Control Design For Nonlinear Systems Research Articles

Near-optimal output tracking controller design for nonlinear systems using an event-driven ADP approach

Abstract In this paper, a novel output tracking control scheme for a class of continuous-time nonlinear system is proposed by using an event-driven adaptive dynamic programming (ADP) approach. Based on the controlled system and the desired reference trajectory, an augmented system is constructed for the optimal tracking control problem (OTCP), where the control law is composed of the steady-state part and the feedback part. According to the standard solution of the OTCP, the feedback part associated to the cost function is to be solved and the steady-state part of the control can be obtained directly. Thus the event-driven near-optimal control method is proposed to solve feedback control of the OTCP, where a single network ADP approach is developed to approximate the optimal cost function. The output tracking error dynamic get converged to zero and the parameters of critic neural network (NN) get converged to the optimal ones by using the designed weight tuning law and event-triggering condition. The stability of the augmented system under the novel control scheme is guaranteed based on Lyapunov theory and two simulation examples are presented to demonstrate the effectiveness of the proposed method.

Practically Oriented Finite-Time Control Design and Implementation: Application to a Series Elastic Actuator

This paper proposes a practically oriented finite-time control design for nonlinear systems under a less ambitious but more practical semiglobal control objective. As one main contribution, the designed finite-time controller can be expressed as a very simple form while the control gain tuning mechanism follows a conventional pole placement manner, which enhances its facility in practical implementations. Moreover, by utilizing a modified nonrecursive homogeneous domination design without preverifying any nonlinearity growth constraints, the control scheme can be directly obtained by totally neglecting the recursive calculations of series virtual controllers. Rigourous semiglobal attractivity and local finite-time convergence analysis are presented to ensure the theoretical justification. A control application and experimental verification to a series elastic actuator demonstrates the control effectiveness and significant performance improvements compared with asymptotical state feedback controllers.

Control of a manipulator robot by neuro-fuzzy subsets form approach control optimized by the genetic algorithms

In this paper, we describe a new form of neuro-fuzzy-genetic controller design for nonlinear system derived from a manipulator robot. The proposed method combines fuzzy logic and neuronal networks which are of growing interest in robotics, the neuro-fuzzy controller does not require the knowledge of the robot parameters values. Furtheremore, the genetic algorithms (GAs) for complex motion planning of robots require an evaluation function which takes into account multiple factors. An optimizing algorithm based on the genetic algorithms is applied in order to provide the most adequate shape of the fuzzy subsets that are considered as an interpolation functions. The proposed approach provides a well learning of the manipulator robot dynamics whatever the assigned task. Simulation and practical results illustrate the effectiveness of the proposed strategy. The advantages of the proposed method and the possibilities of further improvements are discussed.

Learning and Guaranteed Cost Control With Event-Based Adaptive Critic Implementation.

This paper focuses on the event-triggered guaranteed cost control design of nonlinear systems via a self-learning technique. In brief, an event-based guaranteed cost control strategy of nonlinear systems subjects to matched uncertainties is developed, thereby balancing the performance of guaranteed cost and the actuality of limited communication resource. The original control design is transformed into an optimal control problem with an event-based mechanism, where the relationship of guaranteed cost performance compared to the time-based formulation is discussed. A critic neural network is constructed for implementing the event-based optimal control design with stability guarantee. Simulation experiments are carried out to verify the theoretical results in detail.

An Approach to the Design of Nonlinear State-Space Control Systems

An Approach to the Design of Nonlinear State-Space Control Systems

Nonlinear impulsive optimal control synthesis with optimal impulse timing: A pseudo-spectral approach

Following the philosophy of pseudo-spectral approach, a nonlinear variable-time impulsive optimal control system design approach is presented in this paper for a class of problem with hard terminal constraint. In this approach the impulse application time instants are also take as ‘decision variables’ and are fixed through an optimization process in addition to the magnitudes of control at those instants. This gives additional freedom for optimization and hence leads to better performance than the fixed timing approach. Three benchmark problems which include a scalar linear problem, the Van-der Pol’s oscillator problem and an inverted pendulum problem are solved to demonstrate the effectiveness of the new technique. The proposed approach is also computationally efficient owing to the usage of the pseudo-spectral philosophy.

Operator Based Two Loop Nonlinear Forced Vibration Control of a Flexible Plate

SUMMARYA nonlinear forced vibration control method for a flexible plate with piezoelectric actuators is proposed in this paper. A model of a flexible plate, taking into account the hysteresis of the piezoelectric actuator, is given. In addition, the design of nonlinear control system is given by using the operator theory. Finally, the effectiveness of the proposed nonlinear control system is confirmed by simulation and experimental results.

