Application of nonlinear analysis and design Robust control of nonlinear systems Hybrid control systems a b s t r a c tIn this paper, we tackle the problem of trajectory tracking for a particular class of underactuated vehicles with full torque actuation and a single force direction (thrust), which is fixed relative to a body attached frame. Additionally, we consider that thrust reversal is not available. Under some given assumptions, the control law that we propose is able to track a smooth reference position trajectory while minimizing the angular distance to a desired orientation. This objective is achieved robustly, with respect to bounded state disturbances, and globally, in the sense that it is achieved regardless of the initial state of the vehicle. The proposed controller is tested in an experimental setup, using a small scale quadrotor vehicle and a motion capture system.
In this paper, we design a hybrid controller that globally exponentially stabilizes a system evolving on the n-dimensional sphere, denoted by S n . This hybrid controller is induced by a "synergistic" collection of potential functions on S n . We propose a particular construction of this class of functions that generates flows along geodesics of the sphere, providing convergence to the desired reference with minimal path length. We show that the proposed strategy is suitable to the exponential stabilization of a quadrotor vehicle.
A complete methodology to design robust fault detection and isolation (FDI) filters and fault-tolerant control (FTC) schemes for linear parameter varying systems is proposed, with particular focus on its applicability to wind turbines. This paper takes advantage of the recent advances in model falsification using set-valued observers (SVOs) that led to the development of FDI methods for uncertain linear time-varying systems, with promising results in terms of the time required to diagnose faults. An integration of such SVO-based FDI methods with robust control synthesis is described, to deploy new FTC algorithms that are able to stabilize the plant under faulty environments. The FDI and FTC algorithms are assessed by resorting to a publicly available wind turbine benchmark model, using Monte Carlo simulation runs.
In this paper, we show that the existence of centrally synergistic potential functions on the n-dimensional sphere, denoted by S n , is a sufficient condition for the global asymptotic stabilization of a point in S n . Additionally, if these functions decrease exponentially fast during flows and are bounded from above and from below by some polynomial function of the tracking error, then the reference point can be globally exponentially stabilized. We construct two kinds of centrally synergistic functions: the first kind consists of a finite family of potential functions on S n while the second kind consists of an uncountable number of potential functions on S n . While the former generates a simpler jump logic, the latter is optimal in the sense that it generates flows with minimal length.
In this paper, we address the problem of trajectory tracking for a class of underactuated vehicles with full torque actuation and only one dimensional force actuation (thrust). For this class of vehicles, the desired thrust is defined by a saturated control law that achieves global asymptotic stabilization of the position tracking error. The proposed control law also assures that the third component of the angular velocity is regulated to zero. To accomplish this task we propose a hybrid controller that is designed using backstepping techniques and recent developments on synergistic Lyapunov functions. Simulations validating the results are also provided.
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