Recursive Feasibility Research Articles

Bi-level model predictive control for metro networks: Integration of timetables, passenger flows, and train speed profiles

This paper deals with the train scheduling problem for metro networks taking into account time-dependent passenger origin–destination demands and train speed profiles. The aim is to adjust train schedules online according to time-dependent passenger demands so that passenger satisfaction and operational costs are jointly optimized. An extended passenger absorption model that explicitly includes time-dependent passenger origin–destination demands is developed, where the term “absorption” refers to passengers boarding trains. Then, the passenger absorption model is extended to a bi-level framework, where passenger demands and rolling stock availability are considered at the higher level, and detailed timetables and train speed profiles are included at the lower level. A bi-level model predictive control (MPC) approach is developed for the integrated problem. The optimization problems of both levels of the bi-level MPC approach can be converted into mixed-integer linear programming (MILP) problems, which enables us to solve them with existing MILP solvers. We then show that the recursive feasibility of both the higher-level and the lower-level optimization problems can be guaranteed. In this way, we can achieve real-time train scheduling for the metro system. Numerical experiments, based on real-life data from the Beijing metro network, illustrate the effectiveness of the extended passenger absorption model and the proposed bi-level MPC approach.

Rocket Landing Guidance Based on Linearization-Free Convexification

The landing problem of a reusable rocket is generally a highly constrained and nonconvex optimization problem. In this paper, we will convexify the problem without relying on any linearization. Specifically, we propose to quickly determine some of the state variables in advance so that the nonlinearity of the dynamics is greatly reduced, and then we accurately convexify the problem by change of variables and transformation of the optimization objective. This convexification process enables us to design an iterative algorithm that can converge very reliably, and the convergence does not rely on any trust region constraint. It should be highlighted that the algorithm is very efficient, generally taking just milliseconds to converge on a personal computer. Furthermore, by ensuring the recursive feasibility of calling the iterative algorithm in each guidance cycle, we can design a landing guidance algorithm that is able to achieve precise landing under various uncertainties and disturbances. Numerical examples are provided to demonstrate the high performance of the iterative algorithm and the landing guidance algorithm.

Scenario-based model predictive control with probabilistic human predictions for human–robot coexistence

This paper proposes a real-time motion planning scheme for safe human–robot workspace sharing relying on scenario-based nonlinear model predictive control (NMPC), a well-known approach for solving stochastic NMPC problems. A scenario tree is generated via higher-order Markov chains to provide probabilistic predictions of the human motion. Scenario-based NMPC is then used to generate point-to-point motions of the robot manipulator based on the above-mentioned human motion predictions, accounting for safety constraints via speed and separation monitoring (SSM). This means that the robot speed is always modulated to be able to stop before a possible collision with the human occurs. After proving theoretical properties on recursive feasibility and closed-loop stability of the proposed motion planning strategy, this is tested experimentally on a Kinova Gen3 robot interacting with a human operator, showing superior performance with respect to an NMPC scheme not relying on human predictions and to a fixed-path SSM strategy.

Safe Machine-Learning-Supported Model Predictive Force and Motion Control in Robotics

Many robotic tasks, such as human-robot interactions or the handling of fragile objects, require tight control and limitation of appearing forces and moments alongside sensible motion control to achieve safe yet high-performance operation. We propose a learning-supported model predictive force and motion control scheme that provides stochastic safety guarantees while adapting to changing situations. Gaussian processes (GPs) are used to learn the uncertain relations that map the robot’s states to the forces and moments. The model predictive controller uses these Gaussian process models to achieve precise motion and force control under stochastic constraint satisfaction. As the uncertainty only occurs in the static model parts — the output equations — a computationally efficient stochastic MPC formulation is used. analysis of recursive feasibility of the optimal control problem and convergence of the closed loop system for the static uncertainty case are given. Chance constraint formulation and back-offs are constructed based on the variance of the Gaussian process to guarantee safe operation. The approach is illustrated on a lightweight robot in simulations and experiments.

Robust Packetized MPC for Networked Systems Subject to Packet Dropouts and Input Saturation With Quantized Feedback.

