The notion of reproducing kernel Hilbert space (RKHS) has emerged in system identification during the past decade. In the resulting framework, the impulse response estimation problem is formulated as a regularized optimization defined on an infinite-dimensional RKHS consisting of stable impulse responses. The consequent estimation problem is well-defined under the central assumption that the convolution operators restricted to the RKHS are continuous linear functionals. Moreover, according to this assumption, the representer theorem hold, and therefore, the impulse response can be estimated by solving a finite-dimensional program. Thus, the continuity feature plays a significant role in kernel-based system identification. We show that this central assumption is guaranteed to be satisfied in considerably general situations, namely when the input signal is bounded, the kernel is an integrable function, and in the case of continuous-time dynamics, continuous. Furthermore, the strong convexity of the optimization problem and the continuity property of the convolution operators imply that the kernel-based system identification admits a unique solution. Consequently, it follows that kernel-based system identification is a well-defined approach.

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This paper discusses the problem of system identification when frequency domain side-information is available. We mainly consider the case where the side-information is provided as the H_∞-norm of the system being bounded by a given scalar. This framework allows considering different forms of frequency domain side-information, such as the dissipativity of the system. We propose a nonparametric identification approach for estimating the impulse response of the system under the given side-information. The estimation problem is formulated as a constrained optimization in a stable reproducing kernel Hilbert space, where suitable constraints are considered for incorporating the desired frequency domain features. The resulting optimization has an infinite-dimensional feasible set with an infinite number of constraints. We show that this problem is a well-defined convex program with a unique solution. We propose a heuristic that tightly approximates this unique solution. The proposed approach is equivalent to solving a finite-dimensional convex quadratically constrained quadratic program. The efficiency of the discussed method is verified by several numerical examples.

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Airborne wind energy systems convert wind energy into electricity using tethered flying devices, typically flexible kites or aircraft. Replacing the tower and foundation of conventional wind turbines can substantially reduce the material use and, consequently, the cost of energy, while providing access to wind at higher altitudes. Because the flight operation of tethered devices can be adjusted to a varying wind resource, the energy availability increases in comparison to conventional wind turbines. Ultimately, this represents a rich topic for the study of real-time optimal control strategies that must function robustly in a spatiotemporally varying environment. With all of the opportunities that airborne wind energy systems bring, however, there are also a host of challenges, particularly those relating to robustness in extreme operating conditions and launching/landing the system (especially in the absence of wind). Thus, airborne wind energy systems can be viewed as a control system designer’s paradise or nightmare, depending on one’s perspective. This survey article explores insights from the development and experimental deployment of control systems for airborne wind energy platforms over approximately the past two decades, highlighting both the optimal control approaches that have been used to extract the maximal amount of power from tethered systems and the robust modal control approaches that have been used to achieve reliable launch, landing, and extreme wind operation. This survey will detail several of the many prototypes that have been deployed over the last decade and will discuss future directions of airborne wind energy technology as well as its nascent adoption in other domains, such as ocean energy.@en

Projected gradient descent denotes a class of iterative methods for solving optimization programs. In convex optimization, its computational complexity is relatively low whenever the projection onto the feasible set is relatively easy to compute. On the other hand, when the problem is nonconvex, e.g., because of nonlinear equality constraints, the projection becomes hard and thus impractical. In this paper, we propose a projected gradient method for nonlinear programs that only requires projections onto the linearization of the nonlinear constraints around the current iterate, similar to sequential quadratic programming (SQP). The proposed method falls neither into the class of projected gradient descent approaches, because the projection is not performed onto the original nonlinear manifold, nor into that of SQP, since second-order information is not used. For nonlinear smooth optimization problems, we assess local and global convergence to a Karush–Kuhn–Tucker point of the original problem. Further, we show that nonlinear model predictive control is a promising application of the proposed method, due to the sparsity of the resulting optimization problem.

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In this paper, we analyze first-order methods to find a KKT point of the nonlinear optimization problems arising in Model Predictive Control (MPC). The methods are based on a projected gradient and constraint linearization approach, that is, every iteration is a gradient step, projected onto a linearization of the constraints around the current iterate. We introduce an approach that uses a simple ℓ_p merit function, which has the computational advantage of not requiring any estimate of the dual variables and keeping the penalty parameter bounded. We then prove global convergence of the proposed method to a KKT point of the nonlinear problem. The first-order methods can be readily implemented in practice via the novel tool FalcOpt. The performance is then illustrated on numerical examples and compared with conventional methods.

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