We propose a purely data-driven model predictive control (MPC) scheme to control unknown linear time-invariant systems with guarantees on stability and constraint satisfaction in the presence of noisy data. The scheme predicts future trajectories based on data-dependent Hankel matrices, which span the full system behavior if the input is persistently exciting. This paper extends previous work on data-driven MPC by including a suitable constraint tightening which ensures that the closed-loop trajectory satisfies desired pointwise-in-time output constraints. Furthermore, we provide estimation procedures to compute system constants related to controllability and observability, which are required to implement the constraint tightening. The practicality of the proposed approach is illustrated via a numerical example.
We propose an Adaptive MPC framework for uncertain linear systems to achieve robust satisfaction of state and input constraints. The uncertainty in the system is assumed additive, state dependent, and globally Lipschitz with a known Lipschitz constant. We use a non-parametric technique for online identification of the system uncertainty by approximating its graph via envelopes defined by quadratic constraints. At any given time, by solving a set of convex optimization problems, the MPC controller guarantees robust constraint satisfaction for the closed loop system for all possible values of sy…
A novel perspective on the design of robust model predictive control (MPC) methods is presented, whereby closed-loop constraint satisfaction is ensured using recursive feasibility of the MPC optimization. Necessary and sufficient conditions are derived for recursive feasibility, based on the effects of model perturbations and disturbances occurring at one time step. Using these conditions and Farkas' lemma, sufficient conditions suitable for design are formulated. The proposed method is called a closed-loop design, as only the existence of feasible inputs at the next time step is enforced by d…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；University of Trento（特伦托大学）；New York University（纽约大学）
Linear Model Predictive Control (MPC) has been successfully used for generating feasible walking motions for humanoid robots. However, the effect of uncertainties on constraints satisfaction has only been studied using Robust MPC (RMPC) approaches, which account for the worst-case realization of bounded disturbances at each time instant. In this letter, we propose for the first time to use linear stochastic MPC (SMPC) to account for uncertainties in bipedal walking. We show that SMPC offers more flexibility to the user (or a high level decision maker) by tolerating small (user-defined) probabi…
This paper designs a model predictive control (MPC) law for constrained linear systems with stochastic additive disturbances and noisy measurements, minimising a discounted cost subject to a discounted expectation constraint. It is assumed that sensor data is lost with a known probability. Taking into account the data losses modelled by a Bernoulli process, we parameterise the predicted control policy as an affine function of future observations and obtain a convex linear-quadratic optimal control problem. Constraint satisfaction and a discounted cost bound are ensured without imposing bounds …
We present a framework to design nonlinear robust output feedback model predictive control (MPC) schemes that ensure constraint satisfaction under noisy output measurements and disturbances. We provide novel estimation methods to bound the magnitude of the estimation error based on: stability properties of the observer; detectability; set-membership estimation; moving horizon estimation (MHE). Robust constraint satisfaction is guaranteed by suitably incorporating these online validated bounds on the estimation error in a homothetic tube based MPC formulation. In addition, we show how the perfo…
A robust model predictive control (MPC) method is presented for linear, time-invariant systems affected by bounded additive disturbances. The main contribution is the offline design of a disturbance-affine feedback gain whereby the resulting constraint tightening is minimized. This is achieved by formulating the constraint tightening problem as a convex optimization problem with the feedback term as a variable. The resulting MPC controller has the computational complexity of nominal MPC, and guarantees recursive feasibility, stability and constraint satisfaction. The advantages of the proposed…
Adaptive model predictive control (MPC) methods using set-membership identification to reduce parameter uncertainty are considered in this work. Strong duality is used to reformulate the set-membership equations exactly within the MPC optimization. A predicted worst-case cost is then used to enable performance-oriented exploration. The proposed approach guarantees robust constraint satisfaction and recursive feasibility. It is shown that method can be implemented using homothetic tube and flexible tube parameterizations of state tubes, and a simulation study demonstrates performance improvemen…
