The control of underactuated Euler–Lagrange systems with uncertain and switched parameters is an important problem whose solution has many applications. The problem is challenging as standard adaptive control techniques do not extend to this class of systems due to structural constraints that lead to parameterization difficulties. This note proposes an adaptive switched control framework that handles the uncertainty and switched dynamics without imposing structural constraints. A case study inspired by autonomous vessel operations is used to show the effectiveness of the proposed approach.

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Position control for heavy-lift construction vessels is crucial for safe operation during offshore construction. During the various phases of a typical offshore construction assignment, considerable changes in the dynamics of the crane-vessel system occur. Operational hazard was reported if such interchanging dynamics are not properly handled. However, to date and the best of our knowledge, no systematic control solution is reported considering multiphase offshore construction scenarios. This article proposes a switched dynamical framework to model the interchanging phases and to formulate a comprehensive position control solution for heavy-lift vessels. Stability and robustness against modeling imperfections and environmental disturbances are analytically assessed. The effectiveness of the solution is verified on a realistic heavy-lift vessel simulation platform; it is shown that the proposed switched framework sensibly improves accuracy and reduces hazard compared with a nonswitched solution designed for only one phase of the construction scenario.

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Multi-area load frequency control (LFC) selects and controls a few generators in each area of the power system in an effort to dampen inter-area frequency oscillations. To effectively dampen such oscillations, it is required to enhance and lower the control activity dynamically during operation, so as to adapt to changing circumstances. Changing circumstances should cover not only parametric uncertainties and unmodelled dynamics (e.g. aggregated area dynamics and bus dynamics), but also the increasing structural flexibility of modern power systems (e.g. protection mechanisms against faults and cyber-attacks, or topology reconfiguration mechanisms for demand response). As formal stability guarantees around such an attractive adaptive multi-area LFC concept are still lacking, this work proposes framework in which adaptation and switching are combined in a provably stable way to handle parametric uncertainty, unmodelled dynamics, and dynamical interconnections of the power system. Stability is studied in the Lyapunov theory sense using the standard structure-preserving modelling approach, and the resulting adaptive multi-area LFC design is validated using an IEEE 39-bus benchmark.

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This brief proposes a new adaptive-robust formulation for time-delay control (TDC) under a less-restrictive stability condition. TDC relies on estimating the unknown system dynamics via the artificial introduction of a time delay, often referred to as time-delay estimation (TDE). In conventional TDC, the estimation error, called TDE error, is taken to be upper bounded by a constant under the assumption of small time delay and, most importantly, of a priori bounded states. We highlight the issues of such a conventional methodology via an unstable counterexample. Consequently, a new less-restrictive structure for the upper bound of the TDE error is formulated, which has an explicit dependence on system states and is valid for any chosen time delay. This insight leads to a new TDC design, namely, time-delayed adaptive-robust control (TDARC). The effectiveness of TDARC is substantiated via a multiple-degrees-of-freedom robot.

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The literature has proven that attaining good transient behavior in leakage-based robust adaptive control of uncertain switched systems is intrinsically challenging. In fact, because the gains of the inactive subsystems must exponentially vanish during inactive times as an effect of leakage action, new learning transients will repeatedly arise at each switching instant. In this paper, a new leakage-based mechanism is designed for robust adaptive control of uncertain switched systems: in contrast to the available designs, the key innovation of the proposed one is that the adaptive gains of the inactive subsystems can be kept constant to their switched-off values, thus preventing vanishing gains. Bounded stability of the closed-loop switched system is guaranteed thanks to the introduction of an auxiliary gain playing the role of leakage. A benchmark example commonly adopted in adaptive switched literature shows that the proposed strategy can consistently improve the transient behavior under various families of switching signals.

