Control Input Constraints Research Articles

Explicit stochastic model predictive control for anti-pitching a high-speed multihull

Heave and pitch motion control of a high-speed multihull is important for restraining its large heave and pitch motions and improving its seaworthiness. However, stochastic ocean wave disturbances and strict input constraints on the T-foil and the flap highly increase difficulties in heave and pitch motion control. This paper proposes a explicit stochastic model predictive control (ESMPC) approach for anti-pitching the multihull without the violation of the control input constraints. A quadratic cost function is designed for the stochastic receding-horizon optimization of MPC under control input constraints, by considering the stochastic control model for the multihull as the predictive model. Then, the stochastic optimization is converted into deterministic optimization based on a Kalman-filter-based estimator and state mean prediction, and the ESMPC law is obtained by a combination of offline design and online search, which reduces the complexity of online optimization and enhances real-time control performance. The mean-square boundedness of stochastic system state is theoretically analyzed using the Lyapunov theory. The control effectiveness is illustrated by simulations and experiments, from which the pitch motion and the heave motion are reduced by 30% and 40%, respectively.

Inverse optimal missile guidance law under constraints based on prescribed-time explicit reference governor

In this paper, the utilization of inverse-optimality-based prescribed-time explicit reference governor is investigated for missile intercepting against unknown maneuvering targets under performance and control input constraints. With an arctangent-based disturbance observer equipped for disturbance elimination, incorporating the inverse optimality approach into the missile interception guarantees the minimization of a performance index. In the framework of prescribed-time explicit reference governor, the control constraint is translated into a restriction of time-varying invariant set, and it follows the prescribed-time regulation of the applied reference along with the restriction satisfaction. The combined prescribed-time explicit reference governor approach could be transformed into a linear matrix inequality optimization problem, and its online solution over a receding horizon gives a Lyapunov function value for reference regulation and then control decisions in the continuous time. Simulation studies are performed to illustrate the performance of the proposed guidance control law.

Numerical algorithm for optimal control of switched systems and its application in cancer chemotherapy

This paper considers an optimal control problem of switched dynamical systems with control input and system state constraints. Unlike in traditional switched dynamical systems, the switching times cannot be specified directly and they are governed by a state-dependent switching condition. Thus, the existing methods cannot be directly used to solve this problem. To overcome this difficulty, the switching conditions are transformed into a continuous-time inequality constraint by introducing an integer constraint. Further, the original optimal control problem is approximated by using a sequence of constrained non-convex nonlinear parameter optimization problems by using a relaxation method, a control vector parameterization technique, and a time-scaling transformation. Following that, a penalty function-based intelligent optimization algorithm is proposed for obtaining a global optimal solution based on a more effective penalty function method and a more effective intelligent optimization algorithm. The convergence results show that the proposed method is globally convergent. Numerical simulation results show that the proposed method is lower time-consuming, has faster convergence speed, can obtain a better objective function value than the existing typical algorithms, and can achieve a stable and robust performance when considering the small perturbations in constraint conditions or the small perturbations of the model parameters.

A large-stroke rapid motion controller for servo applications with speed and control constraints

Large-stroke rapid motion is required in many industrial servo systems (e.g. pick-and-place applications), on which constraints of control input and motion speed are usually imposed. This paper presents a hybrid control scheme for large-stroke rapid motion in such systems. The controller resorts to the time-optimal control (TOC) for maximum acceleration initially and then switches into a linear control law to achieve smooth settling. A speed regulation stage is inserted in the tracking process to prevent violating the speed constraint. To tackle the unmeasured speed and unknown disturbance, an extended state observer (ESO) can be included in the controller. The controller is applied to a permanent magnet synchronous motor (PMSM) servo system for large-stroke position regulation. Digital simulation via MATLAB is conducted first, followed by an experimental verification using a TMS320F28335 board. The results confirm that the proposed controller can track a wide range of target references with desirable performance under speed constraint and load disturbance and has a competitive advantage over the popular active disturbance-rejection control (ADRC) scheme.

