Control Input Constraints Research Articles

Model predictive control for space robot manipulator modeled by switched systems: A data‐driven approach

AbstractThis article investigates the data‐driven based model predictive control (MPC) problem for a class of space robot manipulator (SRM). First, the SRM system is modeled as a class of discrete‐time switched system to reflect more system characteristics. Second, only the input‐state data are used for end‐to‐end controller design, and the system identification process is avoided. In order to meet the real‐time requirements of the manipulator arm angles, a kind of constrained predictive control method is designed to prevent the overheating or damage of SRM motor, optimizing the cost function for each decision cycle under the safe control input constraints. Then, based on the average dwell time method, the asymptotic stability is assured for the presented SRM system. The design conditions for data‐driven based MPC are provided in the form of linear matrix inequalities. Finally, the effectiveness and advantage for the developed data‐driven based MPC strategy are validated via a case study of SRM system.

Cooperative control of virtually coupled trains considering train-to-train communication cycle: a tube-based model predictive control approach

In this paper, a distributed tube-based model predictive control (TMPC) method is proposed to address the cooperative control of virtually coupled high-speed train (HSTs), which consists of an optimisation control part and a feedback control part. The novelty of this work lies in its pioneering consideration of the inconsistency between the train-to-train (T2T) communication cycle and the train operation control cycle in the cooperative control of virtually coupled trains. Firstly, for the optimisation control part, a distributed MPC scheme is designed based on the nominal train dynamics model to address the cooperative control of trains with different initial states, state constraints and control input constraints. By solving the optimisation control problem of the MPC, the optimal control input sequence and operating state sequence of the train for the next T2T communication cycle can be obtained. Secondly, the recursive feasibility and convergence of the MPC are analysed theoretically. Thirdly, for the feedback control part, an adaptive feedback control law is designed based on the actual train dynamics model, auxiliary dynamic system (ADS) and neural network techniques. In the train operation control cycle, the feedback control part utilises the optimal state sequence from the MPC as a reference for feedback control to deal with the external disturbance and train dynamics modelling inaccuracy. Fourthly, it is theoretically proved that the actual operating state of the train can converge to a small region around the optimal state of the MPC in a finite time. Finally, the effectiveness of the proposed distributed cooperative control scheme is verified by simulations.

Sampled-data static output feedback robust MPC for LPV systems with bounded disturbances

This paper investigates a sampled-data static output feedback robust model predictive control (MPC) approach for continuous-time linear parameter varying (LPV) systems with unknown system states and bounded disturbances. Between two successive sampling time instants, it is assumed that the controlled LPV systems evolve in continuous-time, and the control inputs are piecewise constant. The robust stability conditions and control input constraints on the closed-loop system are considered in the formulated robust MPC optimization. The constraints in the formulated robust MPC optimizations are formulated as linear matrix inequalities (LMIs) and solved as convex optimization. The designed sampled-data static output feedback robust MPC optimization has a simple structure and directly optimizes output feedback controller. Furthermore, the system state constraint sets are on-line updated over the sampling interval. The designed sampled-data static output feedback robust MPC approach has the property of recursive feasibility, and can guarantee robust stability of the controlled continuous-time LPV systems. A simulation example is given to illustrate the effectiveness of the approach.

Application of improved appointed time control in helicopter mode of a tilt-rotor eVTOL aircraft

In this paper, an appointed time sliding mode control scheme is proposed for trajectory tracking control of a tilt-rotor electric vertical takeoff and landing (eVTOL) aircraft. First, the error dynamic model of helicopter mode of the tilt-rotor eVTOL aircraft is presented. Second, an appointed time prescribed performance function (ATPPF) is designed as the expected value of the error, which guides the error to converge to zero at the appointed time. Then, a predefined time controller ensures that the actual error tracks the expected error before the settling time set by the ATPPF. By setting the time parameters of the ATPPF and the predefined time controller to the same value, the actual error will converge to zero vicinity at the appointed time. Finally, the predefined time convergence of the closed-loop system is proved via Lyapunov analysis. The effectiveness of the appointed time control strategy is demonstrated in the simulation results in the presence of external disturbances, dynamic uncertainties and control input constraints.