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In the presence of unmodelled dynamics and uncertainties with no a priori constant bounds, conventional robust adaptation strategies for switched systems cannot allow the control gains of inactive subsystems to remain constant during inactive intervals: vanishing gains are typically required in order to prove bounded stability. As a consequence, these strategies, known in literature as leakage-based adaptive methods, might introduce poor transients at each switching instant. Leakage-based adaptive control becomes even more problematic in the switched nonlinear case, where non-conservative state-dependent upper bounds for uncertainties and unmodelled dynamics are required. This work shows that, for a class of switched Euler–Lagrange systems, such difficulties can be mitigated: a novel leakage-based stable mechanism is introduced which allows the gains of inactive subsystems to remain constant. At the same time, unmodelled dynamics and uncertainties with no a priori bounds can be handled by a quadratic state-dependent upper bound structure that reduces conservativeness as compared to state-of-the-art structures. The proposed design is validated analytically and its performance is studied in simulation with a pick-and-place robotic manipulator example.

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Adaptive Sliding Mode Control (ASMC) aims to adapt the switching gain in such a way to cope with possibly unknown uncertainty. In state-of-the-art ASMC methods, a priori boundedness of the uncertainty is crucial to ensure boundedness for the switching gain and uniformly ultimately boundedness. A priori bounded uncertainty might impose a priori bounds on the system state before obtaining closed-loop stability. A design removing this assumption is still missing in literature. A positive answer to this quest is given by this note where a novel ASMC methodology is proposed which does not require a priori bounded uncertainty. An illustrative example is presented to highlight the main features of the approach, after which a general class of Euler–Lagrange systems is taken as a case study to show the applicability of the proposed design.

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Available control methods for underactuated Euler–Lagrange (EL) systems rely on structure-specific constraints that may be appropriate for some systems, but restrictive for others. A generalized (structure-independent) control framework is to a large extent missing, especially in the presence of uncertainty. This paper introduces an adaptive-robust control framework for a quite general class of uncertain underactuated EL systems. Compared to existing literature, the important attributes of the proposed solution are: (i) avoiding structure-specific restrictions, namely, symmetry condition property of the mass matrix, and a priori bounds on non-actuated states or state derivatives; (ii) considering Coriolis, centripetal, friction and gravity terms to be unknown, while only requiring the knowledge of maximum perturbation around a nominal value of the mass matrix; (iii) handling state-dependent uncertainties irrespective of their linear or nonlinear in parameters structure. These features significantly widen the range of underactuated EL systems the proposed solution can handle in comparison to the available methods. Stability is studied analytically and the performance is verified in simulation using offshore boom crane dynamics.

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The actual performance of model-based path-following methods for unmanned aerial vehicles (UAVs) shows considerable dependence on the wind knowledge and on the fidelity of the dynamic model used for design. This study analyzes and demonstrates the performance of an adaptive vector field (VF) control law which can compensate for the lack of knowledge of the wind vector and for the presence of unmodeled course angle dynamics. Extensive simulation experiments, calibrated on a commercial fixed-wing UAV and proven to be realistic, show that the new VF method can better cope with uncertainties than its standard version. In fact, while the standard VF approach works perfectly for ideal first-order course angle dynamics (and perfect knowledge of the wind vector), its performance degrades in the presence of unknown wind or unmodeled course angle dynamics. On the other hand, the estimation mechanism of the proposed adaptive VF effectively compensates for wind uncertainty and unmodeled dynamics, sensibly reducing the path-following error as compared to the standard VF.

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State-of-the-art adaptive or robust adaptive techniques for several classes of uncertain switched systems demand structural knowledge of the system dynamics in order to appropriately select the regressor terms in the adaptive law. As a result, the number of unknown parameters to be adapted increases with system complexity, which can lead to very complex adaptive laws. In this work we propose, for the relevant class of Euler–Lagrange systems subject to time-dependent slow switching, a switched robust adaptive control framework with reduced complexity: the number of unknown parameter to be adapted is independent on the system complexity, whereas the regressor terms in the adaptive laws do not require any structural knowledge of the system dynamics. Stability analysis is provided to illustrate the benefit of the proposed design, and the performance of the controller is verified using a switched system stemming from the combination of mooring and free-hanging operations in dynamic positioning of offshore ships.@en

