Time-varying State Constraints Research Articles

Dynamic Event-Triggered Adaptive Fixed-Time Fuzzy Tracking Control for Stochastic Nonlinear Systems Under Asymmetric Time-Varying State Constraints

Dynamic Event-Triggered Adaptive Fixed-Time Fuzzy Tracking Control for Stochastic Nonlinear Systems Under Asymmetric Time-Varying State Constraints

Adaptive neural network control for nonholonomic systems with partial/full or without state constraints

In this paper, we present a unifying neural networks-based adaptive control framework for nonholonomic systems with partial/full state constraints or without constraint requirements. By considering the tan-type barrier Lyapunov function, constraint requirements are handled for the x0-subsystem. A novel nonlinear state-dependent function is constructed to meet asymmetric time-varying state constraints for the x-subsystem. Combined with backstepping method, a coordinate transformation is designed to transform the original constrained system into unconstrained system. Then, we put forward the dynamic surface control to eliminate feasibility conditions of virtual controllers. In addition, neural networks can be introduced to compensate for the uncertainties of nonholonomic systems. It is demonstrated that without modifying control structure the adaptive neural networks controller guarantees the stability of nonholonomic systems, while asymmetric time-varying state constraints can be satisfied. Simulation examples of mobile robot systems further validate the efficacy of the devised algorithm.

Adaptive Tracking Control of State-Constrained Strict-Feedback Nonlinear Systems Using Direct Method

In this article, we focus on adaptive tracking control design for strict-feedback nonlinear systems with full state constraints. Unlike the barrier Lyapunov function method, all theoretical results are derived by direct method instead of introducing nonlinear state-dependent transformations, which reduces the calculated amount and the high sensitivity of control signals, and provides a new perspective to solve state-constrained problems. Then, by using the backstepping technique, the proposed adaptive controller maintains that the output closely tracks the desired trajectory, all signals in the closed-loop systems are bounded and the time-varying state constraints are not violated. Finally, two numerical simulations are provided to exhibit the effectiveness and superiority of the proposed adaptive tracking controller.

Time-Optimal Model Predictive Control of Permanent Magnet Synchronous Motors Considering Current and Torque Constraints

In various permanent magnet synchronous motor (PMSM) drive applications the torque dynamics are an important performance criterion. Here, time-optimal control (TOC) methods can be utilized to achieve highest control dynamics. Applying state-of-the-art TOC methods leads to unintended overcurrents and torque over- and undershoots during transient operation. To prevent these unintended control characteristics while still achieving TOC performance the time-optimal model predictive control (TO-MPC) is proposed in this work. The TO-MPC contains a reference pre-rotation (RPR) and a continuous control set model predictive flux control (CCS-MPFC). By applying Pontryagin's maximum principle, the TOC solution trajectories for states and inputs of the PMSM are determined neglecting current and torque limits. With the TOC solution, a flux linkage reference for the CCS-MPFC is calculated that corresponds to a pre-rotation of the operating point in the stator-fixed coordinate system. This pre-rotated flux linkage reference is reached in minimum time without overcurrents and torque over- as well as undershoots by incorporating current and torque limits as time-varying softened state constraints into the CCS-MPFC. Simulative and experimental investigations for linearly and nonlinearly magnetized PMSMs in the whole speed and torque range show that, compared to state-of-the-art TOC methods, overcurrents and torque over- as well as undershoots are prevented by the proposed TO-MPC.

System Transformation-Based Event-Triggered Fuzzy Control for State Constrained Nonlinear Systems With Unknown Control Directions

This paper focuses on the event-triggered (ET) fuzzy tracking control for uncertain state constrained strict-feedback systems with unknown control directions. A novel nonlinear transformed function is developed to transform the constrained system states into the counterpart without any constraints. An ingenious adaptation law is developed to co-design the control law and the ET rule, thereby effectively compensating the sampling error caused by the ET rule under unknown control directions. Based on the presented adaptation law and the Nussbaum gain technique, a novel ET fuzzy tracking control strategy is proposed, which can handle the situations with and without state constraints in a unified way without readjusting the control scheme. Subsequently, the nonlinear transformed function is extended to the time-varying state constraints, and the corresponding ET fuzzy control scheme is also modified to guarantee the closed-loop boundedness. The proposed two control strategies guarantee the satisfactory tracking performance, avoid the violation of the prescribed state constraints, and decrease the communication load effectively. Finally, the usefulness of the developed methods is verified through two simulation examples.

