Predictor-based robust control of uncertain nonlinear systems subject to input delay

10th IFAC Workshop on Time Delay Systems, TDS-2012; Boston, MA; United States; 22 June 2012 through 24 June 2012In this paper, a tracking controller is developed for a class of nonlinear systems subject to time delay in the control input, uncertainties in the dynamic model, and additive disturbances. The control development is based on a novel predictor-like method to address the time delay in the control input. Lyapunov based stability analysis is used to prove semi-global asymptotic tracking. © 2012 IFAC

Robust Predictive Extended State Observer for a Class of Nonlinear Systems with Time-Varying Input Delay

[EN] This paper deals with asymptotic stabilisation of a class of nonlinear input-delayed systems via dynamic output feedback in the presence of disturbances. The proposed strategy has the structure of an observer-based control law, in which the observer estimates and predicts both the plant state and the external disturbance. A nominal delay value is assumed to be known and stability conditions in terms of linear matrix inequalities are derived for fast-varying delay uncertainties. Asymptotic stability is achieved if the disturbance or the time delay is constant. The controller design problem is also addressed and a numerical example with an unstable system is provided to illustrate the usefulness of the proposed strategy.This work was partially supported by: Ministerio de Economía y Competitividad, Spain (TIN2017-86520-C3-1-R); Universitat Politècnica de València (FPI-UPV 2014 PhD Grant); and Israel Science Foundation (Grant No. 1128/14).Sanz Diaz, R.; García Gil, PJ.; Fridman, E.; Albertos Pérez, P. (2020). Robust Predictive Extended State Observer for a Class of Nonlinear Systems with Time-Varying Input Delay. International Journal of Control. 93(2):217-225. https://doi.org/10.1080/00207179.2018.1562204S217225932Ahmed-Ali, T., Cherrier, E., & Lamnabhi-Lagarrigue, F. (2012). Cascade High Gain Predictors for a Class of Nonlinear Systems. IEEE Transactions on Automatic Control, 57(1), 221-226. doi:10.1109/tac.2011.2161795Artstein, Z. (1982). Linear systems with delayed controls: A reduction. 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Disturbance attenuation and rejection for systems with nonlinearity via DOBC approach. International Journal of Robust and Nonlinear Control, 15(3), 109-125. doi:10.1002/rnc.978Karafyllis, I., & Krstic, M. (2017). Predictor Feedback for Delay Systems: Implementations and Approximations. Systems & Control: Foundations & Applications. doi:10.1007/978-3-319-42378-4Krstic, M. (2008). Lyapunov tools for predictor feedbacks for delay systems: Inverse optimality and robustness to delay mismatch. Automatica, 44(11), 2930-2935. doi:10.1016/j.automatica.2008.04.010Léchappé, V., Moulay, E., Plestan, F., Glumineau, A., & Chriette, A. (2015). New predictive scheme for the control of LTI systems with input delay and unknown disturbances. Automatica, 52, 179-184. doi:10.1016/j.automatica.2014.11.003Léchappé, V., Moulay, E. & Plestan, F. (2016). Dynamic observation-prediction for LTI systems with a time-varying delay in the input. 2016 IEEE 55th conference on decision and control (CDC) (pp. 2302–2307).Manitius, A., & Olbrot, A. (1979). Finite spectrum assignment problem for systems with delays. IEEE Transactions on Automatic Control, 24(4), 541-552. doi:10.1109/tac.1979.1102124Mazenc, F. & Malisoff, M. (2016). New prediction approach for stabilizing time-varying systems under time-varying input delay. 2016 IEEE 55th conference on decision and control (CDC) (pp. 3178–3182).Mondie, S., & Michiels, W. (2003). Finite spectrum assignment of unstable time-delay systems with a safe implementation. IEEE Transactions on Automatic Control, 48(12), 2207-2212. doi:10.1109/tac.2003.820147Najafi, M., Hosseinnia, S., Sheikholeslam, F., & Karimadini, M. (2013). Closed-loop control of dead time systems via sequential sub-predictors. 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A predictive extended state observer for a class of nonlinear systems with input delay subject to external disturbances. 2017 IEEE 56th annual conference on decision and control (CDC) (pp. 4345–4350).Sanz, R., Garcia, P., Fridman, E., & Albertos, P. (2018). Rejection of mismatched disturbances for systems with input delay via a predictive extended state observer. International Journal of Robust and Nonlinear Control, 28(6), 2457-2467. doi:10.1002/rnc.4027Shustin, E., & Fridman, E. (2007). On delay-derivative-dependent stability of systems with fast-varying delays. Automatica, 43(9), 1649-1655. doi:10.1016/j.automatica.2007.02.009Suplin, V., Fridman, E., & Shaked, U. (2007). Sampled-data H∞ control and filtering: Nonuniform uncertain sampling. Automatica, 43(6), 1072-1083. doi:10.1016/j.automatica.2006.11.024Yao, J., Jiao, Z., & Ma, D. (2014). RISE-Based Precision Motion Control of DC Motors With Continuous Friction Compensation. 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Time-Varying Input and State Delay Compensation for Uncertain Nonlinear Systems

A robust controller is developed for uncertain, second-order nonlinear systems subject to simultaneous unknown, time-varying state delays and known, time-varying input delays in addition to additive, sufficiently smooth disturbances. An integral term composed of previous control values facilitates a delay-free open-loop error system and the development of the feedback control structure. A stability analysis based on Lyapunov-Krasovskii (LK) functionals guarantees uniformly ultimately bounded tracking under the assumption that the delays are bounded and slowly varying

Interval Prediction for Continuous-Time Systems with Parametric Uncertainties

The problem of behaviour prediction for linear parameter-varying systems is considered in the interval framework. It is assumed that the system is subject to uncertain inputs and the vector of scheduling parameters is unmeasurable, but all uncertainties take values in a given admissible set. Then an interval predictor is designed and its stability is guaranteed applying Lyapunov function with a novel structure. The conditions of stability are formulated in the form of linear matrix inequalities. Efficiency of the theoretical results is demonstrated in the application to safe motion planning for autonomous vehicles.Comment: 6 pages, CDC 2019. Website: https://eleurent.github.io/interval-prediction

Output tracking via sliding modes in causal systems with time delay modeled by higher order pade approximations

Output tracking in a SISO causal uncertain nonlinear system with an output subject to a time delay is considered using sliding mode control. A higher order Pade approximation to a delay function with a known time delay is used to construct a model of a transformed system without a time delayed output and is employed in a feedback sliding mode control. This model functions as a predictor of the plant states and the plant output, but is of nonminimum phase due to the application of the Pade approximation. The method of the stable system center is used to stabilize the internal dynamics of this plant model, and a control is developed using a sliding surface to allow the plant to track an arbitrary reference profile given by an exogenous system with a known characteristic equation. Simulations of the system are performed for the plant model using a first, second and third order Pade approximations and a controller in plant feedback mode. Numerical examples for Pade approximations of increasing order are considered and compare

Normal forms for underactuated mechanical systems with symmetry

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