Class Of Nonlinear Systems Research Articles

Non-fragile sampled-data observers resisting measured noise for a class of nonlinear systems

In this paper, we study non-fragile observers for a class of nonlinear systems with sampled outputs and unknown measurement noise. After an output filtering transformation, an extended nonlinear system is constructed. The sampled outputs with unknown measurement noise are transformed into the state equation of the extended system. Then, an extended non-fragile observer is designed to estimate the states of the extended system, and the unknown measurement noise is estimated by a first-order estimator. On the basis of a time-varying matrix inequality (TMI), it is proven that the observer system can track the extended system well even if there are observer gain perturbations and measured noise. Finally, a nonlinear dynamic model is used to verify the feasibility and validity of the proposed methods.

Singular perturbation-based robust controller for a class of nonlinear systems

Singular perturbation-based robust controller for a class of nonlinear systems

Fixed-time active fault-tolerant control for a class of nonlinear systems with intermittent faults and input saturation

In this paper, the problem of fixed-time active fault-tolerant control is studied for systems with sector-bounded nonlinearities, intermittent faults, and input saturation. Since intermittent faults appear and disappear randomly, a fixed-time scheme is considered in the active fault-tolerant control algorithm, composed of detection, isolation, estimation, and the control unit. Utilizing homogeneity-based observers, the fixed-time state estimation is available in the presence of unknown but bounded disturbances, and a fault diagnosis unit is proposed. An input saturation compensator is introduced to analyze the effect of input saturation, and its auxiliary variables are used in the reconfigurable control law. The fault-tolerant controller, which is constructed via the information provided by the fault diagnosis unit and saturation compensator, has two switching modes. As a consequence, intermittent faults are compensated via the designed active fault-tolerant control method and the system reaches practical stability with the entire convergence time bounded in a fixed time. Finally, the example of a heat control system is exploited to demonstrate the effectiveness of the developed active fault-tolerant control scheme.

Finite-time optimal control for a class of nonlinear systems with performance constraints via critic-only ADP: Theory and experiments

This paper addresses the optimal control problem within the framework of adaptive dynamic programming (ADP) for a class of nonlinear systems subjected to performance constraints. A new finite-time optimal control scheme is developed to stabilize the system by using the critic-only neural network ADP method. Compared with the existing ADP-based optimal control methods with uniformly ultimately bounded stability, the provided control scheme ensures that the controlled system's state and neural network weight estimation error are finite-time stable. It can ensure optimality, prescribed performance, and finite-time stability of the closed-loop control system simultaneously through an integration of ADP, the prescribed performance control technique, and Lyapunov theory. The designed adaptive neural network weight update law can relax the persisting excitation condition. The proposed control scheme is implemented on a robotic experiment platform to achieve trajectory tracking and verify its effectiveness.

Prescribed finite-time safe tracking control based on secure boundary protection method for nonlinear systems with unknown control gains

Aiming to the mutation of the actual output boundary, a prescribed finite-time safe tracking control problem is investigated for a class of nonlinear systems with unknown control gain in this paper. A secure boundary protection method (SBPM) and a new prescribed finite-time performance function (PFTPF) are proposed. The SBPM can construct automatically two adjustable secure boundaries, so that the system meets both the control performance prescribed by the PFTPF and the constraint of the secure boundaries. In order to solve the problem of the excessive jitter of control input caused by the mutation of the output constraint, a bidirectional filtering smoothing mechanism (BFSM) is proposed. The proposed method can effectively deal with the mutation of actual output constraint, and it is not necessary to predict the system output value to adjust the desired output trajectory. Finally, the effectiveness of this proposed method is verified by simulations.

Iterative control framework with application to guidance and attitude control of rockets

Traditional control methods for nonlinear dynamical systems are predicated on verification of complex mathematical conditions related to the existence of a positive-definite Lyapunov function whose value must strictly decrease with time. Rigorous verification of Lyapunov conditions can be extremely difficult in real-world systems with high-dimensional and complex dynamics. In this paper, we present a novel control logic that can be readily applied to a general class of nonlinear systems irrespective of the complexities in their dynamics. The Iterative Control Framework (ICF) is designed to guarantee the convergence of the closed-loop system state to zero without a priori verification of Lyapunov-like conditions. The underlying computational routine runs in the background in real time and reconfigures the control vector at each time step in such a way that when the control input is applied to the system, the system trajectory reaches closer to the desired state. The technique is applicable to a broad class of complex nonlinear systems but is particularly suitable for systems inherently admitting control action of short duration such as missiles, rockets, satellites, and space vehicles. In this work, we focus on the application of ICF to guidance and attitude control of rockets and missiles where actuation is provided via single-use thrusters.

