal with global extremum seeking in presence of local extrema. Moreover, we show that the convergence of the algorithm is proportional to the power of the dither signal. Consequently, the square-wave dither yields the fastest convergence among all dithers of the same frequency and amplitude. We consider extremum seeking of a class of bioprocesses to demonstrate our results and motivate some open research questions for multi-valued objective functions.
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ItemA Unified Framework for Design and Analysis of Networked and Quantized Control Systems(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2009-04-01)We generalize and unify a range of recent results in quantized control systems (QCS) and networked control systems (NCS) literature and provide a unified framework for controller design for control systems with quantization and time scheduling via an emulation-like approach. A crucial step in our proofs is finding an appropriate Lyapunov function for the quantization/time-scheduling protocol which verifies its uniform global exponential stability (UGES). We construct Lyapunov functions for several representative protocols that are commonly found in the literature, as well as some new protocols not considered previously. Our approach is flexible and amenable to further extensions which are briefly discussed.