Control Input Constraints Research Articles

Distributed economic MPC for LFC of multi-area power system with wind power plants in power market environment

The rising penetration of renewable energy and the diverse power transaction mechanisms in power market environment (PME) make the control problem of the power system more difficult. Considering environmental pressure and market competition pressure, it is more important to ensure the economic operation of power system in the control process. This paper presents a novel distributed economic model predictive control (DEMPC) strategy for the load frequency control (LFC) problem of a practical multi-area power system incorporating wind power plants (WPPs) in PME. Meanwhile, the real time economic optimization is achieved by integrating the economic factors into the objective function. A distribution company (DISCO) participation matrix (DPM) is applied to visualize the liberalization of power transactions between the DISCOs and dispatchable generation companies (DGENCOs). Area participation factors (apfs) are introduced to present the allocation of uncontracted load demands. The DEMPC controllers solve the optimization problem of power system with external disturbances and constraints including frequency fluctuation constraint, control input constraints, output power of WPP constraint and pitch angle constraint of the wind turbine. Response results for a three-area power system including WPPs and thermal power plants demonstrate the certain improvement of the system performance with the participation of wind turbines and the high-efficiency of the proposed DEMPC strategy.

Mathematical modelling and model predictive controller design of a quad tiltrotor UAV

A novel convertible unmanned aerial vehicle (UAV) with four tiltable rotors and a tandem-wing system has been developed. Considering the aerodynamic effect caused by the rotor-induced velocity, a mathematical model that contains the traditional free airstream analysis and rotor-induced effect analysis is proposed, from which the precise equilibrium point of the control inputs and states can be derived. Moreover, a control allocation algorithm is designed to provide the mapping relationship between traditional input variables and specific input variables of the UAV, so that the complicated mathematical model can be linearized for the design of model predictive control (MPC) system. In order to handle the control input constraints of the UAV system, an MPC system is applied for the trajectory tracking during the cruising phase. The simulation results demonstrate that the proposed model predictive control system has stability, accuracy without a random disturbance and quick response capabilities with a random disturbance during cruising trajectory tracking, which are in high demand for the quick UAV flight system.

Nonlinear uncertain systems with nonlinear control channel and unilateral input constraints

ABSTRACT In this paper, we study the constraints of control inputs, which is important to system performance, but rarely noticed. To deal with the constraints in practical situations, a new approach is proposed based on using diffeomorphism, which is the first introduced. Based on this transformation, the control input can be regarded as a function of an auxiliary variable. As a result, the value of control input is limited to a prescribed bound by choosing the proper bounded function. That is, it provides a new aspect to deal with the inequality control input constraints. The range of the input bounds is related to the uncertainties and can be designed according to the actual situation. This novel control is proven to guarantee uniform boundedness and uniform ultimate boundedness. In the simulation, we show this control renders a superior performance at a lower control cost, comparing with the LQR control.

Robust model predictive control for constrained networked nonlinear systems: An approximation-based approach

In this paper, a robust approximation-based model predictive control (RAMPC) scheme for the constrained networked control systems (NCSs) subject to external disturbances is proposed. At each sampling instant, the approximate discrete-time model (DTM) is utilized for solving the optimal control problem online, and the control input applied to continuous-time systems can then be determined. Such RAMPC scheme enables to implement MPC for the continuous-time systems in the digital environment, and meanwhile, achieves the state and control input constraints satisfaction in continuous-time sense. Furthermore, we also provide a guideline to determine the allowable sampling period. Sufficient conditions for the feasibility of the RAMPC scheme as well as the associated stability are developed. Finally, the effectiveness of the RAMPC scheme is shown through a numerical simulation.

A Novel Stochastic Predictive Stabilizer for DC Microgrids Feeding CPLs

In this work, a novel nonlinear approach is proposed for the stabilization of microgrids (MGs) with constant power loads (CPLs). The proposed method is constructed based on the incorporation of a pseudo-extended Kalman filter (EKF) into stochastic nonlinear model predictive control (MPC). In order to achieve high-performance and optimal control in dc MGs, estimating the instantaneous power flow of the uncertain CPLs and the available power units is essential. Thus, by utilizing the advantages of the stochastic MPC and the pseudo-EKF, an effective control solution for the stabilization of dc islanded MGs with CPLs is established. This technique develops a constrained controller for practical application to handle the states and control input constraints explicitly; furthermore, as it estimates the current by using the pseudo-EKF, it is a current-senseless approach. As noisy measurements are taken into account for the state estimation, it leads to a less conservative control action rather than the classical robust MPC, whereas it guarantees the global asymptotic stability in the presence of noisy measurements and parameter uncertainty. To validate the performance of the proposed controller, the attained results are compared with state-of-the-art controllers. Furthermore, the implementability of the proposed method is validated using real-time simulations on dSPACE hardware.