A perspective on conditional spectrum-based determination of response statistics of nonlinear systems

This work focuses on determining the stochastic response properties, in the frequency domain, of a general class of nonlinear systems with polynomial nonlinearities. Specifically, the results are presented in terms of the stationary power spectral densities of the system’s displacement and velocity. This is pursued by revisiting the conditional power spectrum concept, with the assumption that the response process is both ergodic and pseudo-harmonic and characterized by an amplitude, and a phase. A theoretical elucidation of an existing formula for the conditional spectrum is attempted. In particular, this concept is interpreted in conjunction with the time averaging approximation made in the definition of the stationary probability density function of a response amplitude quantity, associated with the original nonlinear system. It is shown that a proper definition of the stationary probability density of the response amplitude, along with a reasonable treatment of the distribution over the frequency domain of the amplitude contribution, lead to an improved approximation of the stationary response power spectral density. The treatment involves the averaging of a population of surrogate spectral densities of stationary random responses conforming with the system responses associated with individual values of the amplitudes of the responses. The semi-analytical results have been quite favourably juxtaposed with a large suite of à propos Monte Carlo simulations, both in terms of the shape and of the range of the involved germane frequencies, even for strongly nonlinear systems.

Sliding-Window Matrix Pencil Method for Design Optimization with Limit-Cycle Oscillation Constraints

This paper introduces a novel approach to constrain limit-cycle oscillations in design optimization. The approach builds upon a limit-cycle oscillation constraint that bounds the recovery rate to equilibrium, circumventing the need for bifurcation diagrams. Previous work demonstrated the constraint using approximate recovery rates obtained by evaluating the system state velocity for prescribed states. This work proposes a fully nonlinear matrix pencil method that accurately evaluates the recovery rate based on transient simulations. The proposed method captures the amplitude variation in the recovery rate using a short time window that slides along the time history of a quantity of interest. This sliding-window matrix pencil method is first verified for a typical section model. Sensitivity analyses identify guidelines to obtain accurate recovery rates efficiently. The system is then optimized subject to limit-cycle oscillation, flutter, and side constraints, and the results are compared with the ones based on approximate recovery rates. The sliding-window matrix pencil method allows the optimizer to produce a less conservative design while preventing limit-cycle oscillations at desired operating conditions and amplitudes. The approach introduced in this paper can facilitate the inclusion of limit-cycle oscillation considerations in the design phase of a broad class of nonlinear systems.

Optimized Inverse Dead‐Zone Control Using Reinforcement Learning for a Class of Nonlinear Systems

ABSTRACTIn this article, an optimized inverse dead‐zone control using reinforcement learning (RL) is developed for a class of nonlinear dynamic systems. The dead‐zone is frequently occurred in the nonlinear control system, and it can affect the control performance and even cause the system instable. Hence, it is very requisite to consider the effect of dead‐zone in the design of control strategy. In this proposed optimized inverse dead‐zone control, the basic idea is to find the optimized control as input and the adaptive algorithm to estimate the unknown parameters for the inverse dead‐zone function, so that the available dead‐zone input for system control can be derived. Comparing with traditional methods, on the one hand, the proposed dead zone inverse method is with fewer adaptive parameters, on the other hand, the RL under identifier‐critic‐actor architecture is with the simplified algorithm. Finally, theoretical and simulation results manifest the feasibility of the proposed method.

Recursive terminal sliding mode approximate optimal control strategy based on reconstructed nonlinear systems

For a class of nonlinear systems with unknown internal states and actuator failures, this paper proposes a recursive terminal sliding-mode fault-tolerant control method based on reconfigurable nonlinear systems and further designs an approximate optimal compensated controller based on adaptive dynamic programming, which employs a neural network (NN) to estimate the optimal value function. The system ensures that the tracking error converges to a small set around zero with faster speed and higher accuracy even when the actuator fails. Finally, the convergence of the expanded state observer and the single-evaluation NN weights is demonstrated based on the Lyapunov theory, and the stability of the whole closed-loop system is given. Simulation results and comparisons verify the effectiveness of the proposed control strategy.

Polynomial filter-based adaptive fault-tolerant control for a class of nonlinear systems with multiplicative faults

In this article, the problem of fault-tolerant control is investigated for polynomial nonlinear systems (PNSs) subject to multiplicative faults and measurement noise. Firstly, a matrix Taylor expansion technique is applied to transform the PNS into a linear parameter varying system. Then the polynomial filter is constructed to get estimations of states and unmatched disturbances, which reduces the effect of measurement noise. A novel adaptive fault-tolerant controller is proposed to compensate for multiplicative faults and unmatched disturbances. Furthermore, the condition of the parameter-dependent linear matrix inequality (PDLMI) is deduced, which guarantees the boundedness of tracking errors and estimation errors, and the sum of squares (SOS) decomposition technique is utilized to solve PDLMI. Finally, the simulation of a rotary steerable drilling tool system confirms the feasibility of the proposed adaptive fault-tolerant control framework.

Practical prescribed time tracking control for a class of nonlinear systems with event triggering and output constraints

AbstractThis paper investigates the practical prescribed time tracking for a class of uncertain nonlinear systems based on neural networks and event‐triggered control. Introducing a time‐varying constraint function transforms the original practical prescribed time‐tracking control issue into a tracking error constraint problem. An event‐triggered adaptive control has been proposed, which can effectively reduce the communication burden between the controller and the actuator. Using neural networks to approximate unknown nonlinear functions avoids the differentiation of virtual controllers, thereby reducing the computational burden. In addition, users can independently choose preset time and tracking accuracy without changing the control structure, which remains independent of the initial conditions and any design parameters. Finally, the effectiveness of this method is verified through simulation examples.

