Presence Of Input Constraints Research Articles

An analytical adaptive optimal control approach without solving HJB equation for nonlinear systems with input constraints

AbstractThis paper presents an analytical method to solve the optimal control problem for affine nonlinear systems with unknown drift dynamics. A new non‐quadratic cost function over an infinite horizon is presented that considers input constraints and includes the cost of the feed‐forward component of the control law. The mean value theorem for vector‐valued functions has been used to derive an integral form of this theorem. Based on this theorem, a rigorous proof is provided demonstrating that the cost function can be converted into another form. In the presence of input constraints, this converted form enables extracting the optimal control solution without solving the HJB equation. Additionally, unknown nonlinearity effects in drift dynamics are compensated in the control input. This is accomplished by estimating the unknown drift dynamics via an adaptive neural network (NN) approach. It is proven that the states and weights of NN are uniformly ultimately bounded based on a Lyapunov technique. The necessary and sufficient conditions are provided that ensure the optimality of the infinite horizon optimal control problem with a discount factor. As a result, it is demonstrated that the proposed approach satisfies the optimality criteria. To evaluate the effectiveness of the proposed approach, simulation examples are provided.

Autonomous Spacecraft Attitude Reorientation Using Robust Sampled-Data Control Barrier Functions

This paper presents a provably safe method for constrained reorientation of a spacecraft in the presence of input constraints, bounded disturbances, and fixed frequency zero-order-hold (ZOH) control inputs. The set of states satisfying all pointing and rate constraints, herein called the safe set, is expressed as the intersection of the sublevel sets of several constraint functions, which are subsequently converted into control barrier functions (CBFs). The method then extends prior results on utilizing CBFs with ZOH controllers to the case of relative-degree-2 constraint functions, as occurs in the constrained attitude reorientation problem. The developed sampled-data controller is also shown to remain provably safe in the presence of input constraints and bounded disturbances. Finally, the method is validated and compared to three prior approaches via both low-fidelity and mid-fidelity simulations.

Robust Control Barrier Functions under high relative degree and input constraints for satellite trajectories

This paper presents methodologies for constructing Control Barrier Functions (CBFs) for nonlinear, control-affine systems, in the presence of input constraints and bounded disturbances. More specifically, given a constraint function with high-relative-degree with respect to the system dynamics, the paper considers three methodologies, two for relative-degree 2 and one for higher relative-degrees, for creating CBFs whose zero sublevel sets are subsets of the constraint function’s zero sublevel set Three special forms of Robust CBFs (RCBFs) are developed as functions of the input constraints, system dynamics, and disturbance bounds, such that the resultant RCBF condition on the control input is always feasible for states in the RCBF zero sublevel set. The RCBF condition is then enforced in a switched fashion, which allows the system to operate safely without enforcing the RCBF condition when far from the safe set boundary and allows tuning of how closely trajectories approach the safe set boundary The proposed methods are verified in simulations demonstrating the developed RCBFs in an asteroid flyby scenario for a satellite with low-thrust actuators.

Sliding mode control‐based distributed fault tolerant tracking control for multiple unmanned aerial vehicles with input constraints and actuator faults

AbstractIn this article, the distributed tracking control problem is studied for the formation flight systems of unmanned aerial vehicles (UAVs) in presence of input constraints and actuator faults. Different from the traditional approximation technique, such as radial basis function neural networks and fuzzy logic systems, the novel broad learning system approximation technique is introduced in this study to identify the unknown lumped disturbances including external disturbances, input constraints and additive actuator faults. Combining dynamic surface control technique with the fractional order sliding mode control, a distributed fault tolerant tracking control strategy is developed for the formation flight systems of UAVs. Besides, the adverse effect of multiplicative actuator faults is compensated by the Nussbaum function, such that the satisfactory cooperative tracking control performance of the formation flight systems is obtained. Finally, a simulation experiment is given to demonstrate the superiority of the proposed control scheme compared with other existing results.

