Control Problem For Nonlinear Systems Research Articles

A Further Result on Global Stabilization of a Class of Nonlinear Systems by Output Feedback with Unknown Measurement Sensitivity

In this paper, we provide a further result on the output feedback control problem of nonlinear systems with unknown measurement sensitivity studied in [2]. We provide a gain-scaling output feedback controller and a process of determining the allowed measurement sensitivity. As a result, we show that more nonlinearity and measurement sensitivity can be treated by our method. Various examples are presented to illustrate the improved features of our control method.

Adaptive Numerical Approach for Optimal Control of a Single Train

This paper considers the optimal control problem of a single train, which is formulated as an optimal control problem of nonlinear systems with switching controller. The switching sequence and the switching time are decision variables to be chosen optimally. Generally speaking, it is very difficult to solve this problem analytically due to its nonlinear nature, the complexity of the controller, and the existence of system state and control input constraints. To obtain the numerical solution, by introducing binary functions for every value of the control input, relaxing the binary functions, and imposing a penalty function on the relaxation, the problem is transformed into a parameter optimization problem, which can be efficiently solved by using any gradient-based numerical approach. Then, the authors propose an adaptive numerical approach to solve this problem. Convergence results indicate that any optimal solution of the parameter optimization problem is also an optimal solution of the original problem. Finally, an optimal control problem of a single train illustrates that the adaptive numerical approach proposed by us is less time-consuming and obtains a better cost function value than the existing approaches.

Event-Triggered Adaptive Control for Prescribed Performance Tracking of Constrained Uncertain Nonlinear Systems

This paper studies the prescribed performance tracking control problem for a pure-feedback nonlinear system with full-state constraints. By incorporating the asymmetric barrier Lyapunov functions into the dynamic surface control, we develop an adaptive prescribed performance control scheme, which can ensure that all closed-loop signals remain bounded and the full-state constraints are not violated. Furthermore, we explore the event-triggered adaptive prescribed performance control problem for nonlinear systems with full-state constraints, which can save the limited computing and communication resources. The numerical simulations are provided to illustrate the performances of the designed adaptive controller and the event-triggered adaptive controller.

Tracking Control With Input Saturation and Full-State Constraints for Surface Vessels

To solve the problems of full-state constraints in trajectory tracking of surface vessels, a backstepping technique combining a novel integral barrier Lyapunov function (iBLF) with neural network and sliding mode is proposed. Moreover, the control law is extended to the control problem with input saturation. First, the iBLF-based control approach is applied to the control design. The purpose of the iBLF-based approach is to deal with the constraints without transforming the constraints bound into the tracking errors bound. Second, the Neural Networks (NN) is used to handle with the system uncertainties, and a single parameter online adjustment is used instead of the weights online adjustment of the neural networks to realize the adaptive estimation of a single parameter. Third, defining an auxiliary analysis system to deal with the effect of input saturation on the system, an effective control approach under input saturation is realized. Furthermore, it is proved that the designed control law can guarantee the uniformly ultimately bounded stability of closed-loop system and system state can not violate the constraints. Finally, the simulation results of trajectory tracking control of the surface vessel show that the proposed control approach can effectively solve the control problem of nonlinear systems with full-state constraints, system uncertainties and input saturation.

RBF Networks-Based Weighted Multi-Model Adaptive Control for a Category of Nonlinear Systems With Jumping Parameters

This paper studies the tracking control problem for nonlinear system with largely jumping parameters. To deal with the large uncertainties of system parameters, an RBF networks-based weighted multi-model adaptive control (WMMAC) strategy is designed, in which the model set can be constructed to cover and approximate the variation range of the plant parameters. Correspondingly, the RBF network controller set generates the appropriate global control signals when parameters jumping, and better transient performance is obtained. Different from existing neural network learning methods, two novel learning rules based on the difference value between the current value of an objective function and its optimal value for the RBF networks are developed to achieve a fast convergence rate. The stability of the overall closed-loop system is validated by the virtual equivalent system (VES) theory, and favorable performance of the proposed control strategy is demonstrated by the numerical simulations.

