Feedback Control Of Nonlinear Systems Research Articles

Optimal quadratic full state feedback control of nonlinear affine systems

The solution of the optimal quadratic full-state feedback closed-loop control of a nonlinear affine system problem is presented and solved. This solution uses the State-Dependent Coefficient (SDC) form of a nonlinear system and the Calculus of Variations. Further, it is shown that this solution enables the computation of the value function associated with the respective Hamilton-Jacobi-Bellman equation thus satisfying the necessary and sufficient conditions for optimality. The use of the SDC form representation in the optimal solution for a nonlinear affine system results in an explicit and exact full-state feedback closed-loop control implementation as opposed to the existing open-loop solutions of the optimal control. This solution, like for the linear case, is non-causal and thus cannot be solved in real-time. The closed-loop application involves precomputing a time-varying full-state feedback matrix. The optimal feedback is a linear combination of the current state. The time-varying gain matrix is the backward solution of a non-symmetric matrix Riccati equation. Conditions for the stability of the full-state feedback are presented. This new representation of the optimal solution gives a well-understandable algorithm that enables implementation in the closed loop of the optimal feedback control of a non-linear system which is not possible with the existing optimal open loop representations.

The impact of resource limitation on the pest-natural enemy ecosystem with anti-predator behavior and fear effect

Research on agricultural pest control data indicates that the actual effectiveness of insecticides may exhibit slight variations, influenced by factors such as the type and quantity of pests. Additionally, the development of resistance by pests, as a result of adaptation to the environment, can impact the precision of pest control strategies. Hence we suggest implementing a nonlinear pulse state-dependent feedback control system, considering resource limitations, to investigate the influence of varying pesticide fatality rates on pest outbreaks. This paper takes into account the fear effect and anti-predator behavior to accurately portray the farmland ecosystem. We assessed the phase set and Poincaré map under the conditions for the existence of order-k (where k=1,2,3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$k=1,2,3$\\end{document}) periodic solutions and examined their stability behavior. Remarkably, the system exhibited diverse bifurcation phenomena associated with pesticide-related parameters. Furthermore, the system demonstrated a multistability phenomenon involving the coexistence of the order-1 periodic solution and the limit cycle. This suggests that altering control strategies can disturb the initial coexistence status of pests and natural enemies. It also underscores that resource limitations can indeed impact the outbreak patterns and frequencies of pests. In addition to the variability in pesticide fatality rates, the inclusion of natural enemy releases in the nonlinear pulse strategy contributes to the model exhibiting complex dynamic characteristics. All these findings are substantiated by numerical simulations.

Inverse Optimal Adaptive Fuzzy Output Feedback Control for Nonlinear Systems With Output Quantization

Inverse Optimal Adaptive Fuzzy Output Feedback Control for Nonlinear Systems With Output Quantization

Fixed-Time Observer-Based Output Feedback Control for Nonlinear Systems With Full-State Constraints

This brief investigates the problem of fixed-time state observer-based output feedback control design for nonlinear systems with full-state constraints. First, a fixed-time state observer is constructed to estimate the unknown states, which can accurately estimate the system states within a fixed settling time. Then, by combining the integral barrier Lyapunov function with the backstepping method, the full-state constraints are realized after the fixed time. Meanwhile, the proposed control strategy can directly constrain the states rather than impose constraints on errors, which reduces the conservativeness of the constraint satisfaction condition. The proposed control method ensures that all signals in the closed-loop system are bounded and symmetric state constraints are strictly maintained after the fixed settling time. Finally, simulation results prove the effectiveness of the proposed method.

Adaptive anti‐windup output feedback control for nonlinear systems and its stability analysis

SummaryIn the practical application of adaptive control methods, a windup phenomenon for the systems with input saturation may occur because there exists an input restriction such as saturation of actuator in most actual systems due to physical reasons. In this paper, to alleviate the influence of the windup phenomenon by input saturation, we propose an output feedback exponentially passive (OFEP)‐based adaptive model recovery anti‐windup (AMRAW) control strategy for the stable nonlinear systems with input saturation. Moreover, in order to realize an augmented OFEP system for non‐OFEP nonlinear systems that do not satisfy the OFEP properties, a parallel feedforward compensator (PFC) is introduced, and a radial basis function (RBF) neural network (NN)‐based adaptive feedforward input is designed to attain accurate tracking performance for systems with the PFC. Furthermore, the detailed stability analysis of the proposed AMRAW control system is provided, and the performance of the proposed method is validated through appropriate numerical simulations.