This letter proposes a new adaptive control method for a class of nonlinearly-parametrized switched systems that includes Monod kinetics and Euler-Lagrange systems with nonlinear in parameters form as special cases. As compared to the adaptive switched frameworks proposed in literature, the proposed adaptation framework has the distinguishing feature of updating the gains of the active and inactive subsystems simultaneously: by doing this it avoids high gains for the active subsystems or vanishing gains for the inactive ones. The design is studied analytically and its performance is validated in simulation with a robotic manipulator example.

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With the growing demand of large-scale heavy lift vessels in the deep-sea offshore construction works, high performance of Dynamic positioning (DP) systems is becoming ever crucial. However, current DP systems on board of heavy lift vessels do not consider model uncertainty (typically arising from mooring forces). In this paper, an observer-based robust controller is designed that can tackle model uncertainty in hydrodynamic damping and mooring forces, environmental disturbances as well as can filter out the high-frequency vessel movement. Closed-loop system stability is analytically established in terms of uniformly ultimately boundedness. In addition, several key performance indicators are provided for tuning the performance of the controller. The effectiveness of the proposed control framework is studied in simulation with a crane-vessel system.@en

In the literature of any time-delay control (TDC)-based methods, the boundedness of the error due to time-delay estimation (TDE) is crucial to prove the stability. However, the TDE error has been studied by discretizing the closed-loop system while neglecting the effect of discretization error; consequently, the TDE error is considered to be upper bounded by a constant. This paper proves that such constant upper bound is restrictive in nature due to the explicit involvement of system states in the TDE error. Thereby, without discretizing the closed-loop system, a new structure of the upper bound of TDE error is directly formulated in the continuous-time domain which has an explicit dependency on the system states. Via this formulation, this paper solves the long-standing problem for TDC of having consistent stability analysis and control design in continuous time. Based on the newly proposed structure of TDE error, an enhanced robust control law is formulated. The effectiveness of the proposed method is experimentally substantiated as compared to the conventional TDC using a multiple-degrees-of-freedom robot.

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The adaptive sliding mode control technique relaxes the assumption of known bound of the disturbance in discrete-time systems. However, the existing technique of gain adaptation in discrete-time sliding mode control has issues of gain overestimation and underestimation. Therefore, this paper proposes a technique to adapt the switching gain such that the adaptive gain can tackle the uncertainty without any knowledge of the bound of uncertainty while overcoming the over- and under-estimation problems of switching gain.

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Underestimation and overestimation problems are commonly observed in conventional adaptive sliding mode control (ASMC). These problems refer to the fact that the adaptive controller gain unnecessarily increases when the states are approaching the sliding surface (overestimation) or improperly decreases when the states are getting far from it (underestimation). In this paper, we propose a novel ASMC strategy that overcomes such issues. In contrast to the state of the art, the proposed strategy is effective even when an a priori constant bound on the uncertainty cannot be imposed. Comparative results using a two-link manipulator demonstrate improved performance as compared to the conventional ASMC. Experimental results on a biped robot confirm the effectiveness and robustness of the proposed method under various practical uncertainties.

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This work presents a Lyapunov-based approach to adaptive control of uncertain Euler-Lagrange (EL) systems in a slow switching scenario. Fundamental trade-offs arising from considering uncertain dynamics with unknown uncertainty bounds are presented and discussed. Contrary to the non-switched scenario, the use of acceleration feedback seems to be unavoidable in the switched scenario: this is due to the fact that an acceleration feedback and an appropriate Lyapunov function must be adopted to make the switching law independent from the unknown uncertainty bounds. In the absence of such feedback or using different Lyapunov functions, a stabilizing switching law would exist but could not be determined as it would depend on an unknown uncertainty bound.

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