Concurrent Learning Adaptive Model Predictive Control with Pseudospectral Implementation

This paper presents a control architecture in which a direct adaptive control technique is used within the model predictive control framework, using the concurrent learning based approach, to compensate for model uncertainties. At each time step, the control sequences and the parameter estimates are both used as the optimization arguments, thereby undermining the need for switching between the learning phase and the control phase, as is the case with hybrid-direct-indirect control architectures. The state derivatives are approximated using pseudospectral methods, which are vastly used for numerical optimal control problems. Theoretical results and numerical simulation examples are used to establish the effectiveness of the architecture.Comment: 21 pages, 13 figure

Guidance and Control in Autonomous Debris Removal Space Missions via Adaptive Nonlinear Model Predictive Control

Space debris orbiting around the Earth are becoming a major problem that could impair the future of space exploration. Among the different approaches to this problem that have been proposed in recent years, this work focuses on a possible innovative solution, consisting in an autonomous spacecraft that performs a rendezvous maneuver, collects a debris of unknown mass and then moves to a parking orbit. When the spacecraft collects a debris of unknown mass, the dynamics of the system may change substantially, and this may affect the control stability and performance of the spacecraft. In this paper, a control system is designed, capable of handling situations with time-varying and uncertain parameters, as it occurs in space debris removal missions. A control strategy based on an Adaptive Nonlinear Model Predictive Control (ANMPC) is considered. The unknown mass of the debris is treated as an uncertain parameter and is estimated by means of two different methods (Recursive Average and Extended Kalman Filter (EKF)). Then, the estimated mass is used to update the internal model of the ANMPC, which later solves an on-line optimization problem, providing an optimal trajectory and control action for reaching the debris and then the parking orbit. The simulations carried out show that the proposed control system is able to effectively accomplish the requested task

Regret Guarantees for Online Receding Horizon Learning Control

We address the problem of controlling an unknown linear dynamical system with general cost functions and affine constraints on the control input through online learning. Our goal is to develop an algorithm that minimizes the regret, which is defined as the difference between the cumulative cost incurred by the algorithm and that of a receding horizon controller (RHC) with full knowledge of the system and state and that satisfies the control input constraints. Such performance metric is harder than minimizing the regret w.r.t. the best linear feedback controller commonly adopted in the literature, because the linear controllers might be sub-optimal or violate the constraints throughout. By exploring the conditions under which sub-linear regret is guaranteed, we propose an online receding horizon controller that learns the unknown system parameter from the sequential observation along with the necessary perturbation for exploration. We show that the proposed controller's performance is upper bounded by $\tilde{\mathcal{O}}(T^{3/4})$ for both regret and cumulative constraint violation when the controller has preview of the cost functions for the interval that doubles in size from one interval to the next. We also show that improved upper bound of $\tilde{\mathcal{O}}(T^{2/3})$ can be achieved for both regret and cumulative constraint violation when the controller has full preview of the cost functions.Comment: arXiv admin note: text overlap with arXiv:2010.1132