Adaptive Quantized Output Feedback Control of Nonlinear Systems With Mismatched Uncertainties and Sensor Failures

Adaptive Quantized Output Feedback Control of Nonlinear Systems With Mismatched Uncertainties and Sensor Failures

Command-filter-based finite-time event-triggered adaptive output feedback control for nonlinear systems with state-function constraints

This paper investigates the finite-time (FT) adaptive output feedback control for a class of nonlinear systems with asymmetric state-function constraints and unknown external disturbances. Incorporating the asymmetric barrier Lyapunov function (BLF) into the backstepping technique, a new control approach is proposed to ensure that all states do not cross the constraint boundary. With the help of the command filter, the explosion of complexity induced by repeated differentiations of virtual controllers is eliminated, and the corresponding compensation system is used to offset the filter error. Meanwhile, the fuzzy logic system (FLS) and fuzzy state observer are employed to approximate unknown nonlinear functions and estimate unmeasurable states respectively. For effectively conserve communication resources, a novel adaptive event-triggered controller is proposed such that all signals of the closed-loop system are bounded, the tracking error converges to a small neighborhood containing the origin in finite time. Finally, the feasibility of the fabricated control scheme is verified with two examples.

A dual adaptive robust control for nonlinear systems with parameter and state estimation

Stabilization and learning are imperative to the high-performance feedback control of nonlinear systems. A dual adaptive robust control (DARC) scheme is proposed for nonlinear systems with model uncertainties to achieve a desired level of performance. Only the output of the nonlinear system is accessible in this work, all the states and parameters are learned online. Firstly, the DARC uses the prior physical bounds of systems to design a discontinuous projection with update rate limits which confines the bounds of parameter and state estimation. Then robustness of the nonlinear system can be guaranteed by the deterministic robust control (DRC) method. Secondly, a dual adaptive estimation mechanism (DAEM) is developed to learn the unknown parameters and states of systems. One part of the DAEM is the bounded gain forgetting (BGF) estimator, which is developed to handle inaccurate parameters and parametric variations. The other is the adaptive unscented Kalman filter (AUKF) synthesized for state estimation. The AUKF contains a statistic estimator based on the maximum a posterior (MAP) rule to estimate the unknown covariance matrix. Finally, simulation results illustrate the effectiveness of the suggested method.

New Results on Nonsynchronous-Observer-Based Output-Feedback Control of Fuzzy-Affine-Model-Based Discrete-Time Nonlinear Systems

This work investigates the non-synchronous observer-based output feedback control of nonlinear systems by T-S fuzzy affine models. In order to estimate the unmeasurable system states and handle the non-synchronization issue of premise variables between the observer/controller and the original system, a new non-synchronous piecewise fuzzy affine observer is firstly synthesized to estimate the unmeasurable system state variables. Via utilizing some elegant matrix inequalities with convexification techniques, new observer-based piecewise output feedback controller design results are proposed within the framework of piecewise quadratic Lyapunov functions. Simulation studies are given to illustrate the validity of the developed approach.

Adaptive Fuzzy Output Feedback Tracking Control for Uncertain Nonstrict Feedback Systems With Variable Disturbances via Event-Triggered Mechanism

This article studies the adaptive fuzzy event-triggered output feedback control for nonlinear systems. The systems have the nonstrict feedback structure and variable disturbances simultaneously. A fuzzy state observer with an adaptive parameter is first proposed, and a less conservative condition to solve the observer gains is obtained. By constructing the command filter, the compensator, the fuzzy controller, the event-triggered mechanism, and the adaptive parameter, the adaptive fuzzy output feedback control scheme is built to guarantee that all the signals of the closed-loop systems are bounded, and the tracking errors are less than a prescribed accuracy in finite time. Simulation examples confirm the effectiveness of the proposed method.