Output-Feedback Adaptive Fuzzy Control for Nonlinear Systems Under Time-Varying State Constraints

Output-Feedback Adaptive Fuzzy Control for Nonlinear Systems Under Time-Varying State Constraints

Switched systems with transient unsustainable modes: Stability and feasibility

Externally switched systems have unique characteristics that make it is especially challenging to ensure their stability and feasibility. These challenges are exacerbated when the system contains modes with uncontrollable dynamics, tight input constraints, and/or unstable dynamics. While past results have addressed stability and feasibility of switched systems, little has been done, thus far, for constrained, switched systems with uncontrollable modes. This work examines linear systems in this context with unknown switching signals that have upper and lower bounds on the duration the system will dwell in a mode and constraints on which modes can be switched between. These constraints create a finite number of different possible switching signal statuses, which depend on the current mode and the time spent dwelling in that mode. At design time, state constraints corresponding to each possible status are computed and, at run-time, are activated based on the switching signal status. If these time-varying state constraints respect certain properties, persistent feasibility, convergence, and exponential stability are established under all possible switching signals. This is later extended to be a sequence of state constraints for use in model predictive control. These results are then demonstrated on two numerical examples.

IBLF-Based Fixed-Time Fault-Tolerant Control for Fixed-Wing UAV With Guaranteed Time-Varying State Constraints

This paper proposes a novel adaptive fixed-time fault-tolerant control method for the fixed-wing unmanned aerial vehicle (UAV) subject to asymmetric time-varying full state constraints. The UAV nonlinear dynamics of six-degree-of-freedom (6-DOF) with twelve-state-variables is considered in this article, rather than only longitudinal/lateral or attitude dynamics in most existing results. A novel Integral Barrier Lyapunov Function (IBLF) is applied for the first time to solve the control problem of the UAV with the asymmetric time-varying full state constraints, which reduces the conservativeness of the conventional IBLF-based method. Furthermore, a continuous switching function is introduced to solve the singularity problem which typically appears in the fixed-time control methods when tracking errors approach to zero. It is rigorously proved that all the states are forced in the asymmetric time-varying bounds and the tracking errors of velocity and attitude converge to a residual set around origin within fixed time. Finally, the simulation results are given to validate the effectiveness of the proposed scheme.

DO-Based Adaptive Consensus Control for Multiple MUAVs With Dynamic Constraints

This article investigates the adaptive consensus control problem for a group of multirotor unmanned aerial vehicles (MUAVs) subject to dynamic state constraints and unmatched external disturbances. An adaptive inner–outer loop controller is devised based on the backstepping method, where the issue of “explosion of complexity” is solved via a first-order sliding-mode differentiator. By introducing a barrier function-based state transformation technique into the outer loop controller design, the dynamic constraints covering different types of time-varying state constraints can be addressed without reconfiguring the controller structure. Meanwhile, a neural-network-based disturbance observer is constructed to estimate the external disturbances. Consequently, the applicability and robustness of controller are improved, such that the position tracking control can be implemented in severe environments. Moreover, the inner loop controller is established by virtue of a distributed sliding-mode estimator so as the consensus control for attitude systems of multiple MUAVs can be realized rapidly. Finally, a simulation example is presented to demonstrate the validity and superiority of the proposed control strategy.

Adaptive Control of Euler-Lagrange Systems under Time-varying State Constraints without a Priori Bounded Uncertainty

In this article, a novel adaptive controller is designed for Euler-Lagrangian systems under predefined time-varying state constraints. The proposed controller could achieve this objective without a priori knowledge of system parameters and, crucially, of state-dependent uncertainties. The closed-loop stability is verified using the Lyapunov method, while the overall efficacy of the proposed scheme is verified using a simulated robotic arm compared to the state of the art.

Prescribed Finite-Time Adaptive Neural Tracking Control for Nonlinear State-Constrained Systems: Barrier Function Approach.