Dynamic surface control for satellite attitude of the chained three-body tethered system during deployment

A fixed-time attitude stabilization scheme based on dynamic surface control (DSC) is proposed for the attitude of the three-body chained tethered system during tether deployment. Considering that the angular velocity of the satellite is difficult to measure, an extended state observer (ESO) is introduced to simultaneously compensate for the adverse effects of flexible panel vibrations and uncertain inertia tensors. On this basis, a fixed-time convergence attitude control scheme using DSC is designed, accounting for filtering error compensation. To offset the limitations of traditional fixed-time control strategies that ignore actuator saturation, an auxiliary system is introduced to incorporate control input constraints directly into controller design. The stability of the closed system is analyzed based on Lyapunov theory. Finally, the effectiveness and superiority of the proposed algorithm are verified by numerical simulation.

Distributed Optimal Attitude Synchronization Control of Multiple QUAVs via Adaptive Dynamic Programming.

This article proposes a distributed optimal attitude synchronization control strategy for multiple quadrotor unmanned aerial vehicles (QUAVs) through the adaptive dynamic programming (ADP) algorithm. The attitude systems of QUAVs are modeled as affine nominal systems subject to parameter uncertainties and external disturbances. Considering attitude constraints in complex flying environments, a one-to-one mapping technique is utilized to transform the constrained systems into equivalent unconstrained systems. An improved nonquadratic cost function is constructed for each QUAV, which reflects the requirements of robustness and the constraints of control input simultaneously. To overcome the issue that the persistence of excitation (PE) condition is difficult to meet, a novel tuning rule of critic neural network (NN) weights is developed via the concurrent learning (CL) technique. In terms of the Lyapunov stability theorem, the stability of the closed-loop system and the convergence of critic NN weights are proved. Finally, simulation results on multiple QUAVs show the effectiveness of the proposed control strategy.

A novel finite-time leader-follower consensus control for a disturbed mechanical nonlinear system in presence of actuator saturation

This paper presents a novel leader-follower consensus control for a particular class of nonlinear multi-agent mechanical systems in the presence of control input constraints and external disturbances which includes robot system dynamics with a wide range of potential applications in industry. In this case, one of the agents is selected as the leader to direct the other agents in such a way that the whole system can reach consensus within certain prescribed performance transient bounds. Due to the presence of disturbances in most practical systems, the effect of limited disturbance in the consensus control method has been investigated, and actuator saturation is included in the design process. A terminal sliding mode control method has been adapted to ensure the stability of the overall system and fast finite-time leader-follower consensus control. The simulation results of the multi-agent nonlinear robot system in MATLAB environment, in different scenarios with simultaneous consideration of actuator saturation and external disturbance, will show the efficiency of the proposed control method.

Planar curved path following controller for a small fixed-wing unmanned aerial vehicle with constrained parameters optimized by nonlinear model predictive control

Path following presents a pivotal challenge within the realm of small fixed-wing unmanned aerial vehicles. Firstly, a Lyapunov-stable path guidance law was formulated to follow specific planar curved paths. To ensure differentiability of the guidance law, a modified, smooth saturation function was derived. Secondly, an analysis was conducted to ascertain the interrelationship between control parameters and input constraints, thereby identifying the relevant parameter domains. Thirdly, the nonlinear model predictive control technique was harnessed to optimize both guidance law parameters, enhancing the unmanned aerial vehicle’s capacity to achieve optimal performance in both straight-line and circular path following, hereafter referred to as PFC_NMPC. By leveraging Lyapunov stability arguments for switched systems, the stability of the corresponding nonlinear switched system was guaranteed. In this study, square and circular paths were generated to assess the path-following control of a simulated fixed-wing unmanned aerial vehicle. The performance of various guidance laws, including those with fixed parameters (PFC), those with parameters tuned using fuzzy logic (PFC_FL), PFC_NMPC, vector field, and pure pursuit with line-of-sight, was compared. Notably, the proposed PFC_NMPC method exhibited the ability to expedite the unmanned aerial vehicle’s convergence to the desired path while maximizing the effective flight path length.