Interdependency of Core Temperature and Glabrous Skin Blood Flow in Human Thermoregulation Function: A Pilot Study.

Human thermoregulation is governed by a complex, nonlinear feedback control system. The system consists of thermoreceptors, a controller, and effector mechanisms for heat exchange that coordinate to maintain a central core temperature. A principal route for heat flow between the core and the environment is via convective circulation of blood to arteriovenous anastomoses located in glabrous skin of the hands and feet. This paper presents new human experimental data for thermoregulatory control behavior along with a coupled, detailed control system model specific to the interdependent actions of core temperature and glabrous skin blood flow (GSBF) under defined transient environmental thermal stress. The model was tuned by a nonlinear least-squared curve fitting algorithm to optimally fit the experimental data. Transient GSBF in the model is influenced by core temperature, nonglabrous skin temperature, and the application of selective thermal stimulation. The core temperature in the model is influenced by integrated heat transfer across the nonglabrous body surface and GSBF. Thus, there is a strong cross-coupling between GSBF and core temperature in thermoregulatory function. Both variables include a projection term in the model based on the average rates of their change. Six subjects each completed two thermal protocols to generate data to which the common model was fit. The model coefficients were unique to each of the twelve data sets but produced an excellent agreement between the model and experimental data for the individual trials. The strong match between the model and data confirms the mathematical structure of the control algorithm.

State Quantized Output Feedback Control for Nonlinear Systems via Event-Triggered Sampling

The current article proposes a novel output feedback event-triggered control scheme for nonlinear systems considering state quantization. First, we construct a state observer to track the unavailable system states. Second, a dynamic event-triggered and quantized mechanism is constructed to handle the state sampling and quantization. By designing the event-triggered mechanism to sample the system state, and using the quantizer to filtrate the sampled signals, the wasted resources in the data channels can be effectively reduced, and the communication efficiency can be improved. Then, based on the input-to-state stability method, the asymptotic stability is ensured for the closed-loop systems. Moreover, we propose an event-triggered and quantized control scheme for the nonlinear systems with input delay, and the asymptotic stability is ensured using the Lyapunov–Krasovskii functional method. The proposed output feedback event-triggered and quantized mechanisms can guarantee a positive lower bound of the transmission interval times of communication channels, which means that the Zeno behavior is avoided. Finally, a simulation example is presented to verify the feasibility of the proposed control schemes.

A Blow-Up Function Approach to Global Event-Triggered Prescribed Tracking Output Feedback Control of Nonlinear Systems

In this paper, global event-triggered adaptive prescribed tracking output feedback control is investigated for a class of nonlinear uncertain systems with unknown control direction. Different from the existing works, the design of the tracking error-dependent normalized function and prescribed boundary is based on our uniformly defined blow-up function rather than a specific function, and the asymmetric constraint requirements on tracking error can be achieved by appropriately selecting the blow-up function. By utilizing the Kalman filter ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -filter) and dynamic gain technique, a new reduce-order observer is proposed, which can make the estimated error exponentially converge to zero. In addition, by introducing a dynamic signal into the trigger condition, a novel event-triggered mechanism is proposed, which can extend the trigger time interval and completely counteract the event-triggered errors in terms of asymptotic stability by sacrificing part of the system transient performance. Furthermore, an adaptive controller is designed based on the backstepping method, which ensures the boundedness of the state of the closed-loop system, while regulating the tracking error meets the global prescribed performance requirements and approaches to zero asymptotically. Two examples are given to illustrate the effectiveness of the proposed control scheme.

Finite-time command filtered event-triggered adaptive output feedback control for nonlinear systems with unknown dead-zone constraints

This paper addresses the design of neural network observer and adaptive finite-time tracking controller for uncertain nonlinear with event-triggered inputs and unknown dead-zone constraints. To shorten the convergence time and reduce the computational burden, the finite-time command filter backstepping (CFB) technique is modified by improving the error compensation term, and a novel adaptive output feedback event triggering mechanism is developed in this way. It is proven that the newly presented control strategy achieves the goal of finite-time convergence and effectively saves network bandwidth. Meanwhile, all of the closed-loop signals are bounded, and the tracking performance is guaranteed based on the finite-time CFB method avoiding the problem of complexity explosion. Finally, a practical example is included to verify the validity of the proposed theoretical results.