Neural learning impedance control of lower limb rehabilitation exoskeleton with flexible joints in the presence of input constraints

AbstractThis article presents neural learning based adaptive impedance control for a lower limb rehabilitation exoskeleton with flexible joints (LLREFJ). First, the full model consisting of both the rigid link and the flexible joint is obtained for the LLREFJ. Second, neural networks are used to compensate for the system uncertainties and external disturbance and an adaptive impedance controller is proposed by establishing an impedance error. In order to improve the control performance and enhance the system robustness, periodic dynamics is considered according to the repetitive motion of the rehabilitation process and handled by a repetitive learning algorithm. Then, the stability of the full system is proved rigorously by Lyapunov methods. Finally, comparative simulation reveals that the designed adaptive neural learning controller has improved the control performance.

Fixed-time control under spatiotemporal and input constraints: A Quadratic Programming based approach

This paper presents a control synthesis framework for a general class of nonlinear, control-affine systems under spatiotemporal and input constraints. First, we study the problem of fixed-time convergence in the presence of input constraints. The relation between the domain of attraction for fixed-time stability with respect to input constraints and the required time of convergence is established. It is shown that increasing the control authority or the required time of convergence can expand the domain of attraction for fixed-time stability Then, we consider the problem of finding a control input that confines the closed-loop system trajectories in a safe set and steers them to a goal set within a fixed time. To this end, we present a Quadratic Programming (QP) formulation to compute the corresponding control input. We use slack variables to guarantee the feasibility of the proposed QP under input constraints. Furthermore, when strict complementary slackness holds, we show that the solution of the QP is a continuous function of the system states and establish the uniqueness of closed-loop solutions to guarantee forward invariance using Nagumo’s theorem. To corroborate our proposed methods, we present two case studies, an example of an adaptive cruise control problem and a two-robot motion planning problem.

Global Path-Following for Marine Vessel with Control Lyapunov Function in Input Constraint

For marine vessels, autopilot systems require global stability, even under input constraints. This study proposes a straight-path-following control law that guarantees global asymptotic stabilization in the presence of input constraints. We consider a kinematic model based on the pivoting point as a marine vessel maneuvering model and design a control Lyapunov function (CLF) using the minimum projection method. Finally, a smooth angular velocity input is obtained. This controller satisfies the constraint by determining the range of controller gain. The effectiveness of the proposed method was confirmed by a computer simulation.

Fault-Tolerant Tracking Control of Discrete-Time T-S Fuzzy Systems With Input Constraint

Active fault-tolerant control strategy aimed at tracking is studied for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems in the presence of input constraint and additive fault. In the fault-free case, the state space of the system is partitioned based on the presence or absence of inputs. Using the parallel distributed compensation technique, input-to-state stability is proved for the error dynamics. For input constraint satisfaction, a model predictive control based reference-management unit is proposed in the form of an online optimization module that solves a quadratic programming problem. In the faulty case, the fault-free system is used as a reference model that satisfies the input constraint. Then, the concept of virtual actuator is used to make the behavior of the faulty system similar to the behavior of the fault-free system by controlling the performance degradation. In this article, a full-order observer can be used for fault estimation. In order to keep the control input of the faulty system within the admissible range defined for the fault-free system, a constraint-change scenario is considered. After detecting the fault, the constraint on the input of the fault-free system is changed in a way to keep the control input of the faulty system in the specified range. All design criteria are formulated as a linear matrix inequality problem. In order to evaluate the proposed control approach, simulations are performed on two systems: a 3-DoF helicopter and a 2-D overhead crane.

Robust adaptive multistage anti-windup dynamic surface control for dynamic positioning ships with mismatched disturbance

In this paper, a novel robust adaptive multistage anti-windup control strategy is developed for dynamic positioning ships in presence of input constraint, mismatched disturbance and external disturbance. Based on dynamic surface control technique, a composite control law, where both mismatched and matched disturbances are compensated, is established to stabilize the system without the requirement of solving any partial differential equations. In particularly, the mismatched disturbance caused by the model transformation is analyzed firstly and the better steady performance is achieved. In addition, a novel multistage anti-windup control based on anticipatory activation compensation is constructed to handle the input constraint while the transient performance is improved significantly. Moreover, the stability of the closed-loop system is proven via Lyapunov technique rigorously, and the tracking error can be forced into an arbitrarily small neighborhood around zero. Finally, simulations with comparisons demonstrate the effectiveness of the proposed method.

