Scalable tube model predictive control of uncertain linear systems using ellipsoidal sets

This work proposes a novel robust model predictive control (MPC) algorithm for linear systems affected by dynamic model uncertainty and exogenous disturbances. The uncertainty is modeled using a linear fractional perturbation structure with a time-varying perturbation matrix, enabling the algorithm to be applied to a large model class. The MPC controller constructs a state tube as a sequence of parameterized ellipsoidal sets to bound the state trajectories of the system. The proposed approach results in a semidefinite program to be solved online, whose size scales linearly with the order of the system. The design of the state tube is formulated as an offline optimization problem, which offers flexibility to impose desirable features such as robust invariance on the terminal set. This contrasts with most existing tube MPC strategies using polytopic sets in the state tube, which are difficult to design and whose complexity grows combinatorially with the system order. The algorithm guarantees constraint satisfaction, recursive feasibility, and stability of the closed loop. The advantages of the algorithm are demonstrated using two simulation studies.Comment: Submitted to International Journal of Robust and Nonlinear Contro

Safe and Fast Tracking on a Robot Manipulator: Robust MPC and Neural Network Control

Fast feedback control and safety guarantees are essential in modern robotics. We present an approach that achieves both by combining novel robust model predictive control (MPC) with function approximation via (deep) neural networks (NNs). The result is a new approach for complex tasks with nonlinear, uncertain, and constrained dynamics as are common in robotics. Specifically, we leverage recent results in MPC research to propose a new robust setpoint tracking MPC algorithm, which achieves reliable and safe tracking of a dynamic setpoint while guaranteeing stability and constraint satisfaction. The presented robust MPC scheme constitutes a one-layer approach that unifies the often separated planning and control layers, by directly computing the control command based on a reference and possibly obstacle positions. As a separate contribution, we show how the computation time of the MPC can be drastically reduced by approximating the MPC law with a NN controller. The NN is trained and validated from offline samples of the MPC, yielding statistical guarantees, and used in lieu thereof at run time. Our experiments on a state-of-the-art robot manipulator are the first to show that both the proposed robust and approximate MPC schemes scale to real-world robotic systems.Comment: 8 pages, 4 figures

State-Dependent Dynamic Tube MPC: A Novel Tube MPC Method with a Fuzzy Model of Disturbances

Most real-world systems are affected by external disturbances, which may be impossible or costly to measure. For instance, when autonomous robots move in dusty environments, the perception of their sensors is disturbed. Moreover, uneven terrains can cause ground robots to deviate from their planned trajectories. Thus, learning the external disturbances and incorporating this knowledge into the future predictions in decision-making can significantly contribute to improved performance. Our core idea is to learn the external disturbances that vary with the states of the system, and to incorporate this knowledge into a novel formulation for robust tube model predictive control (TMPC). Robust TMPC provides robustness to bounded disturbances considering the known (fixed) upper bound of the disturbances, but it does not consider the dynamics of the disturbances. This can lead to highly conservative solutions. We propose a new dynamic version of robust TMPC (with proven robust stability), called state-dependent dynamic TMPC (SDD-TMPC), which incorporates the dynamics of the disturbances into the decision-making of TMPC. In order to learn the dynamics of the disturbances as a function of the system states, a fuzzy model is proposed. We compare the performance of SDD-TMPC, MPC, and TMPC via simulations, in designed search-and-rescue scenarios. The results show that, while remaining robust to bounded external disturbances, SDD-TMPC generates less conservative solutions and remains feasible in more cases, compared to TMPC.Comment: 39 pages, 16 figures, 4 tables, 2 appendices, to be submitted to "international journal of robust and nonlinear control", [40] from paper cites our code to be submitted

A set-theoretic generalization of dissipativity with applications in Tube MPC

This paper introduces a framework for analyzing a general class of uncertain nonlinear discrete-time systems with given state-, control-, and disturbance constraints. In particular, we propose a set-theoretic generalization of the concept of dissipativity of systems that are affected by external disturbances. The corresponding theoretical developments build upon set based analysis methods and lay a general theoretical foundation for a rigorous stability analysis of economic tube model predictive controllers. Besides, we discuss practical prodecures for verifying set-dissipativity of constrained linear control systems with convex stage costs.Comment: 14 pages, 2 figure

Probabilistic performance validation of deep learning-based robust NMPC controllers

Solving nonlinear model predictive control problems in real time is still an important challenge despite of recent advances in computing hardware, optimization algorithms and tailored implementations. This challenge is even greater when uncertainty is present due to disturbances, unknown parameters or measurement and estimation errors. To enable the application of advanced control schemes to fast systems and on low-cost embedded hardware, we propose to approximate a robust nonlinear model controller using deep learning and to verify its quality using probabilistic validation techniques. We propose a probabilistic validation technique based on finite families, combined with the idea of generalized maximum and constraint backoff to enable statistically valid conclusions related to general performance indicators. The potential of the proposed approach is demonstrated with simulation results of an uncertain nonlinear system.gencia Estatal de Investigación (AEI)-Spain Grant PID2019-106212RB-C41/AEI/10.13039/501100011