Ascent trajectory tracking method using time-varying quadratic adaptive dynamic programming

Ascent trajectory tracking in the longitudinal plane is a class of nonaffine noncascade nonlinear system control problems with single input and multiple output, which is difficult to control by nonlinear method directly. Adaptive dynamic programming algorithm has the advantages of precise control and adaptability for general nonlinear control problem, and the time-varying quadratic adaptive dynamic programming algorithm proposed in this paper promotes the convergence and calculation speed of the traditional adaptive dynamic programming algorithm. To implement the algorithm effectively, the independent variables of ascent model are substituted in the launching coordinate, and then the model is treated as a discrete nominal trajectory tracking problem. Besides, the heuristic dynamic programming structure is used to train the processed model, and thus only the time-varying weight in the designed evaluation network needs to be updated. Simulation shows that the proposed algorithm can update the control variable online after predicting the cost function offline with the dynamic equations, which is faster than the general adaptive dynamic programming algorithm. In addition, the proposed algorithm can effectively and accurately track the nominal trajectory under the uncertainty of parameters compared with the linear quadratic regulators algorithm.

Composite-Observer-Based Output-Feedback Control for Nonlinear Time-Delay Systems With Input Saturation and Its Application

This paper makes the first attempt to address the global output-feedback tracking control problem for nonlinear systems in the presence of time delay, nonsymmetric input saturation, and external disturbances. As one of the distinctive features, the growth assumptions imposed on system time-delay nonlinearities are removed in this output-feedback case. To handle the unmeasurable states and disturbances, the composite state observer and disturbance observer are constructed simultaneously. Based on these two observers, an output-feedback controller is designed by introducing an auxiliary system to eliminate the effect of input saturation and using a Lyapunov–Krasovskii functional to deal with time delay. It is shown that the designed controller can ensure the closed-loop system to be globally uniformly ultimately bounded. Particularly, instead of converging to an arbitrarily small neighborhood of zero as in related results, the tracking error is proven to be bounded by the saturation input error and design parameters that can be explicitly tuned. Finally, a chemical reactor system is presented to demonstrate the effectiveness and usefulness of the proposed scheme.

Adaptive Fuzzy Sliding Mode Control for Network-Based Nonlinear Systems With Actuator Failures

This paper investigates the robust control problem of nonlinear systems with unknown time-varying actuator faults over digital communication networks. In the study, a new adaptive sliding mode control (SMC) scheme is developed for the investigated nonlinear systems, where the unknown nonlinearity is approximated via the adaptive fuzzy mechanism in the presence of signal quantization. The proposed control law can compensate the time-varying faults and the quantization errors completely by injecting the quantizer parameter into the controller gain. Moreover, in this design, the adaptive fuzzy law is constructed via the quantized state information instead of using the exact original information. Under the proposed quantized SMC scheme, the closed-loop control systems are guaranteed to be asymptotically stable, and the reachability of the sliding surface can be ensured strictly. Finally, two examples are presented to show the effectiveness of the method.

Robust Optimal Control of Nonlinear Systems With System Disturbance During Feedback Disruption

AbstractIn this paper, a robust optimal control problem of nonlinear systems with system disturbance during feedback disruption is considered. This is an extended work of previous time‐delay optimal control results, by adding external disturbance in the considered system. It is shown that there exists an optimal input signal which keeps the performance error within the specified bound for the longest time. Then, it is shown that such an optimal input signal can be approximated by an implementable bang‐bang input signal in terms of control performance. Two examples are given for illustration.

