Asymmetric Full-state Constraints Research Articles

Observer-Based Event-Triggered Bipartite Consensus for Nonlinear Multi-Agent Systems: Asymmetric Full-State Constraints

Observer-Based Event-Triggered Bipartite Consensus for Nonlinear Multi-Agent Systems: Asymmetric Full-State Constraints

Adaptive Finite-Time Fuzzy Control for Uncertain Nonlinear Systems with Asymmetric Full-State Constraints

This paper studies the adaptive finite-time fuzzy control issue associated with uncertain nonlinear systems that exhibit asymmetric constraints on the full state. A distinct function, constrained by nonlinear states, is designed to mitigate the excessive breach of these full-state boundaries. Unlike the standard barrier Lyapunov function (BLF) method, this approach solves symmetric and asymmetric full-state constraints without modifying the controller structure, and it does not require any additional assumptions about virtual control to be met. Simultaneously employing approximating functions using fuzzy logic systems and incorporating dynamic surface control technology integrated with a first-order filter, the unknown nonlinear functions emanating from the suggested controller strategy are estimated. Additionally, this approach addresses the prevalent problem of complexity explosion observed in conventional backstepping techniques. An adaptive finite-time fuzzy tracking control strategy is introduced, ensuring that all signals and tracking errors of the controlled system remain bounded in finite time. Finally, two simulation examples are given to illustrate the effectiveness of the proposed control scheme, confirming that all states remain within the predefined regions.

Adaptive tracking control for stochastic nonlinear systems with asymmetric full state constraints

AbstractThis article addresses the problem of adaptive tracking control for stochastic nonlinear systems with asymmetric full state constraints. Different from the traditional log‐type or tan‐type barrier Lyapunov functions (BLFs), a new asymmetric BLF is proposed in this article. Then, a state feedback controller is constructed with backstepping method so that all signals of the closed‐system are bounded and the asymmetric state constraint is well kept all the time. Without changing the structure of the controller, the design and the analysis for constrained and unconstrained systems are unified. Finally, the effectiveness of proposed control strategy has been demonstrated by simulations of numerical example and the single‐link robot arm model.

Adaptive tracking control for a class of stochastic nonlinear systems with full-state constraints and dead-zone

This paper seeks to address the problem of state-feedback tracking control for a class of stochastic systems whose states are constrained and input is perturbed by dead-zone. A tan-type barrier Lyapunov function (BLF) and a finite-time adaptive law are proposed such that all states of the system are constrained in the defined bounded compact sets. Based on stochastic Lyapunov theorem, an adaptive state-feedback tracking controller is designed to ensure that the considered stochastic system is semiglobally finite-time stable in probability (SGFSP) and the tracking error signal is bounded. Different from the existing control strategies for stochastic systems, the form of BLF can be used for asymmetric constraints without changing the controller, so the analysis of symmetric or asymmetric full-state constraints is unified. Finally, illustrative simulations are provided to verify the effectiveness of the proposed control strategy.

Low-Computation Tracking Control of Nonlinear Systems With Asymmetric Full-State Constraints and Unknown Control Directions

This article considers the tracking control problem for an uncertain feedback nonlinear system with asymmetric time-varying full-state constraints and unknown control directions. We propose a new low-computation full-state constrained robust control algorithm, that removes the feasibility conditions of virtual controllers and solves the unknown control direction problem without using the Nussbaum gain technique. By introducing nonlinear transformation functions, the original constrained systems are converted into new unconstrained tracking error systems, and the new systems eliminate the limitation of the initial conditions. Then, to seek the correct control directions, an orientation function with error conversion is constructed, which avoids introducing Nussbaum-type functions and logic switching rules. The proposed method possesses inherent robustness against model uncertainties and disturbances, and guarantees that the full-state constraints and the tracking error of systems enter into a prescribed set in a fixed time. Finally, simulation examples are presented to demonstrate the superiority and effectiveness of the developed control algorithm.

Fuzzy approximation-based adaptive tracking control for high-order nonlinear systems with asymmetric full-state constraints

This paper studies the adaptive tracking control for a class of constrained high-order nonlinear systems with uncertainties. First, a type of improved asymmetric log-type barrier Lyapunov functions (LBLFs) is constructed to handle the full-state constraints. Second, fuzzy systems are built to approximate the unknown functions in the control system. An adaptive controller is designed on the basis of adding a power integrator technique. Consequently, the designed controller can ensure that the constraints are not breached, while the tracking error approaches an arbitrarily small neighborhood of the origin. The designed controller’s performance can be guaranteed with the disappearance of the constraints. The computational burden of fuzzy approximation is mitigated by the adaptive gain-update law. A numerical example and a practical example are presented to verify the effectiveness of the proposed method.