This article develops a robust packetized predictive control framework to deal with the quantized-feedback control problem of networked systems subject to Markovian packet dropouts and input saturation. In the proposed framework, the Markov chain model of packet dropout is established from the link of the controller to the actuator. To deal with the quantized measurements, a robust packetized predictive control method is presented with a quantized-feedback law. The problem of unreliable transmission is addressed by proposing a packet dropout compensation strategy with a forgetting factor. An augmented Markovian jump system model is established to take the packet dropouts into account. The synthesis of packetized predictive control is then developed by minimizing a worst case cost function with respect to the model uncertainties. The recursive feasibility of the proposed controller design problem and the mean-square stability of the closed-loop systems are proved, respectively. The proposed packetized predictive control method is demonstrated by simulating a four-tank process system.

Distributed Model Predictive Formation Control for a Group of UAVs With Spatial Kinematics and Unidirectional Data Transmissions

This paper proposes a distributed model predictive control (DMPC) algorithm for the formation flight of a group of UAVs modeled by six degree-of-freedom (6-DoF) spatial kinematics. The formation system has a leader-follower structure with the leader cruising at a constant linear velocity during the flight, and the UAVs transmit data in a unidirectional order. The DMPC algorithm utilizes the unidirectional structure through the reception and transmission of an assumed output sequence as the reference trajectory, which is constructed from the solutions to the local DMPC problem and the prediction model. Based on the interactions between UAVs, convergence and stability of the multi-UAV formation are ensured by the terminal constraints and recursive feasibility of the DMPC optimization. Simulations involving time-delays, packet drops and turbulence effect are conducted to verify the effectiveness of the proposed algorithm. Comparisons with non-unidirectional data transmissions further demonstrate that the unidirectional structure plays a critical role in the convergence performance

A Differential Error Based Self-Triggered MPC With Adaptive Prediction Horizon For Discrete Systems

Abstract For discrete time nonlinear networked control systems, a novel self-triggered adaptive model predictive control (MPC) strategy is developed. Different from the existing self-triggered MPC methods that determine the triggering instants based on the difference between the optimal and real states at one single instant, the proposed approach updates the MPC system according to the differential form of the state error of two consecutive sampling moments to effectively reduce the computation and communication burden while maintaining the ideal control performance. In addition, this paper introduces a new adaptive prediction horizon mechanism to the self-triggered MPC, so that the amplitude of prediction horizon contraction is sufficiently large to further reduce the computational burden of the MPC method. Finally, the recursive feasibility and robust stability of this proposed strategy are proved strictly by theoretical analysis, and the simulation comparison results are shown to verify the proposed framework.

Output feedback stochastic MPC for tracking control of quadrotors with disturbances

AbstractIn this paper, the trajectory tracking problem of controlling a constrained quadrotor with unmeasurable system states in an environment with stochastic wind‐gust disturbance is considered. The mathematical model of the quadrotor is divided into the translational system and the rotational system, while only the measurement output of the quadrotor can be accessed. A new output‐based control method is developed for solving this problem. In the translational control system, an output feedback stochastic model predictive control (MPC) algorithm is proposed to generate the optimal control sequence with less conservativeness, by taking into account the information on the distribution of the disturbances and the uncertainty resulting from the attitude tracking error. The closed‐loop probabilistic constraints satisfaction, the recursive feasibility and the stability of the algorithm are further proved. In the rotational system, the active disturbance rejection control (ADRC) method to estimate and compensate for external disturbances is leveraged and robust control for attitude tracking is accomplished. The convergence of the disturbance estimator and the stability proof are provided. Finally, the robustness and effectiveness of the proposed control strategy are verified by an illustrative example.

Robust MPC-RG for an autonomous racing vehicle considering obstacles and the battery state of charge

The design of a controller able to deal with uncertainties and physical constraints plays an essential role in fast and complex systems. Then, a reference governor approach based on model predictive control (MPC-RG) for an autonomous racing vehicle is proposed. The MPC-RG guarantees constraint satisfaction and recursive feasibility online while including obstacle avoidance capability and energy-aware management by solving a multi-objective optimization problem. In particular, a trade-off between maximizing the longitudinal velocity and the state of charge of the vehicle’s battery, as well as minimizing the variation of control actions is adopted. Moreover, the proposed MPC-RG is combined with a state-feedback linear quadratic regulator (LQR) and a Kalman filter (KF) to compensate for modeling errors and exogenous disturbances, as well as to estimate the unmeasured lateral velocity. In fact, for control and estimation purposes, a data-driven Takagi–Sugeno (TS) model trained by an adaptive neuro-fuzzy inference network is used. The performance of the developed approach is assessed in simulations using a well-known case study based on a 1/10 scale RC electric car.

