In this paper, we study the performance of a recently proposed approach for dynamic control allocation (DCA) for an overactuated quadrotor unmanned aerial vehicle (UAV) with tilting and twisting propellers. In DCA, overactuation is exploited to modify a given closed-loop system so that the plant’s output is left unchanged while the steady-state evolution of the control input is optimized with respect to a Lagrange cost. This research is built over an innovative DCA solution recently proposed by the authors, exploiting periodic piecewise polynomial signals. Interestingly, even though the dynamics of the mentioned UAV are highly non-linear, a suitable choice of DCA strategy allows to design of the allocation module simply by using tools developed for the Linear Time Invariant (LTI) case.

This paper addresses the problem of dynamic input allocation for nonlinear systems that exhibit a redundant input configuration and admit a periodic steady-state behavior. The control task is formulated in a general framework that encompasses a wide variety of practical scenarios, providing greater flexibility in the definition of the operators involved. The peculiar challenges posed by nonlinear control allocation problems are then examined from a different perspective, offered by a formulation in the context of optimal control theory. The similarities and differences between the two formulations are highlighted and discussed, with the aim of establishing a link between the two subjects in order to share their respective tools and results. Finally, an algorithm to determine approximate solutions to the control allocation problem is developed and refined using dynamic optimization tools.

This work addresses the input current allocation problem for the magnetic control system of the Tokamak à Configuration Variable (TCV). Given the available actuators (i.e. poloidal field coils) on the TCV device, this work aims to optimize the input current configuration concerning a desired cost function, minimizing the effect on the controlled output, which is, in this case, considered as the plasma shape. This request is formulated as a dynamic control allocation problem, and a solution is proposed, discussed, and validated by numerical simulations on TCV models and data.

The design of optimal control laws for nonlinear systems is tackled without knowledge of the underlying plant and of a functional description of the cost function. The proposed data-driven method is based only on real-time measurements of the state of the plant and of the (instantaneous) value of the reward signal and relies on a combination of ideas borrowed from the theories of optimal and adaptive control problems. As a result, the architecture implements a policy iteration strategy in which, hinging on the use of neural networks, the policy evaluation step and the computation of the relevant information instrumental for the policy improvement step are performed in a purely continuous-time fashion. Furthermore, the desirable features of the design method, including convergence rate and robustness properties, are discussed. Finally, the theory is validated via two benchmark numerical simulations.

A data-driven strategy to estimate the optimal feedback and the value function in an infinite-horizon, continuous-time, linear-quadratic optimal control problem for an unknown system is proposed. The method permits the construction of the optimal policy without any knowledge of the model, without requiring that the time derivatives of the state are available for the design, and without even assuming that an initial stabilizing feedback policy is available. Two alternative architectures are discussed: the first scheme revolves around the periodic computation of some matrix inversions involving the Q-function, whereas the second approach relies on a purely continuous-time implementation of some dynamic systems whose trajectories are uniformly attracted by the solutions to the above algebraic equations. Interestingly, the proposed strategy essentially constitutes a (direct) data-driven implementation of the celebrated Kleinman algorithm, hence subsuming the particularly appealing features of the latter, such as quadratic monotone convergence to the optimal solution. The theory is then validated by the means of practically motivated applications.