Coordination and vibration control for two sets of flexible satellites with input constraints and actuator failures

In this study, we considered the coordination and vibration control for two sets of flexible satellite systems with input constraints and actuator failures. The parameters of both systems were kept uniform, and one was called the master flexible satellite, and the other one was called slave flexible satellite. The two sets of the flexible satellite systems were modelled as partial differential equations. Coordination control laws were designed to turn the master flexible satellite system to the desired angle and then turn the slave system to the angle of the master satellite system. Furthermore, the hyperbolic tangent function was adopted to realize the control input constraint. The adaptive control laws were designed to ensure that the systems work normally even when the actuator fails. Lyapunov’s direct method was adopted and stability analysis was given. Finally, numerical simulations were conducted to validate the results.

Consensus problem for continuous‐time multiagent systems with nonconvex control input and velocity constraints

SummaryIn this work, a consensus problem with nonconvex control input and velocity constraints is studied for continuous‐time multiagent systems. In order to solve this problem, a fully distributed nonlinear algorithm is provided and an analysis approach is proposed based on the contraction property of an equivalent time‐varying system after a model transformation. It is shown that consensus can be achieved under the condition that there exists a directed spanning tree in the union of the communication graphs in each certain time interval. A numerical simulation is provided to show the obtained result.

Active chatter control in turning processes with input constraint

Regenerative chatter is an annoying dynamic phenomenon in machining processes. In this paper, an adaptive sliding mode controller (SMC) is developed for turning chatter mitigation in the presence of control input constraint, parameter uncertainties, and external disturbances. Adaptive laws are employed to estimate parameter uncertainties and disturbances, while a SMC, fulfilling the control input constraint, is designed to mitigate chatter. One unique feature of the developed adaptive approach is that it guarantees chatter suppression even in the presence of control input constraint. Theoretical analyses and experimental investigations are performed, and results demonstrate that the developed SMC with chosen controller parameters guarantees chatter mitigation in the tested examples.

A neural network approach for improving airfoil active flutter suppression under control-input constraints

This study deals with improving airfoil active flutter suppression under control-input constraints from the optimal control perspective by proposing a novel optimal neural-network control. The proposed approach uses a modified value function approximation dynamically tuned by an extended Kalman filter to solve the Hamilton–Jacobi–Bellman equality online for continuously improved optimal control to address optimality in parameter-varying nonlinear systems. Control-input constraints are integrated into the controller synthesis by introducing a generalized nonquadratic cost function for control inputs. The feasibility of using a performance index involving the nonquadratic control-input cost with the modified value function approximation is examined through the Lyapunov stability analysis. Wind tunnel experiments were conducted for controller validation, where an optimal controller synthesized offline via linear parameter-varying technique was used as a benchmark and compared. It is shown, both theoretically and experimentally, that the proposed method can effectively improve airfoil active flutter suppression under control-input constraints.

Formation flight of fixed-wing UAV swarms: A group-based hierarchical approach

This paper investigates a formation control problem of fixed-wing Unmanned Aerial Vehicle (UAV) swarms. A group-based hierarchical architecture is established among the UAVs, which decomposes all the UAVs into several distinct and non-overlapping groups. In each group, the UAVs form hierarchies with one UAV selected as the group leader. All group leaders execute coordinated path following to cooperatively handle the mission process among different groups, and the remaining followers track their direct leaders to achieve the inner-group coordination. More specifically, for a group leader, a virtual target moving along its desired path is assigned for the UAV, and an updating law is proposed to coordinate all the group leaders’ virtual targets; for a follower UAV, the distributed leader-following formation control law is proposed to make the follower’s heading angle coincide with its direct leader, while keeping the desired relative position with respect to its direct leader. The proposed control law guarantees the globally asymptotic stability of the whole closed-loop swarm system under the control input constraints of fixed-wing UAVs. Theoretical proofs and numerical simulations are provided, which corroborate the effectiveness of the proposed method.

