Constraint Tightening Approach Research Articles

Robust constrained nonlinear Model Predictive Control with Gated Recurrent Unit model

In this paper we propose a robust Model Predictive Control where a Gated Recurrent Unit network model is used to learn the input–output dynamics of the system under control. Robust satisfaction of input and output constraints and recursive feasibility in presence of model uncertainties are achieved using a constraint tightening approach. Moreover, new terminal cost and terminal set are introduced in the Model Predictive Control formulation to guarantee Input-to-State Stability of the closed loop system with respect to the uncertainty term.

Compound Event-Triggered Distributed MPC for Coupled Nonlinear Systems.

This article investigates the event-triggered distributed model predictive control (DMPC) for perturbed coupled nonlinear systems subject to state and control input constraints. A novel compound event-triggered DMPC strategy, including a compound triggering condition and a new constraint tightening approach, is developed. In this event-triggered strategy, two stability-related conditions are checked in a parallel manner, which relaxes the requirement of the decrease of the Lyapunov function. An open-loop prediction scheme to avoid periodic transmission is designed for the states in the terminal set. As a result, the number of triggering and transmission instants can be reduced significantly. Furthermore, the proposed constraint tightening approach solves the problem of the state constraint satisfaction, which is quite challenging due to the external disturbances and the mutual influences caused by dynamical coupling. Simulations are conducted at last to validate the effectiveness of the proposed algorithm.

Robust multiplexed piecewise affine MPC-based decentralized control of multi-satellite formations using aerodynamic forces

Aerodynamic forces are well suited to be exploited for Low Earth Orbit satellite formation control. However, some critical gaps still exist in control schemes suitable for multi-satellite formation applications, especially when facing atmospheric environmental uncertainties. This paper proposes a scalable and flexible decentralized control scheme for the multi-satellite formation using only aerodynamic forces. This scheme adopts a strategy of updating the control inputs alternatively and is applicable to various formation configurations with different architectures without increasing the computational complexity and communication pressure of each satellite. Aerodynamic forces are changed by reorienting the satellite, and the linear formation control model with pointing angles as inputs is obtained by the PWA (piecewise affine) approximation method. A decentralized control scheme is proposed in which each satellite only has to communicate with its neighboring satellites and update its own inputs. This control scheme allows various generalizations of formation architectures, such as one that includes local chief satellites. To deal with model uncertainties, an improved MPC algorithm named Robust PWA-MMPC is developed using the constraint tightening approach, and then its feasibility and stability issues are analyzed. Hard-in-the-loop simulations are carried out for formation maintenance and reconfiguration, in which aerodynamic force uncertainties are considered.

A Tube-MPC Approach to Autonomous Multi-Vehicle Racing on High-Speed Ovals

Autonomous vehicle racing has emerged as vibrant, innovative technology development, demonstration platform in recent years. Universities, companies demonstrate their achievements on various vehicles - from 1:10th to full-scale prototypes. One of those platforms is the Dallara AV-21, and the spec-vehicle for the Indy Autonomous Challenge. This paper outlines the robust model predictive control (MPC) concept used within the software stack of the TUM Autonomous Motorsport team. It is based on a simplified friction-limited point mass model and a set of low-level feedback controllers. The remaining model uncertainties are managed via introducing a constraint-tightening approach based on a Tube-MPC approach. In contrast to classical tracking controllers, the optimization problem is formulated to freely optimize the trajectory while staying within certain maximum deviations of the reference. This approach allows to rely on a coarse output of the trajectory planning approach while maintaining smoothness requirements in steering, throttle, and brake actuation. The paper highlights the advantages of the proposed robust reoptimization concept compared to pure tracking formulations. It showcases the performance compared to a classical LQR controller and an MPC, which utilizes a vehicle model with a more sophisticated tire model. The controller achieved a top speed of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{265 kmh}^{-1}$</tex-math></inline-formula> and lateral accelerations up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\text{21 ms}}^{-2}$</tex-math></inline-formula> during a two-vehicle competition involving dynamic overtaking maneuvers on the Las Vegas Motor Speedway, a famous racetrack with turns banked up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$20^{\circ }$</tex-math></inline-formula> .

Robust distributed model predictive control of linear systems: Analysis and synthesis

To provide robustness of distributed model predictive control (DMPC), this work proposes a robust DMPC formulation for discrete-time linear systems subject to unknown-but-bounded disturbances. Taking advantage of the structure of certain classes of distributed systems seen in applications with inter-agent coupling, a novel robust DMPC is formulated. The proposed approach is characterised by separable terminal costs and locally robust terminal sets, with the latter sets adaptively estimated in the online optimisation problem. A constraint tightening approach based on a set-membership approach is used to guarantee constraint satisfaction for coupled subsystems in the presence of disturbances. Under this formulation, the closed-loop system is shown to be recursively feasible and input-to-state stable. To aid in the deployment of the proposed robust DMPC, a possible synthesis method and design conditions for practical implementation are presented. Finally, simulation results with a mass–spring–damper system are provided to demonstrate the proposed robust DMPC.