Control Design for Nonlinear Systems via Controller with Quasi-fixed Parameters

Abstract The paper presents an approach to design a control of nonlinear dynamical systems based on the extended linearization technique of a mathematical model of an object such that a given quadratic cost function is minimized. In this case, the coefficients of the nonlinear controller are determined by solving Riccati matrix equation with state dependent parameters. A realizability problem of the controller of this sort is computational complexity of the realtime solution. The proposed approach solves the problem by controller coefficients searching at each control time subinterval of the whole control time interval. The presented methodology is illustrated by designing chemotherapy administration for the cancer treatment. The mathematical model of the cancer growth includes interaction between tumor cells, healthy normal cells and activated immune cells. Numerical results show effectiveness of the solutions obtained.

Fractional PID controller design for nonlinear systems based on singular perturbation technique

This paper deals with the output regulation of nonlinear control systems in order to guarantee desired performances in the presence of plant parameters variations and external disturbances. The proposed control law structures are based on the fractional order PI (FOPI) and PID (FOPID) control schemes. By introducing the two-time-scale notions in the closed-loop system, the presented design methodology of fractional PID control guarantees desired transients. Then, the singular perturbations technique is used to analyse the closed-loop system properties and to get explicit expressions for evaluation of the controller parameters. The tuning of the controller parameters is based on a constrained optimisation algorithm. Simulation examples are presented to show the effectiveness of the proposed method.

Robust PID controller design for nonlinear systems

AbstractIn this paper the new approach to the design of robust PID controller for the case of nonlinear Lipschitz systems is proposed. The proposed method is based on the uncertain gain scheduling plant model and Bellman Lyapunov equation. The designed robust controller ensures parameter dependent quadratic stability and in the frame of H2performance guaranteed cost. Examples show the effectiveness of the proposed method.

Fractional PID controller design for nonlinear systems based on singular perturbation technique

Fractional PID controller design for nonlinear systems based on singular perturbation technique

State-dependent parameter model identification for inverse dead-zone control of a hydraulic manipulator

The robotic platform in this study has dual, seven-function, hydraulically actuated manipulators, which are being used for research into assisted tele-operation for common nuclear decommissioning tasks, such as pipe cutting. The article concerns the identification of state-dependent parameter (SDP) models for joint angle control. Compared to earlier SDP analysis of the same device, the present work proposes a new way of representing the state-dependent gain and parametrises this using novel regret-regression methods. A mechanistic interpretation of this model yields dead-zone and angular velocity saturation coefficients, and facilitates SDP-based control with an inverse dead-zone. This approach integrates the input signal calibration, system identification and nonlinear control system design steps, using a relatively small data-set, allowing for straightforward recalibration when the dynamic characteristics have changed due to age and use, or after the installation of replacement parts.

Non-fragile control for interval type-2 TSK fuzzy logic control systems with time-delay

The study is concerned with non-fragile controller design for nonlinear systems with time-delay which are described by the interval type-2 Takagi–Sugeno–Kang fuzzy logic control system. Interval type-2 Takagi–Sugeno–Kang fuzzy logic control systems have been used in many applications and shown better outperforms in some cases than their type-1 counterparts. In this paper, a Lyapunov–Krasovskii functional is constructed through the Wirtinger-based integral inequality which is less conservative than the Jensen inequality, then sufficient conditions are obtained to stabilize the interval type-2 Takagi–Sugeno–Kang fuzzy logic control system with time-delay. Two types of controllers are designed, one is normal and the other is non-fragile. Non-fragile controllers make their implementation easier allowing to tune controller parameters automatically. The results are established in the form of linear matrix inequalities, which can be easily solved by MATLAB toolbox, then the controller gain matrices can be developed. Simulation examples in different cases are provided to demonstrate the effectiveness of the proposed method.

Robust state-constrained control design for nonlinear systems with uncertainties using a new barrier Lyapunov function

In this paper, a robust state-constrained control algorithm is proposed by introducing time-varying barrier Lyapunov functions (BLF) for nonlinear systems with uncertainties. Novel time-varying symmetric/asymmetric forms of error barrier functions are investigated in order to relax the requirements of the initial state compared with existing BLF-based literatures. By integrating the proposed time-varying BLF method with the backstepping technique, constraint satisfaction is achieved and signals in closed-loop are uniform asymptotically stable. In addition, the extended state observer technique is utilized to prevent the constraint violation during the transient phase and strengthen the robustness of the control system in the presence of uncertainties. Numerical simulations are implemented to illustrate the attitude tracking performance obtained from the proposed method for a homing missile with angle of attack constraint, parametric uncertainties and external disturbances.

Design of Stable Nonlinear Pitch Control System for a Jet Aircraft by Using Artificial Intelligence

The principal objective of this paper is to present the design of a Swarm Optimized Proportional Integral Derivative controller to obtain the desired pitch angle for a nonlinear pitch control system of a Delta Aircraft (four engine very large cargo jet aircraft). The Bacterial Foraging Optimization technique is applied to optimize the PID controller. A fine-tuned Particle Swarm Optimization PID (PSOPID) controller and a Radial basis function neural controller (RBFNC) for flight control system are designed to compare and establish the superiority of our proposed system. It is established that Bacterial Foraging Optimized PID controller provides better performance in comparison to RBFNC and PSOPID controller in terms of early settling time and overshoot. Finally, it was established that the designed controller along with the Flight control system is robust stable with the help of Kharitonov Stability Criterion.

