The trade-off between optimality and complexity has been one of the most important challenges in the field of robust Model Predictive Control (MPC). To address the challenge, we propose a flexible robust MPC scheme by synergizing the multi-stage and tube-based MPC approaches. The key idea is to exploit the non-conservatism of the multi-stage MPC and the simplicity of the tube-based MPC. The proposed scheme provides two options for the user to determine the trade-off depending on the application: the choice of the robust horizon and the classification of the uncertainties. Beyond the robust horizon, the branching of the scenario-tree employed in multi-stage MPC is avoided with the help of tubes. The growth of the problem size with respect to the number of uncertainties is reduced by handling \emph{small} uncertainties via an invariant tube that can be computed offline. This results in linear growth of the problem size beyond the robust horizon and no growth of the problem size concerning small magnitude uncertainties. The proposed approach helps to achieve a desired trade-off between optimality and complexity compared to existing robust MPC approaches. We show that the proposed approach is robustly asymptotically stable. Its advantages are demonstrated for a CSTR example.
Modeling error or external disturbances can severely degrade the performance of Model Predictive Control (MPC) in real-world scenarios. Robust MPC (RMPC) addresses this limitation by optimizing over feedback policies but at the expense of increased computational complexity. Tube MPC is an approximate solution strategy in which a robust controller, designed offline, keeps the system in an invariant tube around a desired nominal trajectory, generated online. Naturally, this decomposition is suboptimal, especially for systems with changing objectives or operating conditions. In addition, many tub…
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…
Tube-based model predictive control (MPC) methods leverage tubes to bound deviations from a nominal trajectory due to uncertainties in order to ensure constraint satisfaction. This paper presents a novel tube-based MPC formulation based on system level disturbance reachable sets (SL-DRS), which leverage the affine system level parameterization (SLP). We show that imposing a finite impulse response (FIR) constraint on the affine SLP guarantees containment of all future deviations in a finite sequence of SL-DRS. This allows us to formulate a system level tube-MPC (SLTMPC) method using the SL-DRS…
This paper proposes a control architecture for autonomous lane keeping by a vehicle. In this paper, the vehicle dynamics consist of two parts: lateral and longitudinal dynamics. Therefore, the control architecture comprises two subsequent controllers. A longitudinal model predictive control (MPC) makes the vehicle track the desired longitudinal speeds that are assumed to be generated by a speed planner. The longitudinal speeds are then passed to a lateral MPC for lane keeping. Due to the dependence of the lateral dynamics on the longitudinal speed, they are represented in a linear parameter-va…
Model predictive control (MPC) is an effective method for control of constrained systems but is susceptible to the external disturbances and modeling error often encountered in real-world applications. To address these issues, techniques such as Tube MPC (TMPC) utilize an ancillary offline-generated robust controller to ensure that the system remains within an invariant set, referred to as a tube, around an online-generated trajectory. However, TMPC is unable to modify its tube and ancillary controller in response to changing state-dependent uncertainty, often resulting in overly-conservative …
The control of constrained systems using model predictive control (MPC) becomes more challenging when full state information is not available and when the nominal system model and measurements are corrupted by noise. Since these conditions are often seen in practical scenarios, techniques such as robust output feedback MPC have been developed to address them. However, existing approaches to robust output feedback MPC are challenged by increased complexity of the online optimization problem, increased computational requirements for controller synthesis, or both. In this work we present a simple…
Rollout control is an MPC-based control method, in which a controller is periodically activated to schedule the transmission of sensor or actuator data. Therein, a preassigned traffic specification acts as a constraint on the scheduled transmissions, ensuring that they are triggered at an admissible rate for the underlying communication network. In this paper, we extend the theory of rollout control by considering bounded disturbances on the controlled plant in the presence of state and input constraints. We use methods from tube MPC, where the error between the nominal (undisturbed) system, u…
In this paper, we present an effective online tube-based model predictive control (T-MPC) solution for autonomous driving that aims at improving the computational load while ensuring robust stability and performance in fast and disturbed scenarios. We focus on reformulating the non-linear original problem into a pseudo-linear problem by transforming the non-linear vehicle equations to be expressed in a Linear Parameter Varying (LPV) form. An scheme composed by a nominal controller and a corrective local controller is propossed. First, the local controller is designed as a polytopic LPV-H$_{\in…
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…
In this paper, we provide non-averaged and transient performance guarantees for recently developed, tube-based robust economic model predictive control (MPC) schemes. In particular, we consider both tube-based MPC schemes with and without terminal conditions. We show that the closed-loop performance obtained by applying such MPC schemes is approximately optimal when evaluated both on finite and infinite time horizons. These performance bounds are similar to those derived previously for nominal economic MPC. The theoretical results are discussed in a numerical example.
