Robust Model Predictive Control via Random Convex Programming

This paper proposes a new approach to design a robust model predictive control (MPC) algorithm for LTI discrete time systems. By using a randomization technique, the optimal control problem embedded in the MPC scheme is solved for a finite number of realizations of model uncertainty and additive disturbances. Theoretical results in random convex programming (RCP) are used to show that the designed controller achieves asymptotic closed loop stability and constraint satisfaction, with a guaranteed level of probability. The latter can be tuned by the designer to achieve a tradeoff between robustness and computational complexity. The resulting Randomized MPC (RMPC) technique requires quite mild assumptions on the characterization of the uncertainty and disturbances and it involves a convex optimization problem to be solved at each time step. The technique is applied here to a case study of an electro-mechanical positioning syste

Robust Controller for Delays and Packet Dropout Avoidance in Solar-Power Wireless Network

Solar Wireless Networked Control Systems (SWNCS) are a style of distributed control systems where sensors, actuators, and controllers are interconnected via a wireless communication network. This system setup has the benefit of low cost, flexibility, low weight, no wiring and simplicity of system diagnoses and maintenance. However, it also unavoidably calls some wireless network time delays and packet dropout into the design procedure. Solar lighting system offers a clean environment, therefore able to continue for a long period. SWNCS also offers multi Service infrastructure solution for both developed and undeveloped countries. The system provides wireless controller lighting, wireless communications network (WI-FI/WIMAX), CCTV surveillance, and wireless sensor for weather measurement which are all powered by solar energy

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

Algebraic robust control of a closed circuit heating-cooling system with a heat exchanger and internal loop delays

This study demonstrates the use of a simple algebraic controller design for a cooling-heating plant with a through-flow air-water heat exchanger that evinces long internal delays with respect to the robustness to plant model uncertainties and variable ambient temperature conditions during the season. The advantage of the proposed design method consists in that the delays are not approximated but fully considered. Moreover, the reduction of sensitivity to model parameters’ variations yields the better applicability regardless modeling errors or environmental fluctuations. The infinite-dimensional mathematical model of the plant has been obtained by using anisochronic modeling principles. The key tool for the design is the ring special of quasipolynomial meromorphic functions (RQM). The Two-Feedback-Controllers (TFC) rather than the simple negative control feedback loop is utilized, which enables to solve the reference tracking and disturbance rejection independently and more efficiently. The eventual controller is then tuned such that robust stability and robust performance requirements are fulfilled. The tuning procedure is supported by a performance optimization idea. Since the originally obtained controller is of the infinite-dimensional nature, a possible way how to substitute it by a simplified finite-dimensional one is proposed for engineering practice. The functionality of both the controllers is compared and verified by simulations as well as by real measurements which prove a very good performance. © 2016 Elsevier LtdEuropean Regional Development Fund under the project CEBIA-Tech Instrumentation [CZ.1.05/2.1.00/19.0376

Robust trajectory planning for unmanned aerial vehicles in uncertain environments

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2008.Includes bibliographical references (leaves 145-153).As unmanned aerial vehicles (UAVs) take on more prominent roles in aerial missions, it becomes necessary to increase the level of autonomy available to them within the mission planner. In order to complete realistic mission scenarios, the UAV must be capable of operating within a complex environment, which may include obstacles and other no-fly zones. Additionally, the UAV must be able to overcome environmental uncertainties such as modeling errors, external disturbances, and an incomplete situational awareness. By utilizing planners which can autonomously navigate within such environments, the cost-effectiveness of UAV missions can be dramatically improved.This thesis develops a UAV trajectory planner to efficiently identify and execute trajectories which are robust to a complex, uncertain environment. This planner, named Efficient RSBK, integrates previous mixed-integer linear programming (MILP) path planning algorithms with several implementation innovations to achieve provably robust on-line trajectory optimization. Using the proposed innovations, the planner is able to design intelligent long-term plans using a minimal number of decision variables. The effectiveness of this planner is demonstrated with both simulation results and flight experiments on a quadrotor testbed.Two major components of the Efficient RSBK framework are the robust model predictive control (RMPC) scheme and the low-level planner. This thesis develops a generalized framework to investigate RMPC affine feedback policies on the disturbance, identify relative strengths and weaknesses, and assess suitability for the UAV trajectory planning problem. A simple example demonstrates that even with a conventional problem setup, the closed-loop performance may not always improve with additional decision variables, despite the resulting increase in computational complexity. A compatible low-level troller is also introduced which significantly improves trajectory-following accuracy, as demonstrated by additional flight experiments.by Brandon Luders.S.M

Output Feedback Stochastic MPC with Hard Input Constraints

We present an output feedback stochastic model predictive controller (SMPC) for constrained linear time-invariant systems. The system is perturbed by additive Gaussian disturbances on state and additive Gaussian measurement noise on output. A Kalman filter is used for state estimation and an SMPC is designed to satisfy chance constraints on states and hard constraints on actuator inputs. The proposed SMPC constructs bounded sets for the state evolution and a tube-based constraint tightening strategy where the tightened constraints are time-invariant. We prove that the proposed SMPC can guarantee an infeasibility rate below a user-specified tolerance. We numerically compare our method with a classical output feedback SMPC with simulation results which highlight the efficacy of the proposed algorithm.Comment: IEEE American Control Conference (ACC) 2023, May 31 - June 2, San Diego, CA, US

Stability Constraints for Robust Model Predictive Control

This paper proposes an approach for the robust stabilization of systems controlled by MPC strategies. Uncertain SISO linear systems with box-bounded parametric uncertainties are considered. The proposed approach delivers some constraints on the control inputs which impose sufficient conditions for the convergence of the system output. These stability constraints can be included in the set of constraints dealt with by existing MPC design strategies, in this way leading to the “robustification” of the MPC

Robust Model Predictive Control for Linear Parameter Varying Systems along with Exploration of its Application in Medical Mobile Robots

This thesis seeks to develop a robust model predictive controller (MPC) for Linear Parameter Varying (LPV) systems. LPV models based on input-output display are employed. We aim to improve robust MPC methods for LPV systems with an input-output display. This improvement will be examined from two perspectives. First, the system must be stable in conditions of uncertainty (in signal scheduling or due to disturbance) and perform well in both tracking and regulation problems. Secondly, the proposed method should be practical, i.e., it should have a reasonable computational load and not be conservative. Firstly, an interpolation approach is utilized to minimize the conservativeness of the MPC. The controller is calculated as a linear combination of a set of offline predefined control laws. The coefficients of these offline controllers are derived from a real-time optimization problem. The control gains are determined to ensure stability and increase the terminal set. Secondly, in order to test the system's robustness to external disturbances, a free control move was added to the control law. Also, a Recurrent Neural Network (RNN) algorithm is applied for online optimization, showing that this optimization method has better speed and accuracy than traditional algorithms. The proposed controller was compared with two methods (robust MPC and MPC with LPV model based on input-output) in reference tracking and disturbance rejection scenarios. It was shown that the proposed method works well in both parts. However, two other methods could not deal with the disturbance. Thirdly, a support vector machine was introduced to identify the input-output LPV model to estimate the output. The estimated model was compared with the actual nonlinear system outputs, and the identification was shown to be effective. As a consequence, the controller can accurately follow the reference. Finally, an interpolation-based MPC with free control moves is implemented for a wheeled mobile robot in a hospital setting, where an RNN solves the online optimization problem. The controller was compared with a robust MPC and MPC-LPV in reference tracking, disturbance rejection, online computational load, and region of attraction. The results indicate that our proposed method surpasses and can navigate quickly and reliably while avoiding obstacles