Design Of Nonlinear Systems Research Articles

Virtual Sensor Design for Replacement the Faulty Physical Sensors

Abstract: The paper considers the problem of virtual sensor design for nonlinear dynamic systems with non-smooth nonlinearities described by continuous-time models for faulty physical sensor replacement. It is assumed that to solve the problem, the system is equipped by diagnostic system allowing detecting and isolating the faulty sensor. For every such a sensor, the virtual sensor generating estimate replacing the faulty sensor is designed. To solve the problem, so-called logic-dynamic approach is used which does not guarantee optimal solution but uses only methods of linear algebra to solve the problem for systems with non-smooth nonlinearities. The virtual sensor can be designed in the identification canonical form or Jordan canonical form. The advantage of the first form is a standard procedure of the virtual sensor design while Jordan form allows obtaining a simpler solution. The relations allowing designing the virtual sensor both in identification and in Jordan canonical form are derived.

Interval Observer Design for Discrete-Time Nonlinear Dynamic Systems

The paper considers the problem of interval observer design for nonlinear dynamic systems described by discrete-time models under external disturbances, measurement noise, and parametric uncertainties. The problem is to design the observer with fewer dimensions than that of the original system; such an observer must generate upper and lower bounds of admissible values of the prescribed nonlinear function of the original system state vector. To solve the problem, special mathematical tool is used. The advantage of this tool is that it allows studying the systems described by models with non-smoo th nonlinearities. To construct interval observer, the reduced-order model of the original system insensitive or having minimal sensitivity to the disturbances is designed. The designing procedure is based on two algorithms: the first one is intended to design the model of minimal sensitivity; the second one is used to reduce the dimension of the model. The rules are formulated to ensure stability based on the prescribed set of the desirable eigenvalues and feedback. The interval observer consists of two subsystems: the first one generates the lower bound, the second one the upper bound. The relations describing both subsystems are given. To construct such an observer in the nonlinear case, the terms of positive and negative influence of variables describing the model are introduced. These terms allow finding out how the upper and lower bounds of these variables will appear in the interval observer. The conditions under which the observer can be designed are given. The theoretical results are illustrated by an example of three tank system. Simulation results based on the package Matlab show the effectiveness of the developed theory.

Distributed observer design for interconnected nonlinear systems with faults and disturbances based on dynamic event conditions

AbstractThis study investigated the observer design schemes for interconnected nonlinear systems with actuator faults, sensor faults, external disturbances, and limited measured resources. A novel effective distributed estimation scheme is presented for the interconnected nonlinear system to estimate the states, faults, and lumped disturbances, simultaneously. To save communication resources and to improve information utilization, an adaptive event condition is designed in the sensor channel, and the triggered values are utilized to design the observer. Especially, to handle the sensor fault, the output is separated into two parts, and the estimation is realized with the help of a normal one. In the first part of this study, a class of interconnected nonlinear systems with partial loss of effectiveness of sensor fault is considered, and an event‐based distributed estimation scheme is established. In the second part, a class of more universal feedback interconnected nonlinear with both partial loss sensor fault and bias sensor fault is investigated. An augment system is formulated by an augmented vector composed of state and sensor faults. And then the estimation scheme is realized by utilizing the presented event‐based distributed observer. The convergence abilities of both the two conditions are proved and, finally, the estimation performances of the presented observer are verified by a numerical simulation system and an inverted pendulum system.

An Adaptive Controller Design for Nonlinear Active Air Suspension Systems with Uncertainties

Active air spring suspensions can improve the vehicle ride comfort and meanwhile realize the vehicle height regulation, and therefore, they have been widely used and studied. However, to achieve better ride comfort and a satisfactory vehicle body height adjustment, the active air suspension controller becomes an indispensable and significant part of the system. Since the nonlinear suspension system possesses uncertainties, it is difficult to take into account both ride comfort and height regulation. This study innovatively proposes an adaptive control algorithm to specifically address the problem of vehicle height regulation and ride comfort for nonlinear active air suspension systems with uncertainties. The accurate tracking to reference vehicle body height curves is realized, and the ride comfort is also improved. Through simulations with two scenarios, it is illustrated that the active air suspension controller owns better control effectiveness than the PID controller. Compared with the PID controller, the designed controller can track the reference vehicle body height curves faster and more accurately. The result also verifies the priority of the designed controller.