Context-Triggered Robust MPC for Temporal Logic Specifications
Max Planck Institute for Software Systems (MPI-SWS)（马克斯·普朗克软件系统研究所）；Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究院）；University of Birmingham（伯明翰大学）
Approximate non-linear model predictive control with safety-augmented neural networks
Institute for Data Science in Mechanical Engineering, RWTH Aachen University（机械工程数据科学研究所，亚琛RWTH大学）；Institute for Dynamic Systems and Control, ETH Zürich（动态系统与控制研究所，苏黎世联邦理工学院）
Robust tube-based model predictive control (MPC) methods address constraint satisfaction by leveraging an a priori determined tube controller in the prediction to tighten the constraints. This paper presents a system level tube-MPC (SLTMPC) method derived from the system level parameterization (SLP), which allows optimization over the tube controller online when solving the MPC problem, which can significantly reduce conservativeness. We derive the SLTMPC method by establishing an equivalence relation between a class of robust MPC methods and the SLP. Finally, we show that the SLTMPC formulati…
Robust design of autonomous systems under uncertainty is an important yet challenging problem. This work proposes a robust controller that consists of a state estimator and a tube based predictive control law. The class of linear systems under ellipsoidal uncertainty is considered. In contrast to existing approaches based on polytopic sets, the constraint tightening is directly computed from the ellipsoidal sets of disturbances without over-approximation, thus leading to less conservative bounds. Conditions to guarantee robust constraint satisfaction and robust stability are presented. Further…
Economic Model Predictive Control has recently gained popularity due to its ability to directly optimize a given performance criterion, while enforcing constraint satisfaction for nonlinear systems. Recent research has developed both numerical algorithms and stability analysis for the undiscounted case. The introduction of a discount factor in the cost, however, can be desirable in some cases of interest, e.g., economics, stochastically terminating processes, Markov decision processes, etc. Unfortunately, the stability theory in this case is still not fully developed. In this paper we propose …
Learning-based model predictive control (MPC) is an approach designed to reduce the computational cost of MPC. In this paper, a constrained deep neural network (DNN) design is proposed to learn MPC policy for nonlinear systems. Using constrained training of neural networks, MPC constraints are enforced effectively. Furthermore, recursive feasibility and robust stability conditions are derived for the learning-based MPC approach. Additionally, probabilistic feasibility and optimality empirical guarantees are provided for the learned control policy. The proposed algorithm is implemented on the F…
Many popular approaches in the field of robust model predictive control (MPC) are based on nominal predictions. This paper presents a novel formulation of this class of controller with proven input-to-state stability and robust constraint satisfaction. Its advantages are: (i) the design of its main ingredients are tractable for medium to large-sized systems, (ii) the terminal set does not need to be robust with respect to all the possible system uncertainties, but only for a reduced set that can be made arbitrarily small, thus facilitating its design and implementation, (iii) under certain con…
In this paper, the highly acknowledged advantages of the Model Predictive Control (MPC) approach are utilized to regulate the wind turbines' output power in the partial load region. In this region, the purpose of the designed controller is to capture maximum power from the wind. When the wind speed is above rated wind speed (full load region), control strategy is to keep output power and generator speed at their rated value. Because of the wind turbine's nonlinearities and constraints of the variables this is a challenging problem and two MPC-based methods are proposed, i.e. online and offline…
A dual adaptive model predictive control (MPC) algorithm is presented for linear, time-invariant systems subject to bounded disturbances and parametric uncertainty in the state-space matrices. Online set-membership identification is performed to reduce the uncertainty and thus control affects both the informativity of identification and the system's performance. The main contribution of the paper is to include this dual effect in the MPC optimization problem using a predicted worst-case cost in the objective function. This allows the controller to perform active exploration, that is, the contr…
Distributed model predictive control methods for uncertain systems often suffer from considerable conservatism and can tolerate only small uncertainties due to the use of robust formulations that are amenable to distributed design and optimization methods. In this work, we propose a distributed stochastic model predictive control (DSMPC) scheme for dynamically coupled linear discrete-time systems subject to unbounded additive disturbances that are potentially correlated in time. An indirect feedback formulation ensures recursive feasibility of the DSMPC problem, and a data-driven, distributed …