Knee extension tracking and fatigue regulation results using a robust MPC approach in a hybrid exoskeleton

A nonlinear model predictive controller (NMPC) is a promising approach for cooperative control of functional electrical stimulation (FES) and an exoskeleton to assist limb function in people with spinal cord injury (SCI). Potentially, the cooperative control can mitigate the effects of FES-induced muscle fatigue, a significant technical challenge impeding the clinical translation of FES. However, previous NMPC-based cooperative designs have been limited to limb regulation and may not include fatigue regulation in the control objective. In this paper, we design a new NMPC law for limb tracking and fatigue regulation and present experimental results from participants with no disability and a participant with SCI. For robust tracking, this paper augments the NMPC with a Lyapunov-based feedback controller. A terminal controller and terminal constraint regions are specifically derived to show the robust NMPC scheme’s recursive feasibility and to satisfy the input constraints. The experimental results of continuous knee tracking show dynamic allocation of exoskeleton assistance despite decreasing control effectiveness of FES due to muscle fatigue. The robust tube-based MPC reduced the knee angle’s root mean square tracking error by 34% compared to a nominal MPC. It elicited cooperative behavior when it automatically modulated (increased or decreased) FES and motor inputs for different desired fatigue levels while maintaining desired knee angle tracking performance. The statistical t-test showed that the FES input was significantly reduced in the post-fatigue trial (with the desired fatigue level of 1), and the muscle was significantly less fatigued compared to the pre-fatigue experiment (with the desired fatigue level of 0.5).

Design and analysis of event‐triggered predictive sliding mode control for discrete‐time constrained system

AbstractThis paper presents a new approach for designing an event‐triggered predictive sliding mode control (SMC) for discrete‐time systems subject to constraints. The proposed controller is based on an existing reach‐law‐based SMC, and it formulates an optimization control problem (OCP) to generate predictive control actions that satisfy both state and input constraints. An event‐triggered strategy is introduced to reduce the frequency of OCP solving by taking into account the sliding mode controller and unmeasurable states between sampling instants. The paper also analyzes the recursive feasibility of the proposed controller, which ensures the feasibility of each OCP solution. Numerical simulations and comparison studies are performed to validate the theoretical results. The proposed approach offers an effective way to design event‐triggered predictive sliding mode controllers that reduce the computational burden of OCP solving while guaranteeing the satisfaction of system constraints.

Risk-averse receding horizon motion planning for obstacle avoidance using coherent risk measures

This paper studies the problem of risk-averse receding horizon motion planning for agents with uncertain dynamics, in the presence of stochastic, dynamic obstacles. We propose a model predictive control (MPC) scheme that formulates the obstacle avoidance constraint using coherent risk measures. To handle disturbances, or process noise, in the state dynamics, the state constraints are tightened in a risk-aware manner to provide a disturbance feedback policy. We also propose a waypoint following algorithm that uses the proposed MPC scheme for discrete distributions and prove its risk-sensitive recursive feasibility while guaranteeing finite-time task completion. We further investigate some commonly used coherent risk metrics, namely, conditional value-at-risk (CVaR), entropic value-at-risk (EVaR), and g-entropic risk measures, and propose a tractable incorporation within MPC. We illustrate our framework via simulation studies.

A chance‐constrained tube‐based model predictive control for tracking linear systems using data‐driven uncertainty sets

AbstractThis article presents a chance‐constrained tube‐based model predictive control (MPC) method for tracking linear time‐invariant systems based on data‐driven uncertainty sets. By defining the terminal admissible set to consider all the possible steady‐states and reformulating the stochastic tube‐based MPC framework, the proposed method can systematically hedge against the impact of uncertainties and ensure tracking for all reachable operating setpoints. To reduce the conservatism of control performance while enlarging the feasible region, a data‐driven polyhedral uncertainty set is constructed by using the principal component analysis technique, which can effectively capture correlations among uncertain variables. Since state constraint violations in a certain probability are allowed, a probability uncertainty set is constructed by using statistic limit and cutting plane methods to formulate a stochastic tube to ensure constraint satisfaction. The recursive feasibility and stability can be guaranteed if the uncertainties are bounded. The effectiveness of the proposed method is verified by numerical examples and tracking problems of a thickening process.