An improved event-triggered control method for fuzzy systems under membership functions online learning

This paper is concerned with the problem of adaptive event-triggered (AET) based optimal fuzzy controller design for nonlinear networked control systems (NCSs) characterized by Takagi–Sugeno (T–S) fuzzy models. An improved AET communication scheme with a memory adaptive rule is proposed to enhance the utilization of the state response vertex data. Different from the existing ET based results, the improved AET scheme can save more communication resources and acquire better system performance. The sufficient criteria of performance analysis and controller design are presented for the closed-loop control system subject to mismatched membership functions (MFs) and AET scheme. And then, a new MFs online learning algorithm on the basis of the gradient descent approach is employed to optimize the MFs of fuzzy controller and obtain optimal fuzzy controller for further improving system performance. Finally, two simulation examples are presented to verify the advantage and effectiveness of the provided controller design technique.

Homogeneous systems stabilization based on convex embedding

The paper develops control algorithms for a class of affine nonlinear systems using the so-called canonical homogeneous representation. It is demonstrated that such a representation exists for any homogeneous vector field bounded on the unit sphere. It is shown that canonical homogeneous representation is useful for LMI-based control design and stability analysis of nonlinear systems. Theoretical results are supported by numerical examples.

Relaxed nonquadratic H∞ robust constrained event-triggered fuzzy controller design for discrete-time nonlinear systems

This paper introduces an [Formula: see text] robust constrained event-triggered fuzzy controller for discrete-time nonlinear systems in the presence of system parameter uncertainties, the parameter uncertainties of the output matrices and the disturbances, simultaneously. To reduce the communication resources and improve the robust performance, the event-triggered mechanism is incorporated with the [Formula: see text] robust fuzzy controller design. Moreover, by employing the fuzzy modeling of the actuator saturation and a nonquadratic Lyapunov function (NQLF), the ultimate bounded stability (UBS) of the closed-loop system is guaranteed subject to the amplitude limitations of the control signal. This means, a new linear matrix inequality (LMI) problem is derived to ensure the robustness and constraints in an offline scheme based on the event-triggered strategy. Besides, to meet the practical problem to further improve the controlled system performance, the control input rate constraint is also considered and a new LMI condition is provided with no online computational burden. Therefore, the computational burden of the proposed controller is greatly reduced with less conservatism. Two simulation examples including a numerical dynamic system and a truck–trailer system are employed to illustrate the less conservatism and computational complexity of the proposed method compared with the existing approaches.

Sub-optimal controller design for time-delay nonlinear partial differential equation systems: an extended state-dependent differential Riccati equation approach

ABSTRACT In this article, a sub-optimal controller based on Extended State-Dependent Differential Riccati Equation (ESDDRE) is suggested for a class of time-delay nonlinear Partial Differential Equation (PDE) systems. At first, an extended pseudo linearisation presentation for parameterisation form using State-Dependent Coefficients (SDC) is proposed. In this presentation, all the time-delay parts are placed in system matrices as well as in input vectors. By defining a cost function and a Hamiltonian related to the PDE systems, the sub-optimal control law regarded on the ESDDRE is obtained. The stability of the closed-loop system based on the ESDDRE control approach is ensured by using a proper Lyapunov function and also Poincaré inequality. Numerical simulation results for three time-delay nonlinear PDE systems illustrate the appropriate performance of the proposed control approach.

A learning- and scenario-based MPC design for nonlinear systems in LPV framework with safety and stability guarantees

ABSTRACT This paper presents a learning- and scenario-based model predictive control (MPC) design approach for systems modelled in the linear parameter-varying (LPV) framework. Using input-output data collected from the system, a state-space LPV model with uncertainty quantification is first learned through the variational Bayesian inference Neural Network (BNN) approach. The learned probabilistic model is assumed to contain the true dynamics of the system with a high probability and is used to generate scenarios that ensure safety for a scenario-based MPC. Moreover, to guarantee stability and enhance the performance of the closed-loop system, a parameter-dependent terminal cost and controller, as well as a terminal robust positive invariant set are designed. Numerical examples will be used to demonstrate that the proposed control design approach can ensure safety and achieve desired control performance.

Finite-time dissipative control design for one-sided Lipschitz nonlinear singular Caputo fractional order systems

ABSTRACT This paper presents an efficient analytical approach for solving the problem of dissipative control in one-sided Lipschitz singular Caputo fractional-order systems subject to nonlinear perturbations. The approach is based on mathematical transformations, and fractional calculus. A state feedback controller is designed to ensure that the closed-loop system is regular, impulse-free, and finite-time bounded with a dissipativity performance index. The results are established using tractable strict linear matrix inequalities (LMIs) without any equality constraint. Two numerical examples are provided to demonstrate the effectiveness of the proposed approach.