We propose a novel approach to design a robust Model Predictive Controller (MPC) for constrained uncertain linear systems. The uncertain system is modeled as linear parameter varying with additive disturbance. Set bounds for the system matrices and the additive uncertainty are assumed to be known. We formulate a novel optimization-based constraint tightening strategy around a predicted nominal trajectory which utilizes these bounds. With an appropriately designed terminal cost function and constraint set, we prove robust satisfaction of the imposed constraints by the resulting MPC in closed-lo…
This paper presents a robust hierarchical MPC (H-MPC) for dynamic systems with slow states subject to demand forecast uncertainty. The H-MPC has two layers: (i) the scheduling MPC at the upper layer with a relatively long prediction/planning horizon and slow update rate, and (ii) the piloting MPC at the lower layer over a shorter prediction horizon with a faster update rate. The scheduling layer MPC calculates the optimal slow states, which will be tracked by the piloting MPC, while enforcing the system constraints according to a long-range and approximate prediction of the future demand/load,…
A hierarchical Model Predictive Control (MPC) formulation is presented for coupled discrete-time linear systems with state and input constraints. Compared to a centralized approach, a two-level hierarchical controller, with one controller in the upper-level and one controller per subsystem in the lower-level, can significantly reduce the computational cost associated with MPC. Hierarchical coordination is achieved using adjustable tubes, which are optimized by the upper-level controller and bound permissible lower-level controller deviations from the system trajectories determined by the upper…
A data-driven MPC scheme is proposed to safely control constrained stochastic linear systems using distributionally robust optimization. Distributionally robust constraints based on the Wasserstein metric are imposed to bound the state constraint violations in the presence of process disturbance. A feedback control law is solved to guarantee that the predicted states comply with constraints. The stochastic constraints are satisfied with regard to the worst-case distribution within the Wasserstein ball centered at their discrete empirical probability distribution. The resulting distributionally…
A robust adaptive model predictive control (MPC) algorithm is presented for linear, time invariant systems with unknown dynamics and subject to bounded measurement noise. The system is characterized by an impulse response model, which is assumed to lie within a bounded set called the feasible system set. Online set-membership identification is used to reduce uncertainty in the impulse response. In the MPC scheme, robust constraints are enforced to ensure constraint satisfaction for all the models in the feasible set. The performance objective is formulated as a worst-case cost with respect to …
In this work, we propose a tube-based MPC scheme for state- and input-constrained linear systems subject to dynamic uncertainties characterized by dynamic integral quadratic constraints (IQCs). In particular, we extend the framework of $ρ$-hard IQCs for exponential stability analysis to external inputs. This result yields that the error between the true uncertain system and the nominal prediction model is bounded by an exponentially stable scalar system. In the proposed tube-based MPC scheme, the state of this error bounding system is predicted along with the nominal model and used as a scalin…
We propose a simple and computationally efficient approach for designing a robust Model Predictive Controller (MPC) for constrained uncertain linear systems. The uncertainty is modeled as an additive disturbance and an additive error on the system dynamics matrices. Set based bounds for each component of the model uncertainty are assumed to be known. We separate the constraint tightening strategy into two parts, depending on the length of the MPC horizon. For a horizon length of one, the robust MPC problem is solved exactly, whereas for other horizon lengths, the model uncertainty is over-appr…
Networked Control Systems typically come with a limited communication bandwidth and thus require special care when designing the underlying control and triggering law. A method that allows to consider hard constraints on the communication traffic as well as on states and inputs is self-triggered model predictive control (MPC). In this scheme, the optimal length of the sampling interval is determined proactively using predictions of the system behavior. However, previous formulations of self-triggered MPC have neglected the widespread phenomenon of packet loss, such that these approaches might …