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…
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…
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…
Tsinghua University（清华大学）；Beijing National Research Center for Information Science and Technology (BNRist)（北京信息科学与技术国家研究中心）
Model Predictive Control (MPC) has shown the great performance of target optimization and constraint satisfaction. However, the heavy computation of the Optimal Control Problem (OCP) at each triggering instant brings the serious delay from state sampling to the control signals, which limits the applications of MPC in resource-limited robot manipulator systems over complicated tasks. In this paper, we propose a novel robust tube-based smooth-MPC strategy for nonlinear robot manipulator planning systems with disturbances and constraints. Based on piecewise linearization and state prediction, our…
Battery energy storage systems (ESS) are widely used in microgrids to complement high renewables. However, the real-time energy management of microgrids with battery ESS is challenging in two aspects: 1) the evolution process of battery energy level is across-time coupled; 2) uncertainties unavoidably arise in the forecasting process for renewable generation. In this paper, a tube-based model predictive control (MPC) approach is innovatively proposed in accommodating the real-time energy management of microgrids with battery ESS. Firstly, a real-time operation model of battery, including the d…
This paper presents a heterogeneously parameterized tube-based model predictive control (MPC) design applicable to linear parameter-varying (LPV) systems. In a heterogeneous tube, the parameterizations of the tube cross sections and the associated control laws are allowed to vary along the prediction horizon. Two extreme cases that can be described in this framework are scenario MPC (high complexity, larger domain of attraction) and homothetic tube MPC with a simple time-invariant control parameterization (low complexity, smaller domain of attraction). In the proposed framework, these extreme …
The design of cooperative adaptive cruise control is critical in mixed traffic flow, where connected and automated vehicles (CAVs) and human-driven vehicles (HDVs) coexist. Compared with pure CAVs, the major challenge is how to handle the prediction uncertainty of HDVs, which can cause significant state deviation of CAVs from planned trajectories. In most existing studies, model predictive control (MPC) is utilized to replan CAVs' trajectories to mitigate the deviation at each time step. However, as the replan process is usually conducted by solving an optimization problem with information thr…
Georgia Institute of Technology（佐治亚理工学院）；NASA Jet Propulsion Laboratory, California Institute of Technology（美国国家航空航天局喷气推进实验室，加州理工学院）
Learning-based control aims to construct models of a system to use for planning or trajectory optimization, e.g. in model-based reinforcement learning. In order to obtain guarantees of safety in this context, uncertainty must be accurately quantified. This uncertainty may come from errors in learning (due to a lack of data, for example), or may be inherent to the system. Propagating uncertainty forward in learned dynamics models is a difficult problem. In this work we use deep learning to obtain expressive and flexible models of how distributions of trajectories behave, which we then use for n…
Koopman operators are of infinite dimension and capture the characteristics of nonlinear dynamics in a lifted global linear manner. The finite data-driven approximation of Koopman operators results in a class of linear predictors, useful for formulating linear model predictive control (MPC) of nonlinear dynamical systems with reduced computational complexity. However, the robustness of the closed-loop Koopman MPC under modeling approximation errors and possible exogenous disturbances is still a crucial issue to be resolved. Aiming at the above problem, this paper presents a robust tube-based M…
This paper presents two stochastic model predictive control methods for linear time-invariant systems subject to unbounded additive uncertainties. The new methods are developed by formulating the chance constraints into deterministic form, which are treated in analogy with robust constraints, by using the probabilistic reachable set. Firstly, the probabilistically resolvable time-varying tube-based stochastic model predictive control algorithm is designed by employing the time-varying probabilistic reachable sets as the tubes. Secondly, by utilizing the probabilistic positively invariant set, …
This work proposes a novel robust model predictive control (MPC) algorithm for linear systems affected by dynamic model uncertainty and exogenous disturbances. The uncertainty is modeled using a linear fractional perturbation structure with a time-varying perturbation matrix, enabling the algorithm to be applied to a large model class. The MPC controller constructs a state tube as a sequence of parameterized ellipsoidal sets to bound the state trajectories of the system. The proposed approach results in a semidefinite program to be solved online, whose size scales linearly with the order of th…
A powerful result from behavioral systems theory known as the fundamental lemma allows for predictive control akin to Model Predictive Control (MPC) for linear time invariant (LTI) systems with unknown dynamics purely from data. While most of data-driven predictive control literature focuses on robustness with respect to measurement noise, only few works consider exploiting probabilistic information of disturbances for performance-oriented control as in stochastic MPC. In this work, we propose a novel data-driven stochastic predictive control scheme for chance-constrained LTI systems subject t…
Model predictive control (MPC) for uncertain systems in the presence of hard constraints on state and input is a non-trivial problem, and the challenge is increased manyfold in the absence of state measurements. In this paper, we propose an adaptive output feedback MPC technique, based on a novel combination of an adaptive observer and robust MPC, for single-input single-output discrete-time linear time-invariant systems. At each time instant, the adaptive observer provides estimates of the states and the system parameters that are then leveraged in the MPC optimization routine while robustly …
We present Self-Tuning Tube-based Model Predictive Control (STT-MPC), an adaptive robust control algorithm for uncertain linear systems with additive disturbances based on the least-squares estimator and polytopic tubes. Our algorithm leverages concentration results to bound the system uncertainty set with prescribed confidence, and guarantees robust constraint satisfaction for this set, along with recursive feasibility and input-to-state stability. Persistence of excitation is ensured without compromising the algorithm's asymptotic performance or increasing its computational complexity. We de…
We present a novel tube-based data-driven predictive control method for linear systems affected by a bounded addictive disturbance. Our method leverages recent results in the reachability analysis of unknown linear systems to formulate and solve a robust tube-based predictive control problem. More precisely, our approach consists in deriving, from the collected data, a zonotope that includes the true state error set. We show how to guarantee the stability of the resulting error zonotope, which can be exploited to increase the computational efficiency of existing zonotopic data-driven MPC formu…