LMI‐based adaptive output feedback fault‐tolerant controller design for nonlinear systems

SummaryThis paper presents 2‐novel linear matrix inequality (LMI)‐based adaptive output feedback fault‐tolerant control strategies for the class of nonlinear Lipschitz systems in the presence of bounded matched or mismatched disturbances and simultaneous occurrence of actuator faults, including failure, loss of effectiveness, and stuck. The constructive algorithms based on LMI with creatively using Lyapunov stability theory and without the need for an explicit information about mode of actuator faults or fault detection and isolation mechanism are developed for online tuning of adaptive and fixed output‐feedback gains to stabilize the closed‐loop control system asymptotically. The proposed controllers guarantee to compensate actuator faults effects and to attenuate disturbance effects. The resulting control methods have simpler structure, as compared with most existing recent methods and more suitable for practical systems. The merits of the proposed fault‐tolerant control scheme have been verified by the simulation on nonlinear Boeing 747 lateral motion dynamic model subjected to actuator faults.

WCMAC-based control system design for nonlinear systems using PSO

This paper presents a wavelet cerebellar model articulation controller (WCMAC) based adaptive control design for nonlinear systems using a particle swarm optimization (PSO). The WCMAC is the main tracking controller and a robust compensation controller is used to compensate for the residual error. In the WCMAC, the adaptive laws of controller parameters are derived using the gradient descent method. However, the initial values of learning rates of these adaptive laws are very important and they affect much to the performance of control systems. In this paper, the particle swarm optimization algorithm is applied to find the optimal learning rates of the parameter adaptation laws. To show the effectiveness of the proposed approach, numerical simulations of magnetic levitation system and inverted pendulum are provided to confirm the applications of the proposed PSO-WCMAC-based control system. The superiority of the proposed control scheme is also evaluated by quantitative comparison with other control schemes.

Asymptotic Tracking Controller Design for Nonlinear Systems With Guaranteed Performance.

In this paper, a novel adaptive control strategy is presented for the tracking control of a class of multi-input-multioutput uncertain nonlinear systems with external disturbances to place user-defined time-varying constraints on the system state. Our contribution includes a step forward beyond the usual stabilization result to show that the states of the plant converge asymptotically, as well as remain within user-defined time-varying bounds. To achieve the new results, an error transformation technique is first established to generate an equivalent nonlinear system from the original one, whose asymptotic stability guarantees both the satisfaction of the time-varying restrictions and the asymptotic tracking performance of the original system. The uncertainties of the transformed system are overcome by an online neural network (NN) approximator, while the external disturbances and NN reconstruction error are compensated by the robust integral of the sign of the error signal. Via standard Lyapunov method, asymptotic tracking performance is theoretically guaranteed, and all the closed-loop signals are bounded. The requirement for a prior knowledge of bounds of uncertain terms is relaxed. Finally, simulation results demonstrate the merits of the proposed controller.

A novel dynamic proportional-type iterative learning control design for non-linear systems

This paper presents a model-free adaptive iterative learning control (ILC) scheme called a proportional-type ILC scheme for non-linear systems. The obvious characteristic of the proposed ILC scheme is that we can easily finish the ILC task just utilising the Lipschitz constant of the system. In the proposed ILC scheme, the time-vary learning gain can be produced merely by input and output (I/O) measurements. Moreover, the convergence conclusion can be expressed by the ranges of the pseudo-partial derivative and the learning gain. In actual operation, a reasonable and useful convergence condition by a constant is also provided for selection. At last, the effectiveness of the proposed ILC scheme is shown by simulations.

TS fuzzy robust L1 control for nonlinear systems with persistent bounded disturbances

In this paper, a novel technique for Takagi–Sugeno (TS) model-based robust L1 controller design of nonlinear systems is proposed. Two synthesis methods based on quadratic and non-quadratic Lyapunov functions are considered. To design the robust stabilizing controller, a new approach for deriving sufficient conditions associated with the L1 performance criterion in terms of strict linear matrix inequality is proposed. This novel technique results in less pre-chosen scalar design variables and calculation burden. Furthermore, deriving the controller synthesis conditions via a non-quadratic Lyapunov function (NQLF) relaxes the obtained conditions. Therefore, the proposed approaches not only efficiently minimize the effect of persistent bounded disturbance, but also are applicable for wider classes of TS systems. Furthermore, some new lemmas are proposed to facilitate strict LMI formulation and to provide more degrees of freedom. Finally, several numerical and practical examples are presented to show the merits of this paper.