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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]

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]

In this paper, we suggest an improvement to our previously undertaken approach. Briefly, this approach consisted of applying the robust fractional predictive control (RFPC) for a class of constrained fractional systems implementing the min–max optimization technique. The RFPC controller requires resolution of a non-convex min–max optimization problem. The resolution of this problem, however, can only conduce to local solutions. The reason is simple: the objective function to be optimized is non-convex due to the presence of uncertainties. In the present work, we propose a global optimization-based RFPC controller for an uncertain fractional order system. A determinist global optimization method, namely, generalized geometric programming (GGP), is proposed to solve this problem for the uncertain fractional order system. The GGP method consists of converting a non-convex problem into a convex one via the application of variable changes. The technique of the convexification of this method is applied in line with the objective function to be optimized. Consequently, we obtained a new convex criterion and a convex problem. From an experimental point of view, we applied the proposed RFPC to a real thermal system using an STM32 microcontroller in order to control our thermal system. [ABSTRACT FROM AUTHOR]