Output Tracking Control Scheme Research Articles

Adaptive robust output tracking of uncertain strict-feedback nonlinear systems with full state constraints via control schemes with simple structure

In this paper, the problem of output tracking control is considered for a class of uncertain strict-feedback nonlinear systems with virtual control coefficients and full state constraints. It is assumed only that the nonlinear uncertainties of the systems are some smooth functions enough to guarantee the existence of solutions to the differential equations which describe uncertain systems, and that the virtual control coefficients are unknown. Based on backstepping algorithm, by combining the barrier Lyapunov function with an integral inequality reported in the current control literature, a design method is presented whereby a simple adaptive robust output tracking control scheme can be synthesised. The presented design method can evade the repeated differentiation problem appearing in using backstepping algorithm, and need not know all the nonlinear upper bounds of uncertainties, which are repeatedly employed at each step of backstepping procedure. It is also shown that the output tracking error of the uncertain nonlinear systems with both unknown virtual control coefficients and full state constraints can converge uniformly exponentially towards a ball which can be as small as desired. Finally, a numerical example is given, and the corresponding simulations are also implemented to demonstrate the simplicity of the proposed method and the validity of the theoretical results.

Adaptive finite-time direct fuzzy control for a nonlinear system with an unknown control gain based on an observer

An adaptive fuzzy output tracking control scheme is presented for a class of strict-feedback systems with an unknown control gain in this paper. An ideal controller that can achieve finite-time stabilization of the filtered tracking error system is approximated by an ideal fuzzy logic system. The actual fuzzy function is used as the controller to estimate the ideal fuzzy system via on-line adjustment of system parameters. A τ-observer ( i.e., the control error observer) is designed to manage the unknown fuzzy control error. Unlike previous studies, new parameter adaptive laws are constructed in this study, and derivative calculations in the filtered tracking error system are not required. An adaptive direct fuzzy controller based on a τ-observer is thus proposed. The practical finite-time stabilization of the output tracking error and the boundedness of all states in the closed-loop system are also ensured. Finally, the effectiveness of the proposed control criterion is verified via two simulation examples.

A Pole Placement-Based Output Tracking Control Scheme by Finite-and-Quantized Output Feedback

This paper proposes a finite-and-quantized output feedback output tracking control scheme for possibly non-minimum phase discrete-time linear systems that are subject to output quantization and saturation. An analytical pole placement-based control law is proposed by solely utilizing the finite-and-quantized output and the external reference output. The closed-loop stability and output tracking analysis are essentially different from the classical pole placement method. It needs to overcome some new technical issues caused by finite-and-quantized output feedback, such as how to realize closed-loop stability while restricting the finite quantization of the output measurement. This paper demonstrates that by appropriately designing the quantizer’s sensitivity, the proposed control law ensures all closed-loop signals are bounded, and the output tracking error converges to a certain residual set of the origin within a certain finite time, regardless of the existence of unstable zeros and poles in the control systems. Particularly, the residual set can be arbitrarily small under a specified design condition. Finally, a representative example validates the proposed control scheme.

Fixed-time sliding mode output tracking control for second-order switched systems with power integrators

The issue of fixed-time sliding mode output tracking control is addressed for second-order switched systems, where the tracking reference signal is defined by a power-integrator exogenous system. A novel non-singular terminal sliding mode surface is constructed, in which a reference is introduced into the sliding mode surface. Subsequently, an explicit novel fixed-time output tracking control scheme is constructively developed to drive the tracking error into a small neighborhood of the origin in fixed-time. Some sufficient criteria are developed to guarantee that the switched systems track the reference signal in fixed-time. Finally, a numerical example and an application example of an electro-hydraulic system are provided to demonstrate the validity of the proposed method.