The purpose of this article is to present a novel backstepping-based adaptive neural tracking control design procedure for nonlinear systems with time-varying state constraints. The designed adaptive neural tracking controller is expected to have the following characters: under its action: 1) the designed virtual control signals meet the constraints on the corresponding virtual control states in order to realize the backstepping design ideal and 2) the output tracking error tends to a sufficiently small neighborhood of the origin with the prescribed finite time and accuracy level. By combining the barrier Lyapunov function approach with the adaptive neural backstepping technique, a novel adaptive neural tracking controller is proposed. It is shown that the constructed controller makes sure that the output tracking error converges to a small neighborhood of the origin with the prespecified tracking accuracy and settling time. Finally, the proposed control scheme is further tested by simulation examples.

Adaptive fault-tolerant control for the ascent phase of hypersonic vehicle with time-varying full state constraints

In this paper, a novel attitude adaptive fault-tolerant control (FTC) scheme is presented for the ascent phase of hypersonic vehicle (HSV) subject to pneumatic-propulsion coupling and time-varying full state constraints, which are unique to the ascent phase of HSV and are caused by the integrated design of fuselage engine and power system switching. Compared with some existing methods for time-varying constraints, the proposed control method contains a constrained function so that constraints can be incorporated directly into the state, which asymmetric and time-varying state constraints can be handled without feasibility conditions. Moreover, by designing a time-varying scaling function matrix to transform the tracking error, the proposed method enables the practical tracking control to be achieved without any switching for a multi-input multi-output (MIMO) pure-feedback system which is transformed from the ascent phase model of HSV. Besides, to incorporate constraints into the state, an adaptive fault estimation filter is designed to estimate unknown faults and disturbances. It is proved that the proposed FTC scheme can guarantee that the closed-loop control system is stable and the time-varying state constraints are satisfied. Finally, simulation results are provided to illustrate the effectiveness of the proposed FTC scheme.

Adaptive security control of time-varying constraints nonlinear cyber-physical systems with false data injection attacks

In this article, an adaptive security control scheme is presented for cyber-physical systems (CPSs) suffering from false data injection (FDI) attacks and time-varying state constraints. Firstly, an adaptive bound estimation mechanism is introduced in the backstepping control design to mitigate the effect of FDI attacks. Secondly, to solve the unknown sign time-varying state-feedback gains aroused by the FDI attacks, a type of Nussbaum function is employed in the adaptive security control. Then, by constructing a barrier Lyapunov function, it can be ensured that all signals of controlled system are bounded and the time-varying state constraints are not transgressed. Finally, the provided simulation examples demonstrate the effectiveness of the proposed controller.

Special issue on PID control in the information age: Theoretical advances and applications

Special issue on PID control in the information age: Theoretical advances and applications

A novel asymmetrical integral barrier Lyapunov function-based trajectory tracking control for hovercraft with multiple constraints

This paper addresses the trajectory tracking control problem of a hovercraft with asymmetrical time-varying multiple state constraints in the presence of unmodeled dynamics and external disturbances. By using the four-degree-of-freedom vector mathematical model of hovercraft, an extended state observer is adopted to provide the lumped disturbance estimation. Then, the virtual surge velocity and yaw angular velocity control laws are obtained by using a regular log-type barrier Lyapunov function to stabilize the position and yaw errors. In addition, compared with the traditional symmetric integral barrier Lyapunov function, a new asymmetric integral barrier Lyapunov function is introduced to the design process in this paper to address asymmetric state constraint problems. The surge velocity and yaw angular velocity to the inside of the boundary are analyzed to guarantee the safe turning motion or performance required at high speed, and the tracking errors of the closed-loop system are ultimately uniformly bounded by using the cascade system’s stability lemma. The effectiveness of the proposed control scheme is shown via numerical simulations.

Cross backstepping sliding mode control using integral barrier Lyapunov function for cross‐strict feedback systems

Cross-backstepping control for a type of uncertain non-strict-feedback non-linear systems with time-varying partial state constraints is the main subject of this work. Non-strict-feedback non-linear systems are partitioned into two strict-feedback non-linear subsystems: constrained subsystem and unconstrained subsystem. An integral barrier Lyapunov function (IBLF) is used in each step of the backstepping design for the constrained subsystem to guarantee the boundedness of the fictional or actual state tracking errors. The effect of uncertainty is reduced using a hybrid cross-backstepping sliding mode control (SMC) technique. The algorithm employs a systematic approach to developing control laws for non-linear systems with matched and unmatched uncertainties. The simulation results of the proposed controller are juxtaposed with those of the cross backstepping with the time-varying barrier Lyapunov function (TVBLF). The results demonstrate the overall better performance of the proposed method.