Adaptive Output Feedback Control of Nonlinear Systems With Mismatched Uncertainties Under Input/Output Quantization

It is still an open problem to synthesize control with input and output quantizations for nonlinear systems subject to mismatched parametric uncertainties via backstepping design. This is because 1) the output becomes discontinuous and nondifferentiable after quantization, making the conventional recursive backstepping design method unsuitable as the differentiation of the virtual control signals does not exist, while the existing backstepping-based quantized control method is only applicable to systems modeled in normal form or systems without mismatched uncertainties; 2) it is difficult to deal with the impacts of errors caused by output quantization when the virtual control laws contain time-varying estimates of unknown parameters; and 3) since only the quantized output signal is available, the effects of certain items related to unknown parameters in currently available observers become difficult to be explicitly addressed. In this article, we present a solution to this problem by employing a dynamic filtering technique to avoid differentiating virtual control signals in backstepping design, using the parameter projection technique to design the parameter estimator and proposing a new form of state observer to facilitate the development of output feedback control. It is shown that, with the derived adaptive backstepping control involving both input and output quantizations, all the closed-loop signals are ensured bounded and the control performance in terms of the mean square error is adjustable through properly choosing certain design parameters. The benefits and effectiveness of the proposed scheme are also validated by numerical simulation.

Defining urge as an uncontrolled micturition explains pathogenesis, informs cure and helps solve the burgeoning OAB crisis.

BackgroundParallel with the demographic ageing crisis, is a disabling overactive bladder (OAB) crisis (urgency/frequency/nocturia), 30% prevalence in older women, pathogenesis stated as unknown and, according to some learned societies, incurable.Hypothesis/AimsTo review International Continence Society and Integral System paradigms to test our thesis that OAB per se is not a pathological condition, rather, a prematurely activated uncontrolled micturition; pathogenesis being anatomical damage in a nonlinear feedback control system comprising cortical and peripheral (muscle/ligament) components.MethodsWe examined studies from basic science, anatomy, urodynamics, ultrasonic and video xrays, ligament repairs, from which we created a nonlinear binary model of bladder function. We applied a Chaos Theory feedback equation, Xnext = Xc(1 − X) to test our hypothesis against existing concepts and hypotheses for OAB pathogenesis.ResultsThe bladder has ONLY two modes, EITHER closed OR open (micturition). Closure is reflexly controlled cortically and peripherally: muscles contracting against ligaments stretch the vagina to suppress afferent signals to micturate from urothelial stretch receptors. “OAB” can be caused by anatomical damage anywhere in the model, by childbirth or age‐weakened ligaments, which can be repaired to cure all three OAB symptoms. Urodynamic “DO” graphs are interpreted anatomically and by the feedback equation.ConclusionOAB is in crisis. Our thesis of OAB as an uncontrolled micturition from anatomical defects in the bladder control system provides fresh directions for further development of new treatments, nonsurgical and surgical, to help break the crisis and bring hope and cure to 600 million women sufferers.

Nonsmooth dynamical systems: From the existence of solutions to optimal and feedback control

In this paper, we investigate a nonlinear and nonsmooth dynamics system (NNDS, for short) involving two multi-valued maps which are a convex subdifferential operator and a generalized subdifferential operator in the sense of Clarke, respectively. Under general assumptions, by using a surjectivity theorem for multi-valued mappings combined with the theory of nonsmooth analysis and arguments on pseudomonotone operators, the existence of a solution to (NNDS) is proved. Then, an optimal control problem governed by (NNDS) is introduced, and a solvability result for the optimal control problem is established. Moreover, we study a nonlinear feedback control system driven by (NNDS) and an u.s.c. multi-valued feedback map, and employ the Kakutani-Ky Fan fixed point theorem to obtain an existence theorem of solutions for the feedback control problem. Finally, we deliver a convergence result in the sense of Kuratowski describing the changes in the set of solutions for the feedback control problem as the initial data x0 is perturbed in Hilbert space H.