Adaptive event-triggered output tracking control for Markovian jump systems: A robust [formula omitted] MPC approach

This work focuses on the output tracking control for discrete-time Markov jump systems (MJSs) via a model predictive control (MPC) approach. Not only the mean-square stability (MSS), but also the H2 performance and H∞ performance is considered in the MPC controller design. To save communication resources, a version of adaptive event-triggered mechanism (AETM) is utilized. Different from the traditional static event-triggered mechanism, its threshold coefficient is time-varying and can be adjusted in real-time to fit the system evolution. Moreover, the asynchronous switching between the controller modes and the plant modes is taken into account. The design objective is to synthesis an adaptive event-triggered asynchronous MPC controller such that not only the augmented closed-loop system is MSS with a certain level of H2/H∞ performance, but also the communication burden can be reduced to some extent. It is the first attempt to investigate the output tracking control of MJSs via an MPC approach. By constructing a plant model-dependent Lyapunov function, a set of conditions is derived to determine a desired MPC controller. In addition, two MPC related issues, namely recursive feasibility and closed-loop MSS, are also studied. At last, an illustrative example is given to verify the availability of the theoretical findings.

Surviving disturbances: A predictive control framework with guaranteed safety

Rejecting all disturbances is an extravagant hope in safety-critical control systems, hence surviving them where possible is a sensible objective a controller can deliver. In order to build a theoretical framework starting from surviving all disturbances but taking the appropriate opportunity to reject them, a sufficient condition on surviving disturbances is first established by exploring the relation among steady sets of state, input, and disturbance, followed by an output reachability condition on rejecting disturbances. A new robust safety-critical model prediction control (MPC) framework is then developed by embedding the quartet of pseudo steady input, output, state, and disturbance (IOSD) into the optimisation. Unlike most existing tracking MPC setups, a new and unique formulation is adopted by taking the pseudo steady disturbance as an optimisation decision variable, rather than directly driven by the disturbance estimate. This new setup is able to decouple estimation error dynamics, significantly contributing to the guarantee of recursive feasibility, even if the disturbance or its estimate changes rapidly. Moreover, towards optimal coexistence with disturbances, offset-free tracking of a compromised reference can be achieved, if rejecting the disturbance conflicts with safety-critical specifications. Finally, the benefits of the proposed method have been demonstrated by both numerical simulations and experiments on aerial physical interaction.

Membership function‐dependent predictive control for interval type‐2 Takagi–Sugeno fuzzy system

AbstractIn this paper, the problem of membership function‐dependent model predictive control (MFD‐MPC) of interval type‐2 Takagi–Sugeno (IT2 T‐S) fuzzy system is investigated. An online MFD‐MPC optimization problem is formulated to minimize an infinite horizon objective function subject to hard constraints on control input and system state. By using the variable dimension expansion method and dividing the operation domain of independent variables into several subdomains, a subregion‐based state feedback model predictive controller that offers more design flexibility is designed to stabilize the open‐loop fuzzy system. Based on descriptor system theory, the variable mismatching phenomenon between MFs and the coupling between plant, controller, and Lyapunov matrix are eliminated. Then, using the piecewise linear approximation technology, MFD sufficient conditions of low conservatism on guaranteeing recursive feasibility and the stability of IT2 closed‐loop fuzzy system are deduced by tightening terminal constraint set. Finally, a numerical example is provided to further explain the advance of the proposed method.

Distributed and Localized Model Predictive Control—Part II: Theoretical Guarantees

Engineered cyberphysical systems are growing increasingly large and complex. These systems require scalable controllers that robustly satisfy state and input constraints in the presence of additive noise – such controllers should also be accompanied by theoretical guarantees on feasibility and stability. In our companion paper, we introduced Distributed and Localized Model Predictive Control (DLMPC) for large-scale linear systems; DLMPC is a scalable <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">closed-loop</i> MPC scheme in which subsystems need only exchange local information in order to synthesize and implement local controllers. In this paper, we provide recursive feasibility and asymptotic stability guarantees for DLMPC. We leverage the System Level Synthesis framework to express the maximal positive robust invariant set for the closed-loop system and its corresponding Lyapunov function in terms of the closed-loop system responses. We use the invariant set as the terminal set for DLMPC, and show that this guarantees feasibility with minimal conservatism. We use the Lyapunov function as the terminal cost, and show that this guarantees stability. We provide fully distributed and localized algorithms to compute the terminal set offline, and also provide necessary additions to the online DLMPC algorithm to accommodate coupled terminal constraint and cost. In all algorithms, only local information exchange is necessary, and computational complexity is independent of the global system size – we demonstrate this analytically and experimentally. This is the first distributed MPC approach that provides minimally conservative yet fully distributed guarantees for recursive feasibility and asymptotic stability in the nominal and robust settings.

