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In this article, a risk-aware motion control scheme is considered for mobile robots to avoid randomly moving obstacles when the true probability distribution of uncertainty is unknown. We propose a novel model-predictive control (MPC) method for limiting the risk of unsafety even when the true distribution of the obstacles’ movements deviates, within an ambiguity set, from the empirical distribution obtained using a limited amount of sample data. By choosing the ambiguity set as a statistical ball with its radius measured by the Wasserstein metric, we achieve a probabilistic guarantee of the out-of-sample risk, evaluated using new sample data generated independently of the training data. To resolve the infinite-dimensionality issue inherent in the distributionally robust MPC problem, we reformulate it as a finite-dimensional nonlinear program using modern distributionally robust optimization techniques based on the Kantorovich duality principle. To find a globally optimal solution in the case of affine dynamics and output equations, a spatial branch-and-bound algorithm is designed using McCormick relaxation. The performance of the proposed method is demonstrated and analyzed through simulation studies using nonlinear dynamic and kinematic vehicle models and a linearized quadrotor model. The simulation results indicate that, even when the sample size is small, the proposed method can successfully avoid randomly moving obstacles with a guarantee of out-of-sample risk, while its sample average approximation counterpart fails to do so. [ABSTRACT FROM AUTHOR]

This article presents a systematic robust current control design approach for three-phase voltage-source converters. Robustness is guaranteed by combining intrinsic passive properties of the impedance uncertainty at the point of common coupling together with stability results from a passivity-based control theory. This approach ensures stability against typical uncertainty sources at mid and high frequencies, such as cable resonances or other converters interaction, with significant less conservative performances than the obtained with the traditional robust control theory. The approach uses multiobjective controller synthesis formulation that allows us to logically combine robustness requirements with performance objectives avoiding heuristic iteration over the control structure and parameters. The controller synthesis is performed by means of a nonsmooth $\mathcal {H}_{\infty }$ optimization technique that tunes all free parameters of a vector-based controller function, which constraints its structure. This results in a synthesized controller with lower order than those obtained with convex optimization definitions of the $\mathcal {H}_{\infty }$ control problem. The design methodology is validated in time and frequency domain by means of theoretical analysis and experimental results with three usual grid filters: L, LCL, and LLCL. [ABSTRACT FROM AUTHOR]

Advanced control systems are tuned using dynamic models and optimization techniques. This approach frequently involves satisfying multiple conflicting objectives. Tuning robust controllers requires considering a framework that represents the system uncertainties, and its definition is not a trivial task. When dealing with a nonlinear model with many parameters, a high-quality representation requires a massive sampling of variations. In many cases, this represents an inaccessible computational cost for the optimization process. This work presents a new methodology for parameter uncertainty modeling that is oriented to tuning robust controllers based on multiobjective optimization techniques. The uncertainty modeling formulated represents a feasible computational cost and leads to robust solutions without attributing excessive conservatism. The novelty of this process consists in using the multiobjective space to define a set of scenarios with highly representative properties of the global uncertainty framework that formulate the control problem under a predefined minimization strategy. To demonstrate the effectiveness of this methodology, we present a temperature control design in a micro-CHP system under worst-case minimization. Based on the results, particular interest is given to verifying the appropriate formulation of the uncertainty modeling, which represents a 92.8% reduction of the computational cost involved in solving the robust optimization problem under a global uncertainty framework. • Tuning robust controllers requires considering system uncertainty. • Consider feasible computational cost and conservatism. • A new methodology is proposed to define highly relevant models. • The novelty consists of using the multi-objective space to set a characterization. • This process formulates the robust control under a realistic worst case. [ABSTRACT FROM AUTHOR]