A new configuration of composite nonlinear feedback control for nonlinear systems with input saturation

This study proposes a U-control–based Composite Nonlinear Feedback (U-CNF) design procedure. This U-CNF control establishes a double feedback loop framework for generalisation and simplification in designing the CNF control systems. Two controllers, in terms of double dynamic inversion, are designed separately, (1) to stabilise and cancel the nonlinearities and dynamics (convert the plant into an identity matrix) in the inner closed-loop, and then (2) to improve the system transient response by specifying a second-order linear system with a monotonic nonlinear function to smoothly tune the damping ratio. Accordingly, the conventional CNF characteristics in a concise pathway are achieved. The properties show, under proper conditions, the U-CNF control is plant model-free control, applicable to nonaffine nonlinear dynamic systems, and robust against model uncertainty and external disturbance. For the initial bench tests of the first-time proposed U-CNF configuration, the simulated case studies are provided with a transparent procedure to demonstrate the consistency with the analytical results in the numerical computations and to present guidance for applications.

Adaptive Neural Networks Based Robust Output Feedback Controllers for Nonlinear Systems

The performance of the nonlinear control system that is subjected to uncertainty, can be enhanced by implementing an adaptive approach by using the robust output-feedback control and the artificial intelligence neural network. This paper seeks to utilize output feedback control for nonlinear system using artificial intelligence employing neural network. The Two Wheel Mobile Robot (TWMR) is treated as a multi-body dynamic system. The nonlinear swing-up problem is handled by designing an adaptive neural network, which is trained using a modified conventional controller called Linear Quadratic Optimal State Estimator with Integral Control (LQOSEIC). In this paper, the nonlinear system TWMR is stabilized utilizing a robust output feedback control called LQOSEIC. This controller allows a linearized model to emulate a model reference for the original nonlinear system. However, it works for a limited range of operations and will fail if the plant characteristics are unknown or uncertain. An adaptive neural network is used to overcome this problem. The adaptive neural controller is trained offline using LQOSEIC to obtain the initial weights of neurons for the network's hidden layers. After finishing the training, the LQOSEIC will be replaced by the adaptive neural controller. The main advantage of a neuro-controller is its ability to update the weights online depending on the error signal. If there are any disturbances or uncertainties that arises within the concerned nonlinear system, the neuro-controller will be able to handle it because of online learning that compensates for the effect of unpredictable conditions. The proposed adaptive neural network improves control performance and ensures the robust stability of the closed-loop control system. Finally, numerical simulations are used to demonstrate the efficacy of the proposed controllers.

Adaptive FIT-SMC Approach for an Anthropomorphic Manipulator With Robust Exact Differentiator and Neural Network-Based Friction Compensation

In robotic manipulators, feedback control of nonlinear systems with fast finite-time convergence is desirable. However, because of the parametric and model uncertainties, the robust control and tuning of the robotic manipulators pose many challenges related to the trajectory tracking of the robotic system. This research proposes a state-of-the-art control algorithm, which is the combination of fast integral terminal sliding mode control (FIT-SMC), robust exact differentiator (RED) observer, and feedforward neural network (FFNN) based estimator. Firstly, the dynamic model of the robotic manipulator is established for the n-degrees of freedom (DoFs) system by taking into account the dynamic LuGre friction model. Then, a FIT-SMC with friction compensation-based nonlinear control has been proposed for the robotic manipulator. In addition, a RED observer is developed to get the estimates of robotic manipulator joints’ velocities. Since the dynamic friction state of the LuGre friction model is unmeasurable, FFNN is established for training and estimating the friction torque. The Lyapunov method is presented to demonstrate the finite-time sliding mode enforcement and state convergence for a robotic manipulator. The proposed control approach has been simulated in the MATLAB/Simulink environment and compared with the system with no observer to characterize the control performance. Simulation results obtained with the proposed control strategy affirm its effectiveness for a multi-DoF robotic system with model-based friction compensation having an overshoot and a settling time less than 1.5% and 0.2950 seconds, respectively, for all the joints of the robotic manipulator.