Prescribed performance under input saturation for uncertain strict-feedback systems: A switching control approach

We consider the problem of achieving prescribed performance metrics on the output tracking error, for uncertain strict-feedback systems, while satisfying inelastic control input constraints in the form of magnitude saturation. Inspired by the prescribed performance control (PPC) methodology, we propose a switching control strategy comprised of two operational units: a traditional PPC and a Safety Controller. The former enforces the output error to evolve strictly inside a user-defined performance envelope that incorporates all the desired performance characteristics. However, in the presence of input saturation this envelope can be easily violated, leading to PPC instability. On the other hand, the Safety Controller enables the safe escaping, thus avoiding the appearance of this internal instability phenomenon. We prove that the closed-loop system solution is complete and non-zeno. Furthermore, we show that the tracking error evolves inside a modified performance envelope, guaranteeing a prescribed minimum convergence rate and a controlled maximum steady-state error. Simulation studies clarify and verify the theoretical findings.

Robust fault-tolerant control for dynamic positioning of ships with prescribed performance

This study presents a new fault-tolerant control scheme for ship dynamic positioning. The scheme aims to handle unknown disturbances, imprecise fault estimation, and control input constraints. First, an adaptive sliding mode disturbance observer is introduced. This observer effectively reconstructs disturbances in finite time, even without knowledge of their derivative upper bounds. Next, we design a novel prescribed performance function that sets bounds on tracking errors. This function is combined with an auxiliary intermediate control technique to create a high-level controller. Lastly, a robust fault-tolerant control allocation scheme is proposed to redistribute the generalized forces among faulty actuators. It autonomously finds a feasible force vector in the attainable force set. Simulation results are provided to demonstrate the effectiveness of the proposed control scheme.

Three-Dimensional Path Tracking of Over-Actuated AUVs Based on MPC and Variable Universe S-Plane Algorithms

Autonomous Underwater Vehicles (AUVs) are widely used for the inspection of seabed pipelines. To address the issues of low trajectory tracking accuracy in AUV inspection processes due to uncertain ocean current disturbances, this paper designs a new dual-loop controller based on Model Predictive Control (MPC) and Variable Universe S-plane algorithms (S-VUD FLC, where VUD represents Variable Universe Discourse and FLC represents Fuzzy Logic Control) to achieve three-dimensional (3-D) trajectory tracking of an over-actuated AUV under uncertain ocean current disturbances. This paper uses MPC as the outer-loop position controller and S-VUD FLC as the inner-loop speed controller. The outer-loop controller generates desired speed instructions that are passed to the inner-loop speed controller, while the inner-loop speed controller generates control input and uses a direct logic thrust distribution method that approaches optimal energy consumption to distribute the thrust generated by the propellers to the over-actuated AUV, achieving closed-loop tracking of the entire trajectory. When designing the outer-loop MPC controller, the actual control input constraints of the system are considered, and control increments are introduced to reduce control model errors and the impact of uncertain external disturbances on the actual AUV model parameters. When designing the inner-loop S-VUD FLC, the strong robustness of the variable universe fuzzy controller and the easy construction characteristics of the S-plane algorithm are combined, and integral action is introduced to improve the system’s tracking accuracy. The stability of the outer loop controller is proven by the Lyapunov method, and the stability of the inner loop controller is verified by simulation. Finally, simulations show that the over-actuated AUV has fast tracking processes and high tracking result accuracy under uncertain ocean current disturbances, demonstrating the effectiveness of the designed dual-loop controller.

A new Q‐function structure for model‐free adaptive optimal tracking control with asymmetric constrained inputs

SummaryThis article aims to design a model‐free adaptive tracking controller for discrete‐time nonlinear systems with unknown dynamics and asymmetric control constraints. First, a new Q‐function structure is designed by introducing the control input into the tracking error of the next moment, in order to eliminate the final tracking error, avoid the steady control, and ignore the discount factor. Second, via system transformation, a general performance index is developed to overcome the challenge caused by asymmetric constraints of implicit control inputs. By this operation, the constrained tracking problem is converted to an unconstrained optimal tracking problem without the traditional nonquadratic performance function that is only applicable to explicit control inputs. Then, a value‐iteration‐based Q‐learning (VIQL) algorithm is derived to seek the optimal Q‐function and the optimal control policy by using offline data rather than the mathematical model. Next, the convergence, monotonicity, and stability properties of VIQL are investigated to demonstrate that the iterative Q‐function sequence can converge to the optimal Q‐function under ideal conditions. To realize the VIQL algorithm, the critic neural network is employed to approximate the Q‐function. Finally, simulation results and comparative experiments are conducted to demonstrate the validity and effectiveness of the present VIQL scheme.