Observer‐based non‐linear H ∞ attitude control for a flexible satellite

This study focuses on the observer-based non-linear H ∞ (OBNH) attitude control for a flexible satellite with external disturbances and local state-region constraints. By considering the structural features of the attitude system and applying Lyapunov stability theory, the solvable conditions of the OBNH attitude control problem are provided. An advantage of this study is that the state-feedback controller and the reduced-order state observer can be designed independently, thus significantly reducing the complexity of the attitude control algorithm. Furthermore, based on the polynomial sum of squares (SOSs) and the generalised S-procedure techniques, the above problem can be transformed into a convex optimisation problem with SOS constraints. This conversion can effectively overcome the computational difficulties widely present in the control problem of non-linear systems. Finally, a numerical example is given to illustrate the effectiveness and feasibility of the proposed approach.

Adaptive Fault-Tolerant Control for Nonlinear System With Unknown Control Directions Based on Fuzzy Approximation

This paper focuses mainly on the approximation-based fuzzy adaptive fault-tolerant control problem for nonlinear systems with unmodeled dynamics and unknown control directions. With the Nussbaum gain technique and a dynamic signal introduced, the difficulties from the unknown control directions and unmodeled dynamics are successfully overcome. Then, by taking advantage of the adaptive fuzzy control method and backstepping technology, we develop a fuzzy adaptive failure compensation control strategy and guarantee the semi-global boundedness for all signals. A simulation example is carried out to demonstrate the validity of the theoretical findings.

Robust H∞ Control for Nonlinear Systems with Time-varying Delay

The robust Hï‚¥ control problem for nonlinear system with time-varying delay is discussed. The nonlinear condition satisfying a kind of especial linear bound is assumed. By constructing lyapunov krasovskii function and using integral inequality and the linear matrix inequality technique, the sufficient condition of memory less state feedback robust Hï‚¥ controller and the explicit design method for nonlinear systems with time-varying delay are given. Finally, an example is given to illustrate the effectiveness of the design method.

Adaptive anti-disturbance tracking control for nonlinear system with unknown control coefficient

The tracking control problem for nonlinear system with unknown control coefficient and external disturbances is investigated in this article. By inspiring extended state observer and K filter, a novel extended state filter is first developed for state and disturbance observations. Then, by means of backstepping approach, an adaptive composite output feedback controller is constructed based on the state and disturbance estimations. The stability analysis is presented on the basis of the Lyapunov stability method. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed control approach.

Discrete-Time Stable Generalized Self-Learning Optimal Control With Approximation Errors.

In this paper, a generalized policy iteration (GPI) algorithm with approximation errors is developed for solving infinite horizon optimal control problems for nonlinear systems. The developed stable GPI algorithm provides a general structure of discrete-time iterative adaptive dynamic programming algorithms, by which most of the discrete-time reinforcement learning algorithms can be described using the GPI structure. It is for the first time that approximation errors are explicitly considered in the GPI algorithm. The properties of the stable GPI algorithm with approximation errors are analyzed. The admissibility of the approximate iterative control law can be guaranteed if the approximation errors satisfy the admissibility criteria. The convergence of the developed algorithm is established, which shows that the iterative value function is convergent to a finite neighborhood of the optimal performance index function, if the approximate errors satisfy the convergence criterion. Finally, numerical examples and comparisons are presented.

Observer-Based Adaptive Fault-Tolerant Tracking Control of Nonlinear Nonstrict-Feedback Systems.

This paper studies an output-based adaptive fault-tolerant control problem for nonlinear systems with nonstrict-feedback form. Neural networks are utilized to identify the unknown nonlinear characteristics in the system. An observer and a general fault model are constructed to estimate the unavailable states and describe the fault, respectively. Adaptive parameters are constructed to overcome the difficulties in the design process for nonstrict-feedback systems. Meanwhile, dynamic surface control technique is introduced to avoid the problem of "explosion of complexity". Furthermore, based on adaptive backstepping control method, an output-based adaptive neural tracking control strategy is developed for the considered system against actuator fault, which can ensure that all the signals in the resulting closed-loop system are bounded, and the system output signal can be regulated to follow the response of the given reference signal with a small error. Finally, the simulation results are provided to validate the effectiveness of the control strategy proposed in this paper.

