Robust Variable-Horizon MPC with Adaptive Terminal Constraints

European Journal of Control, 2001

A predictive control method is presented for stabilization of discrete-time linear systems with time-dependent parametric perturbations, which yields heuristic fast convergence to origin with respect to a given polyhedral norm. The stability of closed-loop system is proved via the Lyapunov's function method inside a positively invariant set containing origin.

IFAC-PapersOnLine, 2018

The design of optimal or sub-optimal guidance laws for aerospace vehicles remains a challenging task because of its computation difficulties. Recently in literature computationally efficient technique named as MPSC (model predictive spread control) has been proposed to overcome this problem. It combine nonlinear optimal control theory and approximate dynamic programming philosophies and hence embed effective trajectory optimization concepts into guidance law. Here objective is to show the application of MPSC to the generation of guidance law for astronautical as well as atmospheric aerospace vehicles. Here, four different cases were taken, a successful landing of an aircraft, an optimal re-entry guidance path of a spacecraft, an interception of ground target by air launched missile and interception against incoming air target. Performance of the proposed MPSC guidance is demonstrated using a 3DOF simulation which clearly shows the effectiveness of the MPSC guidance law for various application model.  Recently in literature, a nonlinear model predictive static programming (MPSP) technique (Padhi (2009)) which is a combination of nonlinear optimal control theory (Yang (2005)-Cannon (2004)) and dynamic programming (Werbos (1992)) has been proposed. The philosophy is quite similar to optimal control theory based approach. The advantage of this approach is that the control action is guaranteed to be smooth

Mathematics and Computers in Simulation, 2009

The main objective of this work consists of obtaining a new robust and stable Model Predictive Control (MPC). One widely used technique for improving robustness in MPC consists of the Min-Max optimization, where an analogy can be established with the Bounded Data Uncertainties (BDU) method. The BDU is a regularization technique for least-squares problems by taking into account the uncertainty bounds. So BDU both improves robustness in MPC and offers a guided way of tuning the empirically tuned penalization parameter for the control effort in MPC due to the duality that the parameter coincides with the regularization one in BDU. On the other hand, the stability objective is achieved by the use of terminal constraints, in particular the Constrained Receding-Horizon Predictive Control (CRHPC) algorithm, so the original CRHPC-BDU controller is stated, which presents a better performance from the point of view of robustness and stability than a standard MPC.

AIAA Guidance, Navigation, and Control Conference and Exhibit, 2005

This paper presents a receding horizon controller (RHC) that can be used to design trajectories for an aerial vehicle operating in an environment with disturbances. Various constraints are imposed in the problem, such as turning rate limits and bounds on the vehicle speed, and target regions and no-fly zones are included in the environment. The proposed algorithm modifies these constraints to ensure that the on-line RHC optimization remains feasible even when the vehicle is acted upon by unknown, but bounded, disturbances. The approach uses a robust control invariant admissible set as a terminal set that does not need to be a target set of the overall guidance problem. This result extends previous work in two ways: the vehicle is guaranteed to remain safe under the influence of disturbances; and much longer robust trajectories can be constructed on-line. The full algorithm is demonstrated in several numerical simulations.

2014 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, 2014

This work presents a robust trajectory planning method for constrained linear time-invariant systems with uncertain parameters. The proposed trajectory planning method is inspired by receding horizon based control-for example model predictive control (MPC)-which enables the use of advantageous features of MPC, like the flexible choice of the cost functional and the handling of constraints, for trajectory planning purposes. The presented method, namely robust receding horizon based trajectory planning (robust RH-TP) improves the robust performance of the control system which means that the control performance should be as independent as possible from uncertain system parameters. Measurement results for a highly dynamical permanent magnet DC motor show that robust RH-TP is able to improve robust performance compared to (non-robust) RH-TP.

2009

This paper presents the design and implementation of a model predictive control (MPC) system to guide and control a chasing spacecraft during rendezvous with a passive target spacecraft in an elliptical or circular orbit, from the point of target detection all the way to capture. To achieve an efficient system design, the rendezvous manoeuvre has been partitioned into three main phases based on the range of operation, plus a collision-avoidance manoeuvre to be used in event of a fault. Each has its own associated MPC controller. Linear time-varying models are used to enable trajectory predictions in elliptical orbits, whilst a variable prediction horizon is used to achieve finite-time completion of manoeuvres, and a 1-norm cost on velocity change minimises propellant consumption. Constraints are imposed to ensure that trajectories do not collide with the target. A key feature of the design is the implementation of non-convex constraints as switched convex constraints, enabling the use of convex linear and quadratic programming. The system is implemented using commercial-off-the-shelf tools with deployment using automatic code generation in mind, and validated by closed-loop simulation. A significant reduction in total propellant consumption in comparison with a baseline benchmark solution is observed.

Automatica, 1998

We present in this paper a novel nonlinear model predictive control scheme that guarantees asymptotic c1osedloop stability. The scheme can be applied to both stable and unstable systems with input constraints. The objective functional to be minimized consists of an integral square error (ISE) part over a finite time horizon plus a quadratic terminal cost. The terminal state penalty matrix of the terminal cost term has to be chosen as the solution of an appropriate Lyapunov equation. Furthermore, the setup includes a terminal inequality constraint that forces the states at the end of the finite prediction horizon to lie within a prescribed terminal region. If the Jacobian linearization of the nonlinear system to be controlled is stabilizable, we prove that feasibility of the open-loop optimal control problem at time t = 0 implies asymptotic stability of the closed-loop system. The size of the region of attraction is only restricted by the requirement for feasibility of the optimization problem due to the input and terminal inequality constraints and is thus maximal in some sense. ~)

This work presents a model predictive controller (MPC) that is able to handle linear time-varying (LTV) plants with PWM control. The MPC is based on a planner that employs a PAM or impulsive approximation as a hot-start and then uses explicit linearization around successive PWM solutions for rapidly improving the solution by means of linear programming. As an example, the problem of rendezvous of spacecraft for eccentric target orbits is considered. The problem is modeled by the LTV Tschauner-Hempel equations, whose transition matrix is explicit; this is exploited by the algorithm for rapid convergence. The efficacy of the method is shown in a simulation study.

World Congress, 2011

We consider inherent robustness properties of model predictive control (MPC) for continuous-time nonlinear systems with input constraints and terminal constraints. We show that when the linear quadratic control law is chosen as the terminal control law, and the related Lyapunov matrix is chosen as the terminal penalty matrix, MPC with nominal prediction model and bounded disturbances has some degree of inherent robustness. We emphasize that the input constraint sets can be any compact set rather than convex sets, and our results do not rely on the continuity of the optimal cost functional or control law in the interior of the feasible region.

IFAC-PapersOnLine, 2019

We propose a non-linear model predictive scheme for planning fuel efficient maneuvers of small spacecrafts that shall rendezvous space debris. The paper addresses the specific issues of potential limited on-board computational capabilities and low-thrust actuators in the chasing spacecraft, and solves them by using a novel MatLab-based toolbox for real-time non-linear model predictive control (MPC) called MATMPC. This tool computes the MPC rendezvous maneuvering solution in a numerically efficient way, and this allows to greatly extend the prediction horizon length. This implies that the overall MPC scheme can compute solutions that account for the long timescales that usually characterize the low-thrust rendezvous maneuvers. The so-developed controller is then tested in a realistic scenario that includes all the near-Earth environmental disturbances. We thus show, through numerical simulations, that this MPC method can successfully be used to perform a fuel-efficient rendezvous maneuver with an uncontrolled object, plus evaluate performance indexes such as mission duration, fuel consumption, and robustness against sensor and process noises.