Secure P2P Nonfragile Sampled-Data Controller Design for Nonlinear Networked System under Sensor Saturation and DoS Attack

Secure P2P Nonfragile Sampled-Data Controller Design for Nonlinear Networked System under Sensor Saturation and DoS Attack

Boundary Fuzzy Output Tracking Control of Nonlinear Parabolic Infinite-Dimensional Dynamic Systems: Application to Cooling Process in Hot Strip Mills

This paper utilizes a combination of integral control, fuzzy control, and observer-based output feedback control to deal with the issue of nonlinear output tracking control (OTC) design for nonlinear infinite-dimensional dynamic systems. The system dynamics model is represented by a semi-linear parabolic partial differential equation (PDE) with boundary control and non-collocated boundary measurement. Initially, a Takagi-Sugeno (T-S) fuzzy parabolic PDE model is constructed to surmount the OTC design difficulty from the infinite-dimensional nonlinear system dynamics. Subsequently, a fuzzy-observer-based OTC law is proposed via the T-S fuzzy PDE model and the integral control approach. Here, the integral control ensures asymptotic output regulation, and the observer-based output feedback control is employed to conquer the stabilizing control design difficulty caused by the non-collocation between control actuation and measurement. It is shown via the Lyapunov technique with variants of vector-valued Poincaré-Wirtinger's inequality that the suggested fuzzy OTC law drives the measurement output to asymptotically track the desired reference signal and ensures the boundedness of the resulting closed-loop system, provided that a sufficient condition given in the form of linear matrix inequalities is fulfilled. Moreover, the proposed fuzzy-model-based OTC design is also revised for the exponential stabilization case. Finally, extensive simulation results for a numerical example and a cooling process in hot strip mills are provided to examine the effectiveness and merit of the proposed fuzzy OTC scheme.

Adaptive event-based fixed-time tracking design for strict-feedback nonlinear systems with unknown control coefficients

In this paper, we propose a novel Nussbaum-type design to cope with the problem in nonlinear dynamical systems with unknown control directions. First, a Nussbaum-based Lyapunov analysis for fixed-time stability is investigated to lay the theoretical foundation. On this basis, the Nussbaum-type adaptive backstepping control is designed with dynamic surface filters to avoid repeated differentiation. To further reduce the computational complexity, an event-triggered mechanism is combined with the Nussbaum-type gain design. With the above design schemes, the practical fixed-time stability of the overall feedback systems can be guaranteed with theoretical discussion. Finally, the feasibility of the presented design is validated by two simulation examples made in the end.

Virtual Sensors for Nonlinear Discrete-Time Dynamic Systems

The problem of virtual sensor design for nonlinear systems under the disturbance is investigated. Two different mathematical techniques are used to solve the problem: the algebra of functions and the logic-dynamic approach. The first one allows obtaining a general solution while the second one produces a solution for nonlinear systems by linear algebra methods. The virtual sensors are designed to be insensitive to the disturbance based on invariant functions. They estimate the prescribed function of the original system state vector. The practical example illustrates theoretical results.

Finite‐time sub‐optimal control design for control affine nonlinear systems

AbstractA finite‐time suboptimal control strategy named technique is proposed for the control of a class of control‐affine nonlinear dynamic systems in this study. The nonlinear dynamic is expressed as a pseudo‐linear form without linearization. By adding vanishing perturbation terms into the quadratic cost functional and using a power series to represent the co‐state, an approximate solution to the Hamilton–Jacobi–Bellman (HJB) equation can be obtained through solving a differential Riccati equation offline and a series of linear Lyapunov equations with analytical solutions. The obtained suboptimal controller is in a state feedback closed‐form. By tuning the parameters in the perturbation terms, semi‐global stability can be guaranteed. In contrast to the finite‐time state‐dependent Riccati equation technique, the proposed method does not need intensive and iterative numerical computations, which facilitates real‐time implementation. Two examples are utilized to demonstrate the effectiveness and efficiency of this proposed technique.

