Iterative Model Predictive Control Research Articles

Robust learning‐based iterative model predictive control for unknown non‐linear systems

AbstractThis study presents a learning‐based iterative model predictive control (MPC) scheme for unknown (Lipschitz continuous) nonlinear dynamical systems. The proposed method begins by learning the unknown part of the controlled system using a Gaussian process (GP), which helps derive multi‐step reachable sets that are guaranteed to encompass the actual system states. At each time step in each iteration, the MPC controller calculates a sequence of control inputs that robustly satisfy state and control constraints, as well as terminal constraints based on the GP‐based reachable sets. Then only the first control input is applied to the system. After the iteration, the initial state is reset, and the same procedure is executed with the MPC optimization problem defined by the updated terminal set and cost. As iteration goes on, improvement of the control performance is expected since more data is obtained and the environment is progressively explored. The proposed method provides properties such as recursive feasibility and input to state stability of the goal region under certain assumptions. Moreover, bound on the performance cost in each iteration associated with the implementation of the proposed MPC scheme is also analyzed. The results of the simulation study show that the proposed control scheme can iteratively improve the control performance.

Autonomous High-Speed Overtaking of Intelligent Chassis Using Fast Iterative Model Predictive Control

High-speed overtaking is one of the structured driving scenarios of autonomous vehicles (AVs), and safety and real-time control requirements must be fulfilled during this scenario. In this work, we develop an overtaking path-planning and tracking framework for AVs based on the improved artificial potential field (APF) and fast iterative model predictive control (MPC). The improved APF is used to plan a feasible, high-speed overtaking path by considering the constraints of vehicle dynamics and introducing the adjustment factor into the potential function to avoid local optimization and target unreachability problems. In addition, to reduce the computational burden and fulfill the real-time control requirements of trajectory tracking, a fast iterative MPC algorithm is proposed herein. This algorithm adds disturbances that possess the nonlinear characteristics of the real model by using a linearized model. In terms of vehicle configuration, we consider that the target vehicle has the four-wheel steer (4WS)-four-wheel drive (4WD) chassis configuration and the fast iterative MPC is also used to coordinate the conflict between 4WS and direct yaw moment control (DYC) to improve tracking accuracy and vehicle stability during overtaking. Simulink/Carsim co-simulation and hardware-in-the-loop (HIL) tests are conducted to verify the effectiveness of the proposed controller.

Iterative Model Predictive Control for Automatic Carrier Landing of Carrier-Based Aircrafts Under Complex Surroundings and Constraints

Iterative Model Predictive Control for Automatic Carrier Landing of Carrier-Based Aircrafts Under Complex Surroundings and Constraints

Torque Vectoring Control of Distributed Drive Electric Vehicles Using Fast Iterative Model Predictive Control

Torque Vectoring Control of Distributed Drive Electric Vehicles Using Fast Iterative Model Predictive Control

Robocentric Model-Based Visual Servoing for Quadrotor Flights

This article proposes a robocentric formulation for quadrotor visual servoing. This formulation presents the task-specific state dynamics of the quadrotor in its body reference frame. Compared with other visual servoing methods, our method allows tightly and integrated state estimation and control on the same robocentric model, and allows a faster system response in aggressive quadrotor flights. On the theory level, we prove the controllability and observability of the proposed robocentric model. Then, we design an on-manifold Kalman filter for the estimation and an on-manifold iterative model predictive control for motion planning and control. We verify our proposed formulation and controller in two crucial quadrotor flight tasks: 1) hovering; and 2) dynamic obstacle avoidance. Experiment results show that the quadrotor is able to resist large external disturbances and recover its position and orientation from two reference visual features. Moreover, the quadrotor is able to avoid dynamic obstacles reliably at a relative speed up to 7.4 m/s, demonstrating the effectiveness of our visual servoing methods in agile quadrotor flights.

Iterative Model Predictive Control for Piecewise Systems

In this letter, we present an iterative Model Predictive Control (MPC) design for piecewise nonlinear systems. We consider finite time control tasks where the goal of the controller is to steer the system from a starting configuration to a goal state while minimizing a cost function. First, we present an algorithm that leverages a feasible trajectory that completes the task to construct a control policy which guarantees that state and input constraints are recursively satisfied and that the closed-loop system reaches the goal state in finite time. Utilizing this construction, we present a policy iteration scheme that iteratively generates safe trajectories which have non-decreasing performance. Finally, we test the proposed strategy on a discretized Spring Loaded Inverted Pendulum (SLIP) model with massless legs. We show that our methodology is robust to changes in initial conditions and disturbances acting on the system. Furthermore, we demonstrate the effectiveness of our policy iteration algorithm in a minimum time control task.

An iterative model predictive control algorithm for constrained nonlinear systems

AbstractAn iterative model predictive control (MPC) scheme for constrained nonlinear systems is presented. The idea of the method is to detour from the solution of a non‐convex optimization problem using a time‐variant linearization of the nonlinear system model that is adjusted iteratively by solving an iterative quadratic programming optimization problem at each sampling time. The main advantage is the faster resolution of the optimization problem by using quadratic programming instead of non‐convex programming and yet, properly describing the nonlinear dynamics of the process being controlled. In this article, a general framework of the method is presented together with a discussion on the conditions under which the iterations converge and on the uncertainty of its results due to the linearization used, as well as some practical considerations about its implementation. The performance of the proposed controller is illustrated via two examples.

An iterative model predictive control algorithm for UAV guidance

A novel aircraft path–following guidance algorithm based on model predictive control is proposed in this paper. The algorithm tracks a precomputed trajectory and produces reference commands for a low-level attitude controller. To solve the associated nonlinear optimization problem, an iterative scheme is proposed, using as a feasible hotstart the guidance solution provided by a well-behaved L1 navigation law. Simulations show the effectiveness of the algorithm, even in the presence of disturbances such as wind.

Robust model predictive control by iterative optimisation for polytopic uncertain systems

This article addresses robust model predictive control (MPC) for constrained systems with polytopic uncertainty description. Firstly, in the technique which parametrises the infinite horizon control moves into a single state feedback law and invokes the parameter-dependent Lyapunov method for achieving closed-loop stability, the slack matrices are iteratively solved at each sampling time. Secondly, in the technique which parametrises the infinite horizon control moves into a set of free perturbations followed by a single state feedback law, the feedback gains within the switch horizon are iteratively found at each sampling time, rather than just inherited from the previous sampling time. Numerical examples show that iterative MPC can not only improve the control performance, but also enlarge the region of attraction.