Reinforcement Learning-Based Control for Nonlinear Discrete-Time Systems with Unknown Control Directions and Control Constraints

In this work, output-feedback control problems for a class of discrete-time non-affine nonlinear systems with unknown control directions and input constraints are considered by using reinforcement learning (RL) method. Two neural networks (NNs) implement the control: 1) a critic NN that estimates a non-quadratic strategic utility function (SUF) and 2) an action NN that generates optimized control input and minimizes the SUF. The implicit function theorem is applied to obtain the optimal control law since the control is appeared in a non-affine form. For the first time, the discrete Nussbaum gain is introduced to overcome the difficulty that the control directions are unknown and a non-quadratic SUF is used to deal with the control constraints in the RL-based control. The theoretical derivation of the uniformly ultimately boundedness of the NN weights and the closed-loop output tracking error is given. And two numerical examples have been supplied to valid the proposed method.

Explicit model predictive control of semi-active suspension systems with magneto-rheological dampers subject to input constraints

This article presents vibration control of a semi-active quarter-car suspension system equipped with a magneto-rheological damper that provides the physical constraint of a damping force. In this study, model predictive control was designed to handle the constraints of control input (i.e. the limited damping force). The explicit solution of model predictive control was computed using multi-parametric programming to reduce the computational time for real-time implementation and then adopted in the semi-active suspension system. The control performance of model predictive control was compared with that of a clipped linear-quadratic optimal controller, where the damping force was bound using a standard saturation function. Two types of road conditions (bump and random excitation) were applied to the suspension system, and the vibration control performance was evaluated through both simulations and experiments.

Persistification of Robotic Tasks

In this article, we propose a control framework that enables robots to execute tasks persistently, i.e., over time horizons much longer than robots’ battery life. This is achieved by ensuring that the energy stored in the batteries of the robots is never depleted. This condition is framed as a set invariance constraint in an optimization problem whose objective is that to minimize the difference between the robots’ control inputs and nominal control inputs corresponding to the task that is to be executed. We refer to this process as the persistification of a robotic task. Forward invariance of subsets of the state space of the robots is turned into a control input constraint by using control barrier functions. The solution to the formulated optimization problem with energy constraints ensures that the robotic task is persistent. To illustrate the operation of the proposed framework, we consider two tasks whose persistent execution is particularly relevant: environment exploration and environment surveillance. We show the persistification of these two tasks both in simulation and on a team of wheeled mobile robots on the Robotarium.

Prescribed performance dynamic surface control for trajectory tracking of quadrotor UAV with uncertainties and input constraints

To solve the problem of trajectory tracking control for quadrotor UAV with control input saturation, a novel prescribed performance backstepping dynamic surface control scheme is proposed in the presence of the model uncertainties and unknown external disturbances. In this work, the hyperbolic tangent function is introduced to solve the problem of control input saturation, and construct an auxiliary equation to reduce the saturation effect. Furthermore, the method introduces prescribed performance function, and converts the original constrained system into an equivalent unconstrained system through error transformation. Subsequently, dynamic surface technology is introduced to reduce the complexity of the control algorithm. At the same time, the nonlinear extended state observer is designed to estimate the generalised disturbance of the aircraft system. Finally, the Lyapunov function is selected to prove that all signals of the closed-loop system are uniformly ultimately bounded. Taking DJI M100 aircraft as the simulation object, the results show that the designed controller can effectively solve the problem of control input constraints and enable the system to reach the prescribed transient and steady-state tracking performance indexes.

Boundary control for passivity of multiple state or spatial diffusion coupled parabolic complex networks with and without control input constraint

In this paper, the passivity for multiple state or spatial diffusion coupled parabolic complex networks (PCNs) with and without control input constraint are considered. Firstly, we investigate the passivity of multiple state coupled PCNs without control input constraint, and some relevant criteria are derived by devising suitable boundary controller and making use of Lyapunov function method. What is more, the control input constraint for multiple state coupled PCNs is also taken into account, and several sufficient conditions are also derived so as to assure the existence of the boundary controller. In addition, the passivity of multiple spatial diffusion coupled PCNs with and without control input constraint is also investigated. Finally, two simulation examples are presented to verify the validity of the obtained criteria.