Fixed-time output tracking control for a class of uncertain nonlinear MIMO systems

This article proposed a new fixed-time output tracking control scheme for a class of high-order MIMO nonlinear systems with unknown nonlinearities, parameter uncertainties and external disturbances. Firstly, a novel nonsingular recursive integral terminal sliding mode (ITSM) surface is designed by employing appropriate integral function and integer orders. Then the lumped system matched and mismatched uncertainties are estimated by developing a new adaptive fixed-time disturbance observer (AFTDO) based on super-twisting technique. The chattering problem existed in traditional disturbance observer (DO) can be reduced with the proposed AFTDO allowing the gains to adapt the changed derivative of lumped disturbances, effectively. Furthermore, semi-global fixed-time stability analysis is presented by means of Lyapunov stability theorem and it is proved that the system convergence time is independent of the system initial states and allowed to be arbitrarily adjusted based on practical demands. Finally, theoretical results are supported by numerical simulation and experimental results.

Energy-to-Peak Output Tracking Control of Actuator Saturated Periodic Piecewise Time-Varying Systems With Nonlinear Perturbations

This article is focused on the design of an output tracking control scheme for a class of continuous-time periodic piecewise time-varying systems (PPTVSs) with actuator saturation and nonlinear perturbations. The energy-to-peak tracking performance is studied based on an equivalent condition on the definiteness property of matrix polynomials. Considering the actuator saturation and nonlinear perturbation, matrix polynomial-based sufficient conditions are derived through the Lyapunov method using periodic matrix functions. From a perspective of subinterval segmentation aimed at PPTVSs, the proposed conditions can achieve less conservatism for tracking the output of a periodic time-varying reference system, while the controller gains can be computed using convex optimization. Moreover, a heuristic algorithm is constructed to simultaneously guarantee the closed-loop state convergence and the output tracking performance. The reduction in conservatism and the effectiveness of algorithm are demonstrated by illustrative case studies.

Practical output tracking control for nonlinearly parameterized longitudinal dynamics of air vehicles

This paper studies a practical output tracking control problem of the nonlinearly parametrized longitudinal dynamics of air vehicles. To make output tracking errors within an arbitrarily prescribed bound, a practical output control scheme is developed, employing a new integrated framework of a functional bounding technique for handling nonlinearly parametrized dynamics and a nonlinear state-feedback controller structure for regulating the multi-output tracking errors. A coordinate transformation and a control input domination design are used to decouple the air vehicle system into the attitude subsystem and velocity subsystem. The proposed control scheme achieves the closed-loop signals global boundedness and practical output tracking properties, despite the unknown parameters appearing in aerodynamic forces and moments nonlinearly. An air vehicle under additional disturbances is also studied for enhancing the robustness of the proposed controllers. Simulation results on a vehicle model that is affected by the structural flexibility illustrate the effectiveness and robustness of the practical output tracking control scheme.

A New Nussbaum-Type Function and its Application in the Control of Uncertain Strict-Feedback Systems

In this study, an adaptive fuzzy output tracking control scheme is proposed for uncertain strict-feedback systems with unknown control directions. Nussbaum-type functions are designed, with which the effects of multiple unknown control directions can be handled. Compared with the existing Nussbaum-type functions dealing with the same problem, the proposed Nussbaum-type functions have smaller amplitudes that are more conducive to the design of the controller. Fuzzy functions are used to estimate the unknown terms by combining adaptive laws with backstepping procedure. Adaptive fuzzy controller is constructed to guarantee that the output tracking error system is asymptotically stable and all states in the closed-loop system are bounded. Finally, numerical simulation studies are presented to illustrate the effectiveness of the proposed criteria.

Robust adaptive fault‐tolerant tracking control for a class of high‐order nonlinear system with finite‐time prescribed performance

SummaryIn this article, an improved prescribed performance adaptive control strategy is developed to handle the output tracking control problem for a class of nonlinear high‐order systems with actuator faults. The actuator faults considered include the bias fault and gain fault models. A technique of adding a power integrator is utilized to deal with the controller design problem of high‐order system. With the help of backstepping technology and the classic adaptive control, an output tracking control scheme is proposed, which can guarantee that all signals of the closed‐loop system are bounded and the tracking error converges to a finite‐time predetermined region. Finally, the feasibility of the presented control method is tested through the simulation results.

Decoupled control scheme for output tracking of a general industrial nonlinear MIMO system using improved active disturbance rejection scheme

Multivariable systems are broadly found in industrial processes with nonlinearities