Electrical and Electronic Engineering - Research Publications
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ItemNo Preview AvailableReachability of Linear Time-Invariant Systems via Ellipsoidal Approximations(Elsevier BV, 2023-01-01)
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ItemObserver design for non-linear networked control systems with persistently exciting protocols(IEEE, 2020-07)We study the design of state observers for nonlinear networked control systems (NCSs) affected by disturbances and measurement noise, via an emulation-like approach. That is, given an observer designed with a specific stability property in the absence of communication constraints, we implement it over a network and we provide sufficient conditions on the latter to preserve the stability property of the observer. In particular, we provide a bound on the maximum allowable transmission interval (MATI) that guarantees an input-to-state stability (ISS) property for the corresponding estimation error system. The stability analysis is trajectory-based, utilises small-gain arguments, and exploits a persistently exciting (PE) property of the scheduling protocols. This property is key in our analysis and allows us to obtain significantly larger MATI bounds in comparison to the ones found in the literature. Our results hold for a general class of NCSs, however, we show that these results are also applicable to NCSs implemented over a specific physical network called WirelessHART (WH). The latter is mainly characterised by its multi-hop structure, slotted communication cycles, and the possibility to simultaneously transmit over different frequencies. We show that our results can be further improved by taking into account the intrinsic structure of the WH-NCS model. That is, we explicitly exploit the model structure in our analysis to obtain an even tighter MATI bound that guarantees the same ISS property for the estimation error system. Finally, to illustrate our results, we present analysis and numerical simulations for a class of Lipschitz non-linear systems and high-gain observers.
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ItemSynthesis of control Lyapunov functions and stabilizing feedback strategies using exit-time optimal control Part II: Numerical approach(WILEY, 2021-09)Abstract This paper continues the study (Yegorov, Dower, and Grüne et al.) and develops a curse‐of‐dimensionality‐free numerical approach to feedback stabilization, whose theoretical foundation was built in Yegorov et al. and involved the characterization of control Lyapunov functions (CLFs) via exit‐time optimal control. First, we describe an auxiliary linearization‐based technique for the construction of a local CLF and discuss how to determine its appropriate sublevel set that can serve as the terminal set in the exit‐time optimal control problem leading to a global or semi‐global CLF. Next, the curse of complexity is addressed with regard to the approximation of CLFs and associated feedback strategies in high‐dimensional regions. The goal is to enable for efficient model predictive control implementations with essentially faster (though less accurate) online policy updates than in case of solving direct or characteristics‐based nonlinear programming problems for each sample instant. We propose a computational approach that combines gradient enhanced modifications of the Kriging and inverse distance weighting frameworks for scattered grid interpolation. It in particular allows for convenient offline inclusion of new data to improve obtained approximations (machine learning can be used to select relevant new sparse grid nodes). Moreover, our method is designed so as to a priori return proper values of the CLF interpolant and its gradient on the entire terminal set of the considered exit‐time optimal control problem. Supporting numerical simulation results are also presented.
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ItemSynthesis of control Lyapunov functions and stabilizing feedback strategies using exit-time optimal control Part I: Theory(WILEY, 2021-09)Abstract This work studies the problem of constructing control Lyapunov functions (CLFs) and feedback stabilization strategies for deterministic nonlinear control systems described by ordinary differential equations. Many numerical methods for solving the Hamilton–Jacobi–Bellman partial differential equations specifying CLFs typically require dense state space discretizations and consequently suffer from the curse of dimensionality. A relevant direction of attenuating the curse of dimensionality concerns reducing the computation of the values of CLFs and associated feedbacks at any selected states to finite‐dimensional nonlinear programming problems. We propose to use exit‐time optimal control for that purpose. This article is the first part of a two‐part work. First, we state an exit‐time optimal control problem with respect to a sublevel set of an appropriate local CLF and establish that, under a number of reasonable conditions, the concatenation of the corresponding value function and the local CLF is a global CLF in the whole domain of asymptotic null‐controllability. We also investigate the formulated optimal control problem. A modification of these constructions for the case when one does not find a suitable local CLF is provided as well. Our developments serve as a theoretical basis for a curse‐of‐dimensionality‐free approach to feedback stabilization, that is presented in the second part Yegorov et al. (2021) of this work together with supporting numerical simulation results.