On-The-Fly Control of Unknown Smooth Systems from Limited Data

We investigate the problem of data-driven, on-the-fly control of systems with unknown nonlinear dynamics where data from only a single finite-horizon trajectory and possibly side information on the dynamics are available. Such side information may include knowledge of the regularity of the dynamics, monotonicity of the states, or decoupling in the dynamics between the states. Specifically, we develop two algorithms, $\texttt{DaTaReach}$ and $\texttt{DaTaControl}$, to over-approximate the reachable set and design control signals for the system on the fly. $\texttt{DaTaReach}$ constructs a differential inclusion that contains the unknown vector field. Then, it computes an over-approximation of the reachable set based on interval Taylor-based methods applied to systems with dynamics described as differential inclusions. $\texttt{DaTaControl}$ enables convex-optimization-based, near-optimal control using the computed over-approximation and the receding-horizon control framework. We provide a bound on its suboptimality and show that more data and side information enable $\texttt{DaTaControl}$ to achieve tighter suboptimality bounds. Finally, we demonstrate the efficacy of $\texttt{DaTaControl}$ over existing approaches on the problems of controlling a unicycle and quadrotor systems.Comment: Extended version of the final submission to the American Control Conference (ACC) 202

Distributionally Robust Optimization: A Review

The concepts of risk-aversion, chance-constrained optimization, and robust optimization have developed significantly over the last decade. Statistical learning community has also witnessed a rapid theoretical and applied growth by relying on these concepts. A modeling framework, called distributionally robust optimization (DRO), has recently received significant attention in both the operations research and statistical learning communities. This paper surveys main concepts and contributions to DRO, and its relationships with robust optimization, risk-aversion, chance-constrained optimization, and function regularization

Multi-parametric Programming for Model Predictive Control

Model predictive control (MPC) solves a quadratic optimization problem to generate control law in each step. The usual methods of solution for quadratic optimization problem are interior point method, active set method etc. But most of the techniques are computationally heavy to perform the job in small amount of time. So a method is required where on-line computation is less. In multi-parametric quadratic programming (mp-QP) method an off-line computation is done a prior and a binary search tree is prepared. The on-line computation mainly involves a search through the binary-tree. The mp-QP is suitable for the class of optimization problem, where the objective function is to minimize or maximize a performance criterion subject to a given set of constraints where some of the parameter vary between lower and upper bounds. Also mp-QP is suitable for multi-objective optimization, where multi criteria problems can be reformulated as multi-parametric programming problems and a parametrized optimal solution is obtained. Multi-parametric programming is a technique for obtaining: (i) the objective and optimization variable as functions of the varying parameters and (ii) the regions in the space of the parameters where these functions are valid. The newly developed convex optimization solver CVXGEN is utilized successfully for off-line calculations which involves of dividing the parameter space into different polyhedral regions.In each one, the objective function has a constant value. The process involves another kind of optimization problem. For CVXGEN, worst case solving time is in milliseconds, even for a large problem.Thus, the use of CVXGEN minimizes the off-line calculation in mp-QP technique. In this work, an input constraint MPC problem is chosen from existing literature. The problem is solved for both two step prediction and three step prediction cases.The control input and states are ploted for both the MPC problems, and the results are compared

A Sparse Nonlinear Model Predictive Control for Autonomous Space Missions

Propellant consumption minimization is a key factor in space missions, as it strongly affects the duration of any mission. Nowadays, delta-V guidance strategies are obtained by means of classical ground based open loop methods, while academic research has mainly focused on autonomous low-thrust strategies. However, classical methods return instantaneous impulsive thrust actions that are not always feasible in practice, due to the technical limitations of real propulsion systems. In this paper, a novel Nonlinear Model Predictive Control framework for autonomous guidance and control with high-thrust quasi-impulsive maneuvers is presented. The internal prediction model is based on the so-called Modified Equinoctial Orbital Elements, which allow us to overcome relevant singularities given by the standard Keplerian elements. Different NMPC cost functions are compared in order to have a sparse thrust profile, minimize at the same time the propellant consumption and the tracking error with respect to the target orbit. In particular, it is shown how non-quadratic norms could achieve better performances. Finally, an Earth Observation mission, employing different NMPC functionals, is used as a benchmark and the results are compared with the ones coming from the classical astrodynamics solutions