H∞ control with constrained input for completely unknown nonlinear systems using data-driven reinforcement learning method

This paper investigates the H∞ control problem for nonlinear systems with completely unknown dynamics and constrained control input by utilizing a novel data-driven reinforcement learning method. It is known that nonlinear H∞ control problem relies on the solution of Hamilton-Jacobi-Isaacs (HJI) equation, which is essentially a nonlinear partial differential equation and generally impossible to be solved analytically. In order to overcome this difficulty, firstly, we propose a model-based simultaneous policy update algorithm to learn the solution of HJI equation iteratively and provide its convergence proof. Then, based on this model-based method, we develop a data-driven model-free algorithm, which only requires the real system sampling data generated by arbitrary different control inputs and external disturbances instead of accurate system models, and prove that these two algorithms are equivalent. To implement this model-free algorithm, three neural networks (NNs) are employed to approximate the iterative performance index function, control policy and disturbance policy, respectively, and the least-square approach is used to minimize the NN approximation residual errors. Finally, the proposed scheme is tested on the rotational/translational actuator nonlinear system.

A NOTE ON SDRE CONTROL APPLIED IN PREDATOR–PREY MODEL: BIOLOGICAL CONTROL OF SPIDER MITE PANONYCHUS ULMI

The spider mite Panonychus ulmi (P. ulmi) is one of the most important pests of apple plantations. Studies suggested that spider mite Neoseiulus californicus (N. californicus) is able to control spider mite P. Ulmi, minimizing the risk of having leaves with high index of injury, therefore avoiding economic damage. In this work, we consider a predator–prey system, where the prey is the mite P. ulmi and its predator is the spider mite N. californicus. The coefficients for the Lotka–Volterra model with competition between predators are obtained. Here, we will use the state-dependent riccati equation (SDRE) control technique to design a state feedback control, and to determine a state observer. In both cases, it is necessary to solve the quadratic optimal control problem for nonlinear systems. Numerical simulations shown that both approaches are efficient to stabilize the system in a desired point below the critical concentration, allowing us to minimize the level of economic damage.

Optimal vibration control of nonlinear systems with multiple time-delays: An application to vehicle suspension

ABSTRACTThis paper addresses optimal vibration control problem for nonlinear systems with state, control, and measurement delays. By using the functional transformations, the original system is reduced to an equivalent delay-free one. The approximating sequence method is applied to simplify and solve the nonlinear optimal vibration control (NOVC) problem, which is reduced to a linear two-point boundary value problem of approximating sequences. The nonlinear optimal control law is obtained from the convergence solutions by solving a Riccati equation, a Sylvester equation, and the state and adjoint vector differential equations of approximating sequences. The proposed control strategy is applied to design a vibration controller for an active vehicle suspension. The nonlinear vehicle suspension system with delays is modelled, as well as the road disturbance model is established. Comparing with a passive controller and a non-delay-compensation controller (NDCC), the simulations for the designed NOVC are demonstrated. The simulation results illustrate the effectiveness and the simplicity of the proposed approach.

On solution of control problems for nonlinear systems on finite time interval

Abstract: In this paper, a finite-dimensional nonlinear control system is considered on a finite time interval. Research deals with the problem of approach of the system with a target set in the system phase space at a fixed moment of time. A discrete approximation scheme is proposed for solution of the approach problem. Model examples of mechanical systems are given with application of the proposed scheme.

Control Problem of Nonlinear Systems with Applications

1School of Science, Qilu University of Technology, Jinan 250353, China 2Center for Neural Engineering, The Pennsylvania State University, University Park, PA 16802, USA 3Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845, Australia 4Department of Physical Sciences, Redeemer’s University, PMB 230, Ede, Nigeria 5School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China