Consensus tracking of nonlinear multi-agent systems under input saturation with applications: A sector-based approach

This paper focuses on the consensus tracking control of nonlinear multi-agent systems by utilizing the quadratic inner-bounded (QIB) and the one-sided Lipschitz (OSL) conditions in the presence of input saturation constraint under a directed communication topology. A novel sector constraint for the saturation function to formulate consensus control of nonlinear systems under saturating inputs is derived. This sector condition is applied to develop a leader-following consensus of nonlinear agents. A local treatment of the consensus control, ensuring a guaranteed region of stability in the presence of input constraints is provided herein. A computationally simple convex routine-based approach is attained for extraction of the coupling weight and gain of the relative state feedback-based consensus protocol along with the enlargement of the region of stability. Unlike the conventional schemes, the proposed approach can deal with OSL nonlinear agents, effectively employs the information of communication topology in the sector condition, and can be applied to both linear and nonlinear regions of actuators. Moreover, a useful consensus approach for the Lipschitz nonlinear agents is obtained as a particular scenario of the resultant method. Numerical examples to demonstrate the applications and effectiveness of the proposed approach for the input-constrained nonlinear mobile and robotic agents are provided.

Semi-Global Consensus Problems of Discrete-Time Multi-Agent Systems in the Presence of Input Constraints

This paper studies the consensus problems of the discrete-time multi-agent systems (MASs) in the presence of input saturation constraints over directed communication networks. Two kinds of consensus problems, of the leaderless consensus problem with no leader agent and the containment control problem with multiple leader agents, are investigated in this paper. Low gain feedback consensus algorithms based on the improved discretetime parametric algebraic Riccati equation (ARE) are proposed to solve the consensus problems. For the MAS without any leader, the trajectories of all agents converge together when the communication networks contain a directed spanning tree. For the MAS with multiple leaders, the trajectories of all follower agents converge to the convex hull spanned by the leader agents when there is at least one leader agent which is trackable for each follower agent. Simulation examples are provided to verify the theoretical results.

Three-dimensional modeling and input saturation control for a two-link flexible manipulator based on infinite dimensional model

In this paper, the modeling and controlling problem is studied for a two-link rigid-flexible manipulator in three-dimensional (3D) space under input saturation. The dynamics of the 3D manipulator is first derived in infinite dimension model, which is represented by partial differential equations (PDEs). The controller can achieve joint angle control and vibration suppression control in the presence of input constraint. The stability analysis of the closed-loop system is given based on LaSalle’s Invariance Principle. Numerical simulations illustrate the effectiveness of the proposed controller.

Finite-time attitude control for rigid spacecraft subject to actuator saturation

This paper considers the problem of attitude stabilizing control for rigid spacecraft in the presence of input constraints. To address this problem, a smooth model is first presented such that its output is always in agreement with the constraints imposed by the actuators. Then, based on the “adding a power integrator” method and the backstepping technique, a novel finite-time attitude control scheme is proposed. The finite-time stability of the resultant closed-loop system is guaranteed by using the Lyapunov approach. Finally, the effectiveness of the control scheme derived here is illustrated by numerical simulations.

Fuzzy Adaptive DSC Design for an Extended Class of MIMO Pure-Feedback Non-Affine Nonlinear Systems in the Presence of Input Constraints

A novel adaptive fuzzy dynamic surface control (DSC) scheme is for the first time constructed for a larger class of (multi-input multi-output) MIMO non-affine pure-feedback systems in the presence of input saturation nonlinearity. First of all, the restrictive differentiability assumption on non-affine functions has been canceled after using the piecewise functions to reconstruct the model for non-affine nonlinear functions. Then, a novel auxiliary system with bounded compensation term is firstly introduced to deal with input saturation, and the dynamic system employed in this work designs a bounded compensation term of tangent function. Thus, we successfully relax the strictly bounded assumption of the dynamic system. Additionally, the fuzzy logic systems (FLSs) are used to approximate unknown continuous systems functions, and the minimal learning parameter (MLP) technique is exploited to simplify control design and reduce the number of adaptive parameters. Finally, two simulation examples with input saturation are given to validate the effectiveness of the developed method.

NON-LINEAR DIRECT JOINT CONTROL FOR MANIPULATOR HANDLING A FLEXIBLE PAYLOAD WITH INPUT CONSTRAINTS

In this paper, we propose a non-linear control strategy for a robotic manipulator handling a flexible payload in the presence of input constraints and input disturbances, which does not require end-point boundary control.