A Low-Power Multi-High-Gain Observer Design for a Class of Nonlinear Systems

A Low-Power Multi-High-Gain Observer Design for a Class of Nonlinear Systems

Immersion and Invariance Adaptive Control for a Class of Nonlinear Systems With Uncertain Parameters

Immersion and Invariance Adaptive Control for a Class of Nonlinear Systems With Uncertain Parameters

Simultaneous interval estimation of actuator fault and state for a class of nonlinear systems by zonotope analysis

In this paper, an actuator fault and state interval estimation method for a class of nonlinear systems is proposed by integrating observer design and zonotope analysis. For the considered systems, we present a novel unknown input observer structure with broad applications. The design procedure is based on H∞ method to decrease the influence of unknown but bounded process disturbances and measurement noise. Moreover, a novel interval estimation method is presented based on zonotope analysis to obtain tighter intervals. Numerical simulations of a quadruple-tank system are conducted to assess the performance of the proposed approach.

Input delay compensation of nonlinear systems with uncertain time-varying parameters

A robust adaptive control law is designed for the class of nonlinear systems with uncertain time-varying parametric dynamics and input delays. The Constitution of control law design is based on filtered tracking errors, previous values of control input and estimate of uncertain parameters which is updated by the update law. An arbitrary large input delay compensation is guaranteed by deriving sufficient control gain conditions using Lyapunov-Krassovskii based stability analysis. The efficacy of the design is verified by Simulation results of two-link robot manipulator dynamical system.

Switched Observer Design for a Class of Non-Linear Systems

This paper is concerned with the switched observer design for a class of systems subject to locally Lipschitz non-linearities. By performing a suitable description of the estimation error dynamics into a linear parameter varying (LPV) system representation, sufficient conditions for the existence of a switching output injection gain are proposed such that the asymptotic stability of the estimation error is guaranteed. These conditions can be conveniently expressed by means of linear matrix inequalities (LMIs), which are easily computationally tractable. A numerical example is provided to show the favorable performance achieved by the proposed observer, which can be applied to a large class of non-linear systems.

Fixed-time disturbance observers-based fault-tolerant control for a class of nonlinear systems with prescribed performance

This paper explores the issue of fault-tolerant control for a class of nonlinear systems that encounter the actuator fault and external disturbances. The uncertainties arising from the actuator fault and external disturbances are treated as lumped uncertainties, and fixed-time observers are designed to observe them. The fault-tolerant controller with full-state constraints is then developed using the fixed-time backstepping method, integrating the Improved Prescribed Performance Function (IPPF) method and the Barrier Lyapunov Function (BLF) method. Additionally, command filters with error compensations are devised to resolve the ‘explosion of complexity’ problem during the controller derivation process. The parameters of the designed controller are optimised using the Northern Goshawk Optimization (NGO) algorithm to enhance nonlinear systems’ dynamic performance. Lastly, the validity and practicality of the proposed approach are verified through the comparative study of simulations and experiments, with the permanent magnet synchronous motor (PMSM) position system employed as a case study.

Unscented recursive three-step filter based unbiased minimum-variance estimation for a class of nonlinear systems

For the direct feedthrough system where unknown input affects both process equation and measurement equation, an unscented recursive three-step filter based unbiased minimum-variance (URTSF-UMV) estimation algorithm is proposed. The algorithm is based on the unbiased minimum-variance (UMV) method and uses statistical linearisation technology to approximate the nonlinear system and the nonlinear measurement function to linear regression form. The estimation of unknown input is obtained from innovation through weighted least-squares (WLS) estimation. The approximate linear regression form allows us to process the nonlinear system with unknown input direct feedthrough by using the UMV state estimation framework, and derive the filter by minimising the trace of the state error covariance of the measurement update under the unbiased condition. The URTSF-UMV requires that the unknown input distribution matrix is full column rank. We use the full rank decomposition method to deal with the nonlinear system containing the unknown input rank-deficient distribution matrix. The effectiveness of the URTSF-UMV algorithm is demonstrated through an illustrative simulation example.

Fault detection for saturated nonlinear system subject to redundant channel and additive time‐varying delays

AbstractUnder the influence of sensor saturation and packet dropout, this paper is concerned with the fault detection (FD) problem for a class of nonlinear systems with two additive time‐varying delay components. In the addressed measurement model, the sensor is assumed to have two communication channels, which can contribute to improving the probability of successfully delivering the measurements. A FD filter is designed to generate residual signals, and the sufficient criteria are established to ensure the stochastic finite‐time stability (SFTS) of the residual system with performance constraint by constructing new Lyapunov‐Krasovskii functionals. Based on the established criteria, the explicit expression of the desired FD filter is obtained via solving a set of linear matrix inequalities (LMIs). Finally, the usefulness of the proposed FD scheme is verified by a simulation example.