Disturbance rejection tube model predictive levitation control of maglev trains

Magnetic levitation control technology plays a significant role in maglev trains. Designing a controller for the levitation system is challenging due to the strong nonlinearity, open-loop instability, and the need for fast response and security. In this paper, we propose a Disturbance-Observe-based Tube Model Predictive Levitation Control (DO-TMPLC) scheme combined with a feedback linearization strategy for the levitation system. The proposed strategy incorporates state constraints and control input constraints, i.e., the air gap, the vertical velocity, and the current applied to the coil. A feedback linearization strategy is used to cancel the nonlinearity of the tracking error system. Then, a disturbance observer is implemented to actively compensate for disturbances while a TMPLC controller is employed to alleviate the remaining disturbances. Furthermore, we analyze the recursive feasibility and input-to-state stability of the closed-loop system. The simulation results indicate the efficacy of the proposed control strategy.

Disturbance-observer-based event-triggered model predictive control of nonlinear input-affine systems

This paper proposes a novel disturbance-observer-based event-triggered model predictive control (DEMPC) framework for a class of nonlinear input-affine systems with state and control input constraints as well as unmatched disturbances to simultaneously enhance the robustness of standard MPC and reduce computational resource utilization. First, a nonlinear disturbance observer is designed to compensate for disturbances actively. Next, a constant-threshold-type event-triggering mechanism (CTETM) is designed in terms of the state prediction deviation caused by the remaining disturbances. Subsequently, a DEMPC algorithm is constructed using the disturbance estimation information, the CTETM, and the so-called dual-mode scheme. Furthermore, rigorous theoretical analysis is provided, involving robust constraint fulfillment, Zeno phenomenon prevention, recursive feasibility, and stability. Particularly for systems with only matched disturbances, it is proven that continuous disturbance compensation would result in a possibly lower triggering frequency and enhanced control performance for the DEMPC compared to conventional EMPC without introducing additional conservatism into the state constraints. In the end, simulation studies are performed to illustrate the effectiveness of the proposed framework.

Designing a Model Predictive Controller for Displacement Control of Axial Piston Pump

Variable displacement hydraulic pumps are widely used for energy efficiency, and they often have a mechanical feedback mechanism to ensure target tracking control performance and stability of tilt angle control. Furthermore, there are many examples which add electronic control to realize higher tracking control performance. However, in such cases, the control performance is significantly affected by the dynamic characteristics of the mechanical feedback mechanism, and this problem prevent its widespread use. Additionally, tilt angle control is susceptible to changes in dynamic characteristics and load pressure depending on the operating point, and there are constraints on the tilt angle. Hence, high control performance cannot be obtained without considering these nonlinearities. In this study, the variable displacement pump without mechanical feedback mechanism is focused on, and the objective of this study is to design a displacement control system for a hydraulic pump based on a model predictive control (MPC) that can consider various constraints on the design step. An adaptive system, which handles changes in dynamic characteristics and the effects of load pressure, is introduced. Additionally, the control performance of adaptive MPC is compared to adaptive model matching-based MPC with inverse optimization that can optimally design the weight matrices of the evaluation function without trial and error. Furthermore, in order to improve the transient response, a variable control input constraints are added in these two control systems. Experimental results of control performance have shown that the proposed method achieved a high tracking performance and short settling time, which confirmed the effectiveness of the variable control input constraints.

Disturbance Rejection Event-Triggered Robust Model Predictive Control for Tracking of Constrained Uncertain Robotic Manipulators.

A novel hierarchical control framework combining computed-torque-like control (CTLC) with disturbance-observer-based event-triggered robust model predictive control (DO-ET-RMPC) is proposed for the trajectory tracking control of robotic manipulators with bounded disturbances and state and control input constraints. The CTLC approach is first used to cancel the exact nonlinear dynamics of the original tracking error system to obtain a set of decoupling linear tracking error subsystems, thus reducing the optimization complexity of model predictive control (MPC). The composite DO-ET-RMPC scheme is then developed based on the so-called dual-mode MPC approach to robustly stabilize the tracking error subsystems, which could improve the robustness of MPC and save its computational resources simultaneously. The continuous-time theoretical properties of the DO-ET-RMPC scheme, considering disturbances and state and control input constraints simultaneously, are provided for the first time, including the avoidance of Zeno behavior, robust constraint satisfaction, recursive feasibility, and stability. In the end, the superiorities of the proposed control scheme are verified by the comparative simulations.