Adaptive Event-Triggered Model Predictive Load Frequency Control for Power Systems

This paper investigates the adaptive event-triggered (AET) output feedback model predictive control (MPC) method for the load frequency control (LFC) problem of hybrid power system involving the thermal power and the photovoltaic power. First, an AET communication mechanism, which possesses the ability to dynamically adjust the trigger threshold parameter according to an adaptive law, is addressed to reducing the communication overhead, while keeping the required control performance; Second, the output feedback model predictive controller which is composed of an off-line designed state observer and an on-line solved optimization problem, is proposed using the techniques of quadratic boundedness and S-procedure. The state observer gain is obtained by off-line maximizing the trace of a matrix which is closely related to minimal positively invariant set; While the output feedback MPC strategy is acquired by expressing the infinite horizon control moves as a free control move and a linear feedback law based on the estimated state; Third, the recursive feasibility of the on-line optimization problem and the stability of the closed-loop system are analyzed by the fact that the estimated state and estimation error will converge to the presented minimal positively invariant set. Finally, MATLAB and its linear matrix inequality (LMI) toolbox are used to solve the optimization problem, and the LFC system with load disturbance is simulated and analyzed. The simulation results show that the proposed method is feasible and effective.

Uncertainties and Output Feedback in Rollout Event-Triggered Control

The fact that event-triggered control (ETC) often exhibits an improved performance-communication tradeoff over time-triggered control renders it especially useful for Networked Control Systems (NCSs). However, it has proven difficult to characterize the traffic produced by ETC a priori. Rollout ETC addresses this issue by using a triggering and control law that is <i>implicitly</i> defined by the solution to an optimal control problem (OCP), instead of an explicit one as in classical ETC. This allows to directly incorporate predefined constraints on the transmission traffic as well as on states and inputs. In this article, we examine the practically relevant case when output instead of state measurements are available, and measurements as well as the LTI plant are subject to uncertainties. To address these challenges, we adapt methods from robust tube-based model predictive control and propose three different strategies to implement an error feedback in an NCSs setup, the applicability of which depends on the capabilities of the actuator. We establish recursive feasibility, robust constraint satisfaction and convergence. Finally, we illustrate our results in a numerical example.

Distributed model predictive control for heterogeneous vehicle platoon with unknown input of leading vehicle

In this paper, a distributed model predictive control (DMPC) algorithm for a platoon of heterogeneous vehicles is proposed. The leading vehicle is allowed to be driven by a non-zero and time-varying input, rather than traveling at a constant velocity. Except for individual state and input constraints for each vehicle, all vehicles are coupled via state-coupled inter-vehicular spacing constraints and state-coupled cost functions, which maintain the unidimensional platoon formation with satisfactory transient performance. Each vehicle communicates with its neighboring vehicles, and may not know the leading vehicle’s kinetic status information. The control input of each following vehicle is computed by a local optimization problem established by each vehicle’s local information and the assumed state information from its neighbors. By designing distributed terminal control laws for following vehicles, dividing each state-coupled set into several specific subsets, and then forcing each following vehicle to optimize its state constrained in the assigned subsets, the coupled constraints and cost functions can be decoupled, and thus a distributed and parallel computing method can be adopted to compute the control inputs of all following vehicles. Based on the tailored terminal equality constraints together with the tailored terminal control laws, the recursive feasibility of local MPC optimization problems is achieved at all time steps and the asymptotic stability of each vehicle is also guaranteed. The effectiveness of the proposed DMPC method is demonstrated in simulation, and the advantage of the proposed DMPC dealing with the leading vehicle’s non-zero, inaccessible, and time-varying input is highlighted by a comparison simulation for heterogeneous vehicle platoon with a continuously changing leading vehicle velocity.