Synchronization Control of Dynamic Positioning Ships Using Model Predictive Control

Underway replenishment is essential for ships performing long-term missions at sea, which can be formulated into the problem of leader-tracking configuration. Not only the position and orientation but also the velocities are required to be controlled for ensuring the synchronization; additionally, the control inputs are constrained. On this basis, in this paper, a novel synchronization controller on account of model predictive control (MPC) for dynamic positioning (DP) ships is devised to achieve underway replenishment. Firstly, a novel synchronization controller based on MPC is devised to ensure the synchronization of not only the position and orientation but the velocities; furthermore, it is a beneficial solution for its advantages in handling the control input constraints ignored in most studies of underway replenishment. Secondly, a neurodynamic optimization system is applied to the implementation of MPC, which can improve the computational efficiency and shorten the simulation time. Thirdly, stability, frequently neglected by traditional MPC, is ensured by the means of adding a terminal cost function exported from the Lyapunov equation into the objective function. Finally, the effectiveness and advantages of the proposed control design are illustrated by extensive simulations.

Bounded Observer-Based Consensus Algorithm for Robust Finite-Time Tracking Control of Multiple Nonholonomic Chained-Form Systems

This article is concerned with the leader–follower consensus tracking problem for multiagent systems with nonholonomic high-order chained-form dynamics subject to external disturbances. A novel distributed and bounded observer is first developed for each follower to estimate the leader information in a finite time. Then, a bounded fast terminal sliding-mode control protocol is constructed for each follower to track the estimated leader's states leading to the fast convergence performance as well as strong robustness. Contrary to some existing finite-time consensus tracking schemes, the control input constraint is taken into account by utilizing hyperbolic tangent saturation function to reduce the risk of the actuator saturation. Moreover, an approximation-based technique is introduced to reduce the conservatism of the upper bound of convergence time. Finally, some simulations for a set of wheeled mobile robots are carried out to demonstrate the efficiency of the proposed control algorithm.

Fault‐tolerant control design for a class of nonlinear systems with actuator malfunctions

AbstractThis article presents a single‐hidden‐layer feedforward network (SLFN) aided fault‐tolerant control (FTC) scheme for a class of nonlinear systems subject to actuator faults. First, the upper bounds of the norms of the unknown functions, which cover information of actuator faults and amplitude saturation degrees, are deployed. The upper bounds are approximated by SLFNs with adaptive techniques. Subsequently, a sliding mode control approach is presented to allow for prompt corrective reactions, with explicit consideration of multivariable conditions and control input constraints. Finally, simulation results based on a nonlinear Boeing 747 aircraft model are presented to demonstrate the effectiveness of the proposed FTC scheme.

Distributed Control of Networked Nonlinear Systems via Interconnected Takagi–Sugeno Fuzzy Systems With Nonlinear Consequent

This article deals with the problem of designing nonlinear distributed control laws for continuous-time networked nonlinear heterogeneous systems with bounded sector nonlinear interconnections. The networked system is a combination of interconnected Takagi–Sugeno (TS) fuzzy systems with nonlinear consequent subject to state and control input constraints. The new sufficient conditions, taking into account state constraints and actuators saturation, are derived in terms of linear matrix inequalities. Further, it is shown that the closed-loop system can be made asymptotically stable while reducing the conservatism over decentralized and linear distributed control laws derived following the same method. At the same time, the maximization of the estimate of the domain of attraction (DoA) for the closed-loop system is pursued. Finally, two cases are presented to illustrate the effectiveness of the proposed design approach: 1) an electrical power system composed of two-machine subsystems and 2) a network of multiple inverted pendulums connected by nonlinear springs.

Adaptive model predictive control for an omnidirectional mobile robot with friction compensation and incremental input constraints

In this paper, an adaptive model predictive control (MPC) scheme with friction compensation, subject to incremental control input constraints and parameter uncertainties, is proposed for a three-wheeled omnidirectional mobile robot (OMR). The proposed control framework is in a cascaded structure, wherein the outer-loop is kinematic-based control and the inner-loop is designed based on adaptive linear MPC. First, a complex nonlinear dynamic model of the OMR in the world coordinate frame is transformed and partially linearized into a reduced nonlinear model in the moving coordinate system. The nonlinearity of the reduced model only arises from Coulomb friction. Then an estimated system is established for the reduced nonlinear system, with an adaptive update law estimating the system uncertain parameters. To facilitate the linear MPC design, part of the control efforts is derived by feedback compensation of the Coulomb friction forces, resulting in a linear estimated system. The other part is designed by a constrained linear MPC. Feasibility and stability analyses are given for the proposed adaptive MPC scheme. Finally, experimental comparisons with model-based MPC are carried out to verify the effectiveness of the proposed control scheme.