Robust Control of Underwater Vehicle-Manipulator System Using Grey Wolf Optimizer-Based Nonlinear Disturbance Observer and H-Infinity Controller

This paper proposes a new trajectory tracking scheme for the constrained nonlinear underwater vehicle-manipulator system (UVMS). For overcoming the unmodeled uncertainties, external disturbances, and constraints of control inputs in the operation of UVMS, a modified constrained H∞ controller with a basic computed-torque controller (CTC) and a new designed nonlinear disturbance observer (NDO) are proposed. The CTC gives the nominal model-based control. The NDO is designed based on the system dynamics and used to online provide the estimation of the lumped disturbances. However, the designed NDO is an observer of biased estimation, i.e., it has a blind domain of disturbance estimation which cannot be rejected. In order to reject the biased estimation, the modified constrained H∞ controller is designed but with new features. To the best of our knowledge, the conventional H∞ robust controller is generally designed by calculating the Riccati equation offline and ignoring the constraints of control inputs made by the physical actuators, which are poor in handling the time-varying environment. In order to solve these issues, the modified constrained H∞ robust controller online optimized by grey wolf optimizer (GWO) is designed to ensure the control system has a compensation of the biased estimation, a satisfied constrained control input, and a fast calculation. In this paper, we modify the prior method of offline calculating the Riccati equation of the conventional H∞ robust controller to be an online optimization scheme and proposed a new constrained evaluation function. The new constrained evaluation function is online optimized by the GWO, which can both find out the constrained suboptimal control actions and compensate the biased estimation of the NDO for the UVMS. The whole system stability is proved. The effectiveness of the fast online calculation, tracking accuracy, and lumped disturbances rejection is shown by a series of UVMS simulations.

A robust constrained control approach for flexible air‐breathing hypersonic vehicles

AbstractThis article investigates the robust adaptive control system design for the longitudinal dynamics of a flexible air‐breathing hypersonic vehicle (FAHV) subject to parametric uncertainties and control input constraints. A combination of back‐stepping and nonlinear disturbance observer (NDO) is utilized for exploiting an adaptive output‐feedback controller to provide robust tracking of velocity and altitude reference trajectories in the presence of flexible effects and system uncertainties. The dynamic surface control is introduced to solve the problem of “explosion of terms.” A new NDO is developed to guarantee the proposed controller's disturbance attenuation ability and to performance robustness against uncertain aerodynamic coefficients. To deal with the problem of actuator saturation, a novel auxiliary system is exploited to compensate the desired control laws. The stability of the presented NDO and controller is analyzed. Simulation results are given to demonstrate the effectiveness of the presented control strategy.

Cooperative Formation Control Under Switching Topology: An Experimental Case Study in Multirotors.

This article presents a novel design algorithm for the cooperative formation control of multirotors with directed and switching topology. A key strategy is to transform the formation control problem into an output agreement problem for which a class of cooperative controllers with successive loops is developed to achieve output agreement. For practical implementation, velocities and accelerations of the controlled multirotors are restricted to within desired ranges by introducing appropriate saturations to the loops. It is proved that each controlled multirotor admits an invariant set property, and the formation control objective can be achieved if a mild joint connectivity condition is satisfied by the switching topology. Along the way, this article also proves a result of independent interest in the output agreement problem subject to both velocity and control input constraints with switching topology. Numerical simulations and physical experiments are employed to verify the effectiveness of the proposed design.

Event-triggered synchronization of discrete-time neural networks: A switching approach

This paper investigates the event-triggered synchronization control of discrete-time neural networks. The main highlights are threefold: (1) a new event-triggered mechanism (ETM) is presented, which can be regarded as a switching between the discrete-time periodic sampled-data control and a continuous ETM; (2) a saturating controller which is equipped with two switching gains is designed to match the switching property of the proposed ETM; (3) a dedicated switching Lyapunov–Krasovskii functional is constructed, which takes the sawtooth constraints of control input into account. Based on these ingredients, the synchronization criteria are derived such that the considered error systems are locally stable. Whereafter, two co-design problems are discussed to maximize the set of admissible initial conditions and the triggering threshold, respectively. Finally, the effectiveness and advantages of the proposed method are validated by two numerical examples.

Distributed Containment Control of Fractional-order Multi-agent Systems with Double-integrator and Nonconvex Control Input Constraints

This paper mainly considers the distributed containment control problem for continuous-time fractional-order multi-agent systems (FOMASs) with double-integrator, where the control input of each agent is constrained to lie in a nonconvex set. A distributed projection containment control algorithm is designed for each follower. To finish the convergence analysis, the original closed-loop system is first changed into an equivalent one by a proper model transformation and the method of the L1 interpolation approximation is introduced to deal with the projection operator. Then, by using the properties of the convex hull and the Mittag-Leffler function, it is shown that the largest distance between the followers and the convex hull spanned by leaders tends to zero asymptotically, while all agents’ control inputs are constrained to stay in their corresponding nonconvex constraint sets. Finally, numerical simulations are provided to verify the effectiveness of the theoretical results.