Anti-Saturation-Based Adaptive Sliding-Mode Control for Active Suspension Systems With Time-Varying Vertical Displacement and Speed Constraints

In this article, an adaptive sliding-mode control scheme is developed for a class of uncertain quarter vehicle active suspension systems with time-varying vertical displacement and speed constraints, in which the input saturation is considered. The integral terminal SMC is adopted to improve convergence accuracy and avoid singular problems. In addition, neural networks are used to model unknown terms in the system and the backstepping technique is taken into account to design the actual controller. To guarantee that the time-varying state constraints are not violated, the corresponding Barrier Lyapunov functions are constructed. At the same time, a continuous differentiable asymmetric saturation model is developed to improve the stability of the system. Then, the Lyapunov stability theory is used to verify that all signals of the resulting system are semi globally uniformly ultimately bounded, time-varying state constraints are not violated, and error variables can converge to the small neighborhood of 0. Finally, results of the simulation of the designed control strategy are given to further prove the effectiveness.

Barrier Lyapunov function-based fixed-time FTC for high-order nonlinear systems with predefined tracking accuracy

This article proposes a fixed-time adaptive fault-tolerant control methodology for a larger class of high-order (powers are positive odd integers) nonlinear systems subject to asymmetric time-varying state constraints and actuator faults. In contrast with the state-of-the-art control methodologies, the distinguishing features of this study lie in that: (a) high-order asymmetric time-varying tan-type barrier Lyapunov function (BLF) is devised such that the state variables can be convergent to the preassigned compact sets all the time provided their initial values remain therein, which not only preserves the constraints satisfaction, but warrants the validity of the adopted neural network approximator; (b) the proposed control design ensures the tracking errors converge to specified residual sets within fixed time and makes the size of the convergence regions of tracking errors adjustable a priori by means of a new BLF-based tuning function and a projection operator; (c) a variable-separable lemma is delicately embedded into the control design to extract the control terms in a “linear-like” fashion which not only overcomes the difficulty that virtual control signals appear in a non-affine manner, but also solves the problem of actuator faults. Comparative simulations results finally validate the effectiveness of the proposed scheme.

Finite-Time Fuzzy Adaptive Constrained Tracking Control for Hypersonic Flight Vehicles With Singularity-Free Switching

This article proposes a fuzzy adaptive design solving the finite-time constrained tracking for hypersonic flight vehicles (HFVs). Actuator dynamics and asymmetric time-varying constraints are considered when solving this problem. The main features of the proposed design lie in 1) introducing a novel piecewise but differentiable switching control law, with an appropriate design thought to avoid the singularity issues typical of finite-time control; 2) handling actuator magnitude, bandwidth, and rate constraints, thanks to the introduction of an auxiliary compensating system counteracting the adverse effects caused by actuator physical constraints, while guaranteeing the closed-loop stability; and 3) handling asymmetric time-varying state constraints, thanks to the introduction of tan-type barrier Lyapunov functions working for both constrained and unconstrained scenarios. Comparative simulation results illustrate the effectiveness of the proposed strategy over existing methods for HFVs in terms of convergence, smoothness, actuator performance, and constraints satisfaction.

Reinforcement learning-based close formation control for underactuated surface vehicle with prescribed performance and time-varying state constraints

This paper studies close formation control problem with prescribed performance and time-varying state constraints for a group of 4-degrees-of-freedom (DOF) underactuated surface vehicles (USVs) subject to actuator faults, input saturation and input delay. A finite-time sliding mode control (SMC) scheme based on reinforcement learning (RL) algorithm is introduced to guarantee prescribed formation performance without violating velocity error constraints. By using actor-critic neural network (NN)-based RL algorithm, the actuator faults and system uncertainties are accurately estimated. Afterwards, an exponential decreasing boundary function is developed to suppress overshoot more reasonably, and a novel mechanism of switching gain is given to alleviate chattering inherent in SMC while the RL-based compensation term is constructed to handle the formation accuracy problem caused by the reduced switching gain. Besides, auxiliary nonlinear continuous function and Pade approximation have been successfully applied to process actuator saturation and input delay, respectively. Numerical simulations and experimental results are exhibited to verify the effectiveness and superior formation performance of the proposed control method.