Containment control of fractional discrete-time multi-agent systems with nonconvex constraints

This paper is devoted to the containment control problem of fractional discrete-time multi-agent systems (FDTMASs) with nonconvex velocity and control input constraints. First, distributed containment controllers with nonlinear projection algorithms are proposed for all followers. Then, some sufficient conditions are deduced during the convergence analysis of the closed-loop systems. By using Lyapunov stability theory and properties of fractional calculus, it proved that the containment control of the systems could be achieved with the distributed containment controller. Finally, some numerical examples are given to show the correctness of the proposed theoretical results.

Prescribed‐time control with explicit reference governor for a class of constrained cascaded systems

AbstractDifferent from both finite‐time control (where the settling time depends on the initial condition) and fixed‐time control (whose settling time is subject to an upper bound but varies due to uncertainties and nonlinearities), the prescribed‐time control achieves regulation in prescribed finite time, even under uncertain nonlinearities. This article investigates the prescribed‐time regulation problem for a class of cascaded systems with integral form and control input constraints. The establishment of prescribed‐time property consists of the prescribed‐time regulation controller and prescribed‐time explicit reference governor (PT‐ERG), both of which satisfy the prespecified time requirement. For an elegant implementation, the feasibility for the separate design of controller and governor is guaranteed through a developed prescribed‐time cascaded stable theory. For the prescribed‐time controller, the proposed smooth time‐varying controller provides the prescribed‐time convergence based on a residual‐time‐dependent scaling transformation. For the PT‐ERG dealing with the control input constraints, a reference trajectory with a fixed minimum convergence rate provides an elegant compromise between performance and constraints which keeps the constraint satisfied and tracking errors in an invariant set. Both theoretical analysis and numerical simulations verify the effectiveness of the proposed control scheme.

Extended state observer–based output feedback control for spacecraft pose tracking with control input saturation

This article proposed an extended state observer (ESO)–based output feedback control scheme for rigid spacecraft pose tracking without velocity feedback, which accounts for inertial uncertainties, external disturbances, and control input constraints. In this research, the 6-DOF tracking error dynamics is described by the exponential coordinates on SE(3). A novel continuous finite-time ESO is proposed to estimate the velocity information and the compound disturbance, and the estimations are utilized in the control law design. The ESO ensures a finite-time uniform ultimately bounded stability of the observation states, which is proved utilizing the homogeneity method. A non-singular finite-time terminal sliding mode controller based on super-twisting technology is proposed, which would drive spacecraft tracking the desired states. The other two observer-based controllers are also proposed for comparison. The superiorities of the proposed control scheme are demonstrated by theory analyses and numerical simulations.

Distributed optimization for discrete-time multiagent systems with nonconvex control input constraints and switching topologies* *Projectsupported by the National Engineering Research Center of Rail TransportationOperation and Control System, Beijing Jiaotong University (GrantNo. NERC2019K002).

This paper addresses the distributed optimization problem of discrete-time multiagent systems with nonconvex control input constraints and switching topologies. We introduce a novel distributed optimization algorithm with a switching mechanism to guarantee that all agents eventually converge to an optimal solution point, while their control inputs are constrained in their own nonconvex region. It is worth noting that the mechanism is performed to tackle the coexistence of the nonconvex constraint operator and the optimization gradient term. Based on the dynamic transformation technique, the original nonlinear dynamic system is transformed into an equivalent one with a nonlinear error term. By utilizing the nonnegative matrix theory, it is shown that the optimization problem can be solved when the union of switching communication graphs is jointly strongly connected. Finally, a numerical simulation example is used to demonstrate the acquired theoretical results.

A neuro-observer-based optimal control for nonaffine nonlinear systems with control input saturations

In this study, an adaptive neuro-observer-based optimal control (ANOPC) policy is introduced for unknown nonaffine nonlinear systems with control input constraints. Hamilton–Jacobi–Bellman (HJB) framework is employed to minimize a non-quadratic cost function corresponding to the constrained control input. ANOPC consists of both analytical and algebraic parts. In the analytical part, first, an observer-based neural network (NN) approximates uncertain system dynamics, and then another NN structure solves the HJB equation. In the algebraic part, the optimal control input that does not exceed the saturation bounds is generated. The weights of two NNs associated with observer and controller are simultaneously updated in an online manner. The ultimately uniformly boundedness (UUB) of all signals of the whole closed-loop system is ensured through Lyapunov’s direct method. Finally, two numerical examples are provided to confirm the effectiveness of the proposed control strategy.