Full-state time-varying asymmetric constraint control for non-strict feedback nonlinear systems based on dynamic surface method

We investigate the tracking control problem for a non-strict feedback nonlinear system with external disturbance and time-varying asymmetric full state constraints. Firstly, the unknown nonlinear term with external disturbance in the system are estimated by fuzzy logic system. The backstepping method is applied to the design of adaptive fuzzy controller. However, to prevent that the constraints are overstepped by introducing an improved log-type time-varying asymmetric barrier Lyapunov function (TABLF) in each step of backstepping design. Secondly, the dynamic surface control (DSC) is introduced in the designed algorithm to solve the computational explosion problem of controller caused by the derivative of control law. The proposed control scheme can speed up the tracking speed of the system. Compared with the previous work, it is verified that the combination of DSC and TABLF can obtain good performance within the constraint range, and can ensure fast and stable tracking convergence under external disturbance. Finally, two simulation examples verify the performance of the adaptive controller.

Adaptive NN finite-time tracking control for PMSM with full state constraints

This paper addresses the tracking control problem for a class of permanent magnet synchronous motors (PMSM) systems with asymmetric full-state constraints. To overcome the difficulty of controller design caused by the state constraint problems of system, a nonlinear transformation function i introduced to transform the state constraint problems into a non-constraint problems. Then, radial basis function neural networks (NN) is employed to approximate the uncertainties in the system. In addition, by combining the techniques of command filter and finite-time control, a novel virtual control signal and modified error compensation signals are proposed to construct the actual control law, which solves the problems of “explosion of complexity” and “singularity”. It is shown that all signals of the closed-loop system are bounded and the tracking error remains in a small neighborhood of the origin in finite time. Finally, the simulations show the performance and feasibility of the proposed control scheme.

Neuro-learning-based adaptive control for state-constrained strict-feedback systems with unknown control direction

A neural networks (NNs)-based learning policy is proposed for strict-feedback nonlinear systems with asymmetric full-state constraints and unknown gain directions. A state-constrained function is introduced such that the proposed adaptive control policy works for systems with constraints or without constraints in a unified structure. Furthermore, the unified state-constrained function can also deal with symmetric and asymmetric constraints without changing adaptive structures, which also avoids discontinuous actions. With Nussbaum gain technique and NNs-based approximation technique, the proposed control method can also effectively deal with the unknown signs of control gains, and matched and mismatched uncertainties are also solved by NN approximation technique. According to the Lyapunov theory, the tracking errors can be proved to be semi-globally uniformly ultimately bounded (SGUUB). Finally the effectiveness of the proposed scheme is validated by numerical simulations.

Neuroadaptive fault-tolerant control of state constrained pure-feedback systems: A collective backstepping design

In this work, we present a neuroadaptive and fault-tolerant tracking control scheme for uncertain nonlinear pure-feedback systems in the presence of time-varying and asymmetric full state constraints and unanticipated actuation failures. Instead of using multi-step recursive backstepping design, we employ a one-step approach for control development. By introducing a nonlinear coordinate transformation, we convert the original nonlinear system with asymmetrical state constraints into a new augmented one free from state constraints, which allows for the complete obviation of the feasibility conditions in the strategy. Furthermore, by making use of the feature from skew symmetric matrix in the augmented system, we develop the neural adaptive control algorithms collectively without the need for repetitive design procedure, in which only one Lyapunov function and one step derivation are involved, leading to a design approach whose synthesis complexity does not increase with the order of the system.

Removing feasibility conditions on practical preassigned finite-time tracking for state-constrained high-order nonlinear systems

This paper investigates practical preassigned finite-time tracking control for state-constrained high-order nonlinear systems. Fuzzy systems are utilised to remove frequently used growth assumptions on completely unknown nonlinearities. By integrating nonlinear transformed functions with a key coordinate transformation into control design, full-state constraints can be handled without imposing feasibility conditions in traditional barrier Lyapunov function-based control methods. It is rigorously proved that the states of fuzzy systems remain within a specific compact set, on which fuzzy approximation is valid. Besides, asymmetric full-state constraints aren't violated for all time, and the tracking error converges to the prescribed small region around zero in a preassigned finite-time. Two simulation examples show the effectiveness and advantages of this control scheme.

Tracking control of MIMO nonlinear systems under full state constraints: A Single-parameter adaptation approach free from feasibility conditions

This paper investigates the tracking control problem of a class of multi-input multi-output (MIMO) nonlinear systems under asymmetric full-state constraints. By integrating a nonlinear transformed function (NTF) with the upper bound estimation technique, we develop a robust adaptive dynamic surface control (DSC) method that exhibits several attractive features: 1) both symmetric and asymmetric state constraints are directly addressed without the need for converting the state constraints into new constraints on tracking errors (as used in the Barrier Lyapunov Function (BLF) in most existing works). Such control scheme (with its structure unchanged) is also applicable to the systems free from state constraints; 2) the undesirable feasibility conditions on virtual control laws commonly involved in most existing works are completely eliminated; and 3) the utilization of NTF-based DSC and upper bound estimation technique not only avoids the explosion of complexity problem in traditional backstepping design, but also allows a structurally simple and computationally inexpensive control scheme to be developed, in which only one single parameter updating is needed, significantly reducing the design complexity and online computation. The effectiveness of the proposed scheme is verified via simulation.