Learning-Based SMPC for Reference Tracking Under State-Dependent Uncertainty: An Application to Atmospheric Pressure Plasma Jets for Plasma Medicine

The increasing complexity of modern technical systems can exacerbate model uncertainty in model-based control, posing a great challenge to safe and effective system operation under closed loop. Online learning of model uncertainty can enhance control performance by reducing plant–model mismatch. This article presents a learning-based stochastic model predictive control (LB-SMPC) strategy for reference tracking of stochastic linear systems with additive state-dependent uncertainty. The LB-SMPC strategy adapts the state-dependent uncertainty model online to reduce plant–model mismatch for control performance optimization. Standard reachability and statistical tools are leveraged along with the state-dependent uncertainty model to develop a chance constraint-tightening approach, which ensures state constraint satisfaction in probability. The stability and recursive feasibility of the LB-SMPC strategy are established for tracking time-varying targets, without the need to redesign the controller every time the target is changed. The performance of the LB-SMPC strategy is experimentally demonstrated on an atmospheric pressure plasma jet (APPJ) testbed with prototypical applications in plasma medicine and materials processing. Real-time control comparisons with learning-based MPC with no uncertainty handling and offset-free MPC showcase the usefulness of LB-SMPC for predictive control of safety-critical systems with hard-to-model and/or time-varying dynamics.

Robust Approximation-Based Event-Triggered MPC for Constrained Sampled-Data Systems

In this paper, an approximation-based event-triggered model predictive control (AETMPC) strategy is proposed to implement event-triggered model predictive control for continuous-time constrained nonlinear systems under the digital platform. In the AETMPC strategy, both of the optimal control problem (OCP) and the triggering conditions are defined in a discrete-time manner based on approximate discrete-time models, while the plant under control is continuous time. In doing so, sensing load is alleviated because the triggering condition does not need to be checked continuously, and the computation of the OCP is simpler since which is calculated in the discrete-time framework. Meanwhile, robust constraints are satisfied in a continuous-time sense by taking inter-sampling behavior into consideration, and a novel constraint tightening approach is presented accordingly. Furthermore, the feasibility of the AETMPC strategy is analyzed and the associated stability of the overall system is established. Finally, this strategy is validated by a numerical example.

A Constraint-Tightening Approach to Nonlinear Stochastic Model Predictive Control under General Bounded Disturbances

This paper presents a nonlinear model predictive control strategy for stochastic systems with state- and input-dependent, finite-support disturbances subject to individual chance constraints. Our approach uses an online computed stochastic tube to ensure stability, constraint satisfaction, and recursive feasibility in the presence of stochastic uncertainties. The shape of the tube and the constraint backoff is based on an offline computed incremental Lyapunov function.

Robust model predictive control for satellite formation keeping with eccentricity/inclination vector separation

This study presents model predictive formation control based on an eccentricity/inclination vector separation strategy. Alternative collision avoidance can be accomplished by using eccentricity/inclination vectors and adding a simple goal function term for optimization process. Real-time control is also achievable with model predictive controller based on convex formulation. Constraint-tightening approach is address as well improve robustness of the controller, and simulation results are presented to verify performance enhancement for the proposed approach.

An adaptive constraint tightening approach to linear model predictive control based on approximation algorithms for optimization

SummaryIn this paper, we propose a model predictive control scheme for discrete‐time linear invariant systems based on inexact numerical optimization algorithms. We assume that the solution of the associated quadratic program produced by some numerical algorithm is possibly neither optimal nor feasible, but the algorithm is able to provide estimates on primal suboptimality and primal feasibility violation. By adaptively tightening the complicating constraints, we can ensure the primal feasibility of the approximate solutions generated by the algorithm. We derive a control strategy that has the following properties: the constraints on the states and inputs are satisfied, asymptotic stability of the closed‐loop system is guaranteed, and the number of iterations needed for a desired level of suboptimality can be determined. The proposed method is illustrated using a simulated longitudinal flight control problem. Copyright © 2014 John Wiley &amp; Sons, Ltd.

On Feasibility, Stability and Performance in Distributed Model Predictive Control

In distributed model predictive control (DMPC), where a centralized optimization problem is solved in distributed fashion using dual decomposition, it is important to keep the number of iterations in the solution algorithm small. In this technical note, we present a stopping condition to such distributed solution algorithms that is based on a novel adaptive constraint tightening approach. The stopping condition guarantees feasibility of the optimization problem and stability and a prespecified performance of the closed-loop system.

Model Predictive Control with on-off Input and its Application to Attitude Control

Robust model predictive control with On-Off input of system is researched in this paper. The constraint tightening approach is adopted to ensure robustness of algorithm. By variable horizon approach, i.e. take the predictive horizon as the decision variable, the property of finite-time arrival within an arbitrary target set is guaranteed. Convergence of the algorithm is proved, and the maximum predictive horizon for the states entry to an arbitrary target set is determined. Finally, the method is applied to the attitude control of exo-atmospheric aerocraft, the simulation results show the effectiveness of the proposed method.

Robust variable horizon model predictive control for vehicle maneuvering

This paper provides a new method of robust maneuver control with guaranteed finite-time arrival and satisfaction of constraints, despite the action of an unknown but bounded disturbance. The new method extends the constraint tightening approach to robust model predictive control of constrained linear systems by combining it with a variable horizon. This relaxes the requirement for the target to be an invariant set, which is assumed by many stabilizing MPC formulations but can be restrictive in vehicle maneuvering applications. The target sets for vehicle maneuvers are typically determined by the mission requirements and are not generally invariant sets. The new controller guarantees finite-time arrival within an arbitrary target set, i.e. not necessarily invariant, and is therefore applicable when the target is predetermined by other factors. Several simulation examples are presented including spacecraft rendezvous control with sensor visibility constraints and UAV guidance through obstacle fields. Copyright © 2006 John Wiley & Sons, Ltd.