Event-Triggered Extended Dissipativity Fuzzy Filter Design for Nonlinear Markovian Switching Systems against Deception Attacks

This article is concerned with the adaptive-event-triggered filtering problem as it relates to a class of nonlinear discrete-time systems characterized by interval Type-2 fuzzy models. The system under investigation is susceptible to Markovian switching and deception attacks. It is proposed to implement an improved event-triggering mechanism to reduce the unnecessary signal transmissions on the communication channel and formulate the extended dissipativity specification to quantify the transient dynamics of filtering errors. By resorting to the linear matrix inequality approach and using the information on upper and lower membership functions, stochastic analysis establishes sufficient conditions for the existence of the desired filter, ensuring the mean-squared stability and extended dissipativity of the augmented filtering system. Further, an optimization-based algorithm (PSO) is proposed for computing filter gains at an optimal level of performance. The developed scheme was finally tested through experimental numerical illustrations based on a single-link robot arm and a lower limbs system.

Dynamic event-triggered controller design for nonlinear systems: Reinforcement learning strategy

The current investigation aims at the optimal control problem for discrete-time nonstrict-feedback nonlinear systems by invoking the reinforcement learning-based backstepping technique and neural networks. The dynamic-event-triggered control strategy introduced in this paper can alleviate the communication frequency between the actuator and controller. Based on the reinforcement learning strategy, actor–critic neural networks are employed to implement the n-order backstepping framework. Then, a neural network weight-updated algorithm is developed to minimize the computational burden and avoid the local optimal problem. Furthermore, a novel dynamic-event-triggered strategy is introduced, which can remarkably outperform the previously studied static-event-triggered strategy. Moreover, combined with the Lyapunov stability theory, all signals in the closed-loop system are strictly proven to be semiglobal uniformly ultimately bounded. Finally, the practicality of the offered control algorithms is further elucidated by the numerical simulation examples.

Reduced-Complexity LMI Conditions for Admissibility Analysis and Control Design of Singular Nonlinear Systems

We present a reduced-complexity control approach for a class of descriptor nonlinear systems with a nonlinear derivative matrix, possibly singular. To this end, a systematic approach is proposed to obtain an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">equivalent</i> polytopic representation of a given nonlinear system within a compact set of the state-space. This modeling approach has two particular features compared to the related Takagi–Sugeno (T–S) fuzzy model-based framework. First, the model complexity only grows <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">proportionally</i> , rather than exponentially, with the number of premise variables. Second, the vertices of the proposed polytopic models can admit an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infinite</i> number of representations for the same predefined set of premise variables. This <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nonuniqueness</i> feature allows introducing some specific slack variables at the modeling step to reduce the control design conservatism. Based on the proposed polytopic representation and Lyapunov stability theory, we derive reduced-complexity admissibility analysis and design conditions, expressed in terms of linear matrix inequalities, for the considered class of descriptor systems. In particular, a new nonlinear control law is proposed for regular descriptor systems to avoid using the extended redundancy form, which may yield numerically complex and conservative results due to the imposed special control structure. Both numerical and physically motivated examples are given to demonstrate the interests of the new control approach with respect to existing T–S fuzzy model-based control results.

Adaptive Fuzzy Appointed-Time Control for Uncertain Systems Bounded by Positive Functions

This brief presents an appointed-time prescribed performance control design for uncertain nonlinear systems via adaptive fuzzy technique. Compared with existing results, the controller achieves appointed-time tracking control for higher-order nonlinear systems with uncertainties bounded by positive functions. Firstly, barrier Lyapunov functions integrated with appointed-time prescribed performance functions are designed to cope with the requirements of output constraints and quantitative performance constraints. Then, adaptive fuzzy systems are constructed to approximate the unknown continuous upper-bound functions of the uncertainties. Subsequently, through the backstepping framework, a novel adaptive fuzzy appointed-time control scheme is proposed for the uncertain nonlinear system bounded by positive functions. Thus, the appointed settling time, predetermined steady-state error, and quantitative transient-state performance of the closed-loop system are ensured. Finally, the fixed-time convergence of the closed-loop system is proved via Lyapunov analysis, while comparative simulations are conducted to illustrate the superiority of the proposed scheme.

Controller design of robot nonlinear system based on the improved fuzzy sliding mode control

In this paper, the input-output finite time stability of fuzzy sliding mode control in nonlinear robot systems is discussed. Specifically, the system considers more realistic factors, such as uncertainty, nonlinearity, interference, and state delay. An improved fuzzy sliding mode control (FSMC) scheme is developed, which is considered in most results of FSMC schemes. Based on the input-output finite-time stability characteristics and the proposed control scheme, the objective of this work is to reduce the effects of uncertainty, nonlinearity, disturbance, and state delay. Finally, the effectiveness and superiority of the proposed method are verified by simulation and comparison with other reference methods.