357 research outputs found

    Backstepping and Sequential Predictors for Control Systems

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    We provide new methods in mathematical control theory for two significant classes of control systems with time delays, based on backstepping and sequential prediction. Our bounded backstepping results ensure global asymptotic stability for partially linear systems with an arbitrarily large number of integrators. We also build sequential predictors for time-varying linear systems with time-varying delays in the control, sampling in the control, and time-varying measurement delays. Our bounded backstepping results are novel because of their use of converging-input-converging-state conditions, which make it possible to solve feedback stabilization problems under input delays and under boundedness conditions on the feedback control. Our sequential predictors work is novel in its ability to cover time-varying measurement delays and sampling which were beyond the scope of existing sequential predictor methods for time-varying linear systems, and in the fact that the feedback controls that we obtain from our sequential predictors do not contain any distributed terms

    New advances in H∞ control and filtering for nonlinear systems

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    The main objective of this special issue is to summarise recent advances in H∞ control and filtering for nonlinear systems, including time-delay, hybrid and stochastic systems. The published papers provide new ideas and approaches, clearly indicating the advances made in problem statements, methodologies or applications with respect to the existing results. The special issue also includes papers focusing on advanced and non-traditional methods and presenting considerable novelties in theoretical background or experimental setup. Some papers present applications to newly emerging fields, such as network-based control and estimation

    On Observer-Based Control of Nonlinear Systems

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    Filtering and reconstruction of signals play a fundamental role in modern signal processing, telecommunications, and control theory and are used in numerous applications. The feedback principle is an important concept in control theory. Many different control strategies are based on the assumption that all internal states of the control object are available for feedback. In most cases, however, only a few of the states or some functions of the states can be measured. This circumstance raises the need for techniques, which makes it possible not only to estimate states, but also to derive control laws that guarantee stability when using the estimated states instead of the true ones. For linear systems, the separation principle assures stability for the use of converging state estimates in a stabilizing state feedback control law. In general, however, the combination of separately designed state observers and state feedback controllers does not preserve performance, robustness, or even stability of each of the separate designs. In this thesis, the problems of observer design and observer-based control for nonlinear systems are addressed. The deterministic continuous-time systems have been in focus. Stability analysis related to the Positive Real Lemma with relevance for output feedback control is presented. Separation results for a class of nonholonomic nonlinear systems, where the combination of independently designed observers and state-feedback controllers assures stability in the output tracking problem are shown. In addition, a generalization to the observer-backstepping method where the controller is designed with respect to estimated states, taking into account the effects of the estimation errors, is presented. Velocity observers with application to ship dynamics and mechanical manipulators are also presented

    Backstepping for Uncertain Nonlinear Systems with a Delay in the Control

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    International audienceThe recent new backstepping control design strategy based on the introduction of artificial delays and/or dynamic extensions is adapted to a family of systems. That way, globally asymptotically stabilizing control laws for fundamental systems which cannot be handled by other techniques are determined

    Integrating Vehicle Slip and Yaw in Overarching Multi-Tiered Automated Vehicle Steering Control to Balance Path Following Accuracy, Gracefulness, and Safety

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    Balancing path following accuracy and error convergence with graceful motion in steering control is challenging due to the competing nature of these requirements, especially across a range of operating speeds and conditions. This paper demonstrates that an integrated multi-tiered steering controller considering the impact of slip on kinematic control, dynamic control, and steering actuator rate commands achieves accurate and graceful path following. This work is founded on multi-tiered sideslip and yaw-based models, which allow derivation of controllers considering error due to sideslip and the mapping between steering commands and graceful lateral motion. Observer based sideslip estimates are combined with heading error in the kinematic controller to provide feedforward slip compensation. Path following error is compensated by a continuous Variable Structure Controller (VSC) using speed-based path manifolds to balance graceful motion and error convergence. Resulting yaw rate commands are used by a backstepping dynamic controller to generate steering rate commands. A High Gain Observer (HGO) estimates sideslip and yaw rate for output feedback control. Stability analysis of the output feedback controller is provided, and peaking is resolved. The work focuses on lateral control alone so that the steering controller can be combined with other speed controllers. Field results provide comparisons to related approaches demonstrating gracefulness and accuracy in different complex scenarios with varied weather conditions and perturbations

    Neural network-based adaptive global sliding mode MPPT controller design for stand-alone photovoltaic systems

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    The increasing energy demand and the target to reduce environmental pollution make it essential to use efficient and environment-friendly renewable energy systems. One of these systems is the Photovoltaic (PV) system which generates energy subject to variation in environmental conditions such as temperature and solar radiations. In the presence of these variations, it is necessary to extract the maximum power via the maximum power point tracking (MPPT) controller. This paper presents a nonlinear generalized global sliding mode controller (GGSMC) to harvest maximum power from a PV array using a DC-DC buck-boost converter. A feed-forward neural network (FFNN) is used to provide a reference voltage. A GGSMC is designed to track the FFNN generated reference subject to varying temperature and sunlight. The proposed control strategy, along with a modified sliding mode control, eliminates the reaching phase so that the sliding mode exists throughout the time. The system response observes no chattering and harmonic distortions. Finally, the simulation results using MATLAB/Simulink environment demonstrate the effectiveness, accuracy, and rapid tracking of the proposed control strategy. The results are compared with standard results of the nonlinear backstepping controller under abrupt changes in environmental conditions for further validation

    Backstepping controller synthesis and characterizations of incremental stability

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    Incremental stability is a property of dynamical and control systems, requiring the uniform asymptotic stability of every trajectory, rather than that of an equilibrium point or a particular time-varying trajectory. Similarly to stability, Lyapunov functions and contraction metrics play important roles in the study of incremental stability. In this paper, we provide characterizations and descriptions of incremental stability in terms of existence of coordinate-invariant notions of incremental Lyapunov functions and contraction metrics, respectively. Most design techniques providing controllers rendering control systems incrementally stable have two main drawbacks: they can only be applied to control systems in either parametric-strict-feedback or strict-feedback form, and they require these control systems to be smooth. In this paper, we propose a design technique that is applicable to larger classes of (not necessarily smooth) control systems. Moreover, we propose a recursive way of constructing contraction metrics (for smooth control systems) and incremental Lyapunov functions which have been identified as a key tool enabling the construction of finite abstractions of nonlinear control systems, the approximation of stochastic hybrid systems, source-code model checking for nonlinear dynamical systems and so on. The effectiveness of the proposed results in this paper is illustrated by synthesizing a controller rendering a non-smooth control system incrementally stable as well as constructing its finite abstraction, using the computed incremental Lyapunov function.Comment: 23 pages, 2 figure

    Observer-Based Adaptive Control

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    The work present in this master thesis relates to output feedback adaptive control and observer design of nonlinear systems, and in particular of robot manipulators. A continuous-time velocity observer and a discrete-time adaptive velocity observer for robots are shown, and an observer backstepping controller is also proposed, which can be used together with both the observers. The resulting closed-loop system is proven to be semiglobally asymptotically stable with respect to both the velocity observation error and the tracking error, and stable with respect to the parameter estimation error. Furthermore an on-line parameter estimation method for a class of nonlinear system is presented, which can be easily extended for the robot equation. Unfortunately the way to use it in combination with the previous observer-controller has not been found and it has not been used in the experiments. In the Appendix A some technical details about the al-gorithm implementation are included, and in the Appendix B a paper already submitted to the 2002 Conference in Decision and Control is included, in which the adaptive output-feedback control scheme is extended for ship control. All the work has been conducted in the Department of Automatic Control, Lund Institute of Technology, Lund University
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