Singular perturbation-based saturated adaptive control for underactuated Euler–Lagrange systems

This paper proposes a saturated smooth adaptive controller for regulating a certain type of underactuated Euler–Lagrange systems (UELSs) with modeling uncertainties and control saturations based on a singular perturbation approach. Compared with relevent literature, the advantages of the proposed controller include: (1) it renders the UELS semiglobally asymptotically track the desired position without the violation of control input constraints; (2) high-order derivatives of positions are not required in its implementation. The Hoppensteadt’s Theorem is employed to show that the proposed saturated controller renders the UELS semiglobally asymptotically stable about the desired set point with the satisfaction of control input constraints. The control effectiveness is validated by simulations on a two-link compliant robot arm.

Leader–follower consensus control for a nonlinear multi-agent robot system with input saturation and external disturbance

This paper addresses the leader–follower consensus control problem for a nonlinear multi-agent robot system with control input constraint and external disturbances. Robot system is one of the most important practical systems in the industry. Due to the presence of disturbances in most practical systems, this paper considers the issue of finite-time leader–follower consensus control of the nonlinear multi-agent robot system along with actuator saturation and bounded disturbance. The modified terminal sliding mode control method is suggested for the system which is able to guarantee the stability of the overall system and fast finite-time leader–follower consensus control. For two different scenarios, the simulation of multi-agent robot system has been performed. The results show the effectiveness of the proposed control method.

Combined Constrained Robust Least Squares Approach and Block-Pulse Functions Technique for Tracking Control Synthesis of Uncertain Bilinear Systems with Multiple Time-Delayed States under Bounded Input Control

The present study tackles the tracking control problem for unstructured uncertain bilinear systems with multiple time-delayed states subject to control input constraints. First, a new method is introduced to design memory state feedback controllers with compensator gain based on the use of operational properties of block-pulse functions basis. The proposed technique permits transformation of the posed control problem into a constrained and robust optimization problem. The constrained robust least squares approach is then used for determination of the control gains. Second, new sufficient conditions are proposed for the practical stability analysis of the closed-loop system, where a domain of attraction is estimated. A real-world example, the headbox control of a paper machine, demonstrates the efficiency of the proposed method.

Couple-Group Consensus for First Order Discrete-Time Multiagent Systems With Competition-Cooperation and Input Saturation Constraints

Collaborative consensus control of multiagent systems has become an important research topic in the field of artificial intelligence in recent years. This paper deals with the couple-group consensus for the first order discrete-time systems with input saturation constraints. Compared to most previous studies, this article focuses on the control input constraints phenomenon in couple-group consensus problem. Based on the relationship between competition and cooperation, a new negotiation protocol is designed to achieve couple-group consensus. Furthermore, combining graph theory with Lyapunov theorem, the control gain condition is obtained. Finally, the results of numeric modeling show that the method is correctness and effectiveness.

Robust data‐driven fixed‐order controller synthesis: Model matching approach

In this paper, a new data-driven fixed-order H ∞ controller design method based on convex optimisation is proposed for linear single input single output systems. The proposed non-parametric frequency domain data based approach renders the need for a mathematical model of the controlled plant unnecessary. First, a semi-definite convex optimisation algorithm is proposed to simultaneously compute a minimal uncertainty model and an optimal nominal model from the experimental data. Then the H ∞ robust performance condition, control input constraints and the closed-loop model matching objective are described by convex functions with respect to the parameters of the controller. The usefulness and efficiency of the proposed approach are verified experimentally with application to the control of a thrust vector control system.

Robust Hierarchical Adaptive Fuzzy Relative Motion Coordination for Feature Points of Two Rigid Bodies With Input and Output Constraints

A model-based six-degrees-of-freedom relative motion coordinated control approach is proposed based on the adaptive hierarchical fuzzy logic system and the adaptive backstepping technique for the relative position tracking and attitude synchronization between feature points of two rigid bodies subject to control input constraints, output constraints, and model uncertainties. The control input saturation is compensated by the nonlinear anti-windup compensator, and the output constraints are handled by the barrier Lyapunov function-based backstepping design. The unknown misalignment vector of the feature point with respect to the center of the mass for the chaser is estimated by the element-wise adaptive law, while the model uncertainties and unknown dynamical couplings are compensated by the adaptive hierarchical fuzzy logic system to decrease the computational burden with respect to the traditional adaptive fuzzy systems. The ultimately uniformly bounded convergence of the relative pose and relative velocities is analyzed in the Lyapunov framework and the effectiveness of the proposed approach is validated by the numerical simulations.