Convergence analysis of feedback-based iterative learning control with input saturation

The use of feedback-based iterative learning control (ILC) has been widely reported in the literature to reduce large transient errors in the iteration-domain. Using both feedback and feed-forward (ILC) would result in large control input. However, due to the existence of hardware limitation, input constraints exist. Such a hard constraint might lead to unacceptable performances such as unstable trajectories in the time-domain and steady-state error in the iteration-domain. In this paper, a feedback-based ILC design is proposed for a class of linear-time-invariant system in the presence of input constraints. The proposed control scheme consists of two parts: one (feedback) deals with the performance in time domain while the other (ILC) ensures ensure the perfect tracking performance. With the help of composite energy function, it is shown that the proposed algorithm can ensure the perfect tracking performance in the presence of hard input constraints under appropriate assumptions. Simulation results support the theoretical findings.

Robust adaptive control for dynamic positioning ships in the presence of input constraints

This note investigates the dynamic positioning control problem of full-actuated marine vehicles in the presence of system uncertainties and input constraints. In the control algorithm, the ship model uncertainty is approximated by the radial-basis-function neural networks. The effect of input saturation is analyzed by the auxiliary system, states of the auxiliary system are employed to develop the control scheme. By virtue of the dynamic surface control technique, the inherent problem of “explosion of complexity” problem occurred during conventional Backstepping design framework is avoided. The semi-global uniformly ultimately bounded stability of the closed-loop is guaranteed by Lyapunov theory. Since the minimal learning parameterization based adaptive law is derived, the number of parameters updated online is reduced to 6. Consider the servo-system uncertainty, the control inputs of interest are achieved as the measurable propeller pitch whose characteristics would facilitate the implementation of the algorithm in the practical engineering. Finally, by employing a supply vessel as the plant, comparison simulations are conducted to demonstrate the effectiveness and robustness of the proposed algorithm.

Trajectory Tracking Control of a Quadrotor Aerial Vehicle in the Presence of Input Constraints

In this paper, we address the control problem of a Quadrotor Aerial Vehicle (QAV) in the presence of the input constraints. For this purpose, a separation principle is applied in the control design. The QAV model is decoupled and constructed as a cascaded structure to handle its underactuated property. By imposing the constraints on the orientation angles, we show that the QAV will be never overturned. Then, a combination of the backstepping method, barrier Lyapunov and saturation functions is used in the control design for each subsystem to deal with both input and output constraints. Our design renders the cascaded system of the QAV into the form in which an Input-to-State Stable (ISS) subsystem is driven by an asymptotic subsystem, and hence the stability of the overall cascaded system of the QAV is ensured. In addition, the tracking errors are guaranteed to converge to the origin. Simulation results are provided to illustrate the effectiveness of the proposed control.

Model reference adaptive attitude control for near space hypersonic vehicle with mismatched uncertainties

In this paper, a new model reference adaptive attitude control based on backstepping approach is presented for near space hypersonic vehicle with mismatched uncertainties. Firstly, the attitude dynamic model of near space hypersonic vehicle is divided into two control loops, which is composed of an attitude angle control loop and an attitude angular rate control loop. Secondly, a novel model reference adaptive attitude control approach is proposed by introducing reference model to avoid the calculating expansion problem in backstepping technique. Meanwhile, the reference models for every loop are independently designed to improve the tracking performance. The stability of attitude control system is strictly proven by using Lyapunov stability theory. Finally, the simulation results demonstrate that the attitude control system by applying the proposed method has good stability, dynamic property and strong robustness in the presence of input constraints and parameters perturbation.

Modified Newton method based iterative learning control design for discrete nonlinear systems with constraints

This paper considers the design of iterative learning control laws for classes of nonlinear dynamics. In particular, a new Newton method design is developed for discrete nonlinear systems in the presence of input constraints, where such constraints will arise in applications. The new design is based on the use of a penalty function and an iterative method for solving an unconstrained nonlinear optimization problem with an algorithm that has monotonic and super linear convergence characteristics. In this new algorithm the input inequality constraints are transformed into equality form by adding auxiliary variables. A cost function is then minimized to produce the new iterative learning control law design. Finally, a simulation based case study is given to illustrate the performance of the new design.