MODEL PREDICTIVE CONTROL OF EXOSKELETON JOINT ANGLES

Lower limb exoskeletons are used for rehabilitation purposes, so their precise control is an important issue. Classical controllers are often unable to provide high accuracy and speed, which can lead to errors in exoskeleton operation. Complexities associated with lower limb exoskeleton control systems arise from the dynamic and nonlinear nature of human locomotion. Solving these complexities involves designing modern control systems. One of the modern approaches is Model Predictive Control, which, predicting future deviations of system state variables, performs optimization calculations and selects such input signals, in which case the error will tend to the minimum value. This controller is widely used for controlling nonlinear dynamic systems with constraints. Considering this fact, it was proposed to develop a controller with a predictive model for controlling the angles of the exoskeleton joints. Control with a predictive model assumes that the dynamic equations of the control object are known, so a nonlinear mathematical model of the lower limb exoskeleton was firstly designed, taking into account the mechanical and electromechanical components. An examination of the exoskeleton state variables and control input constraints, which were taken into account during the design of the controller, was performed, and a reduction function was defined, according to which the controller with a predictive model should perform an optimization calculation, thereby enabling the reduction of errors or inaccuracies. Simulations performed in the MATLAB/Simulink environment validate the effectiveness and accuracy of the developed controller, showing small deviations between the desired and actual joint angles during dynamic motions. Future efforts will focus on improving control quality and validating results through empirical studies, thereby strengthening the role of model predictive controllers for the design of exoskeleton control systems.

Rolling self-triggered distributed MPC for dynamically coupled nonlinear systems

The mutual influences caused by dynamic couplings in large-scale systems increase the difficulty in the design and analysis of distributed model predictive control (DMPC), and require information exchange among subsystems which calls for a scheduling strategy to save communication resources in communication-limited environments. To circumvent the two problems, we design a rolling self-triggered DMPC strategy for large-scale dynamically coupled systems with state and control input constraints. First, the optimal control problem where the cost is subject to the coupled dynamic and the constraints are subject to the uncoupled counterpart is proposed, forming the dual-model DMPC that is simple in design and analysis but yields good control performance. Second, the information exchange only occurs at some specified triggering instants determined by a rolling self-triggered mechanism, saving communication resources more significantly. The effectiveness of the designed strategy is verified by numerical simulations.

Speed control with low complexity for multiple autonomous vehicles in roundabouts

The paper introduces a high level speed control method for the coordination of multiple autonomous vehicles (AVs) in roundabout scenarios. The aim of the control method is to guarantee collision-free motion of the AVs, and similarly, to minimize their traveling time. In the method a priority-based ordering process of the AVs is used, which enforces the time-efficient motion of the AVs. The collision-free motion is guaranteed through an optimization-based method including control input constraints. The ordering process and the optimization form a low complexity solution, which requires low computation effort. The proposed control strategy is involved in the high level of a hierarchical control structure. The effectiveness of the proposed control strategy is illustrated by simulation examples and Hardware-in-the-Loop demonstration.

Distributed constrained control for multi‐train systems with multiple cars

AbstractIn practical multi‐train systems, there are four different kinds of necessary nonlinearities cause by the interactive forces between adjacent cars, the nonlinear resistances, the input constraints, and the velocity constraints. However, most of the existing works on distributed control for multi‐train systems only focused one or two kinds of these nonlinearities. To the best of our knowledge, there are only a few works considering three kinds of these nonlinearities. In this paper, the effects of control input and velocity constraints, interactive forces between adjacent cars and the train running resistance on the system are studied, and a distributed cooperative control algorithm based on the state information of adjacent cars is proposed. The analysis is given based on model transformations, appropriate parameter selection and convex analysis. It is proved that all trains finally run in a given formation even when the inputs and velocities of all trains are constrained to lie in some given sets. Numerical simulation examples are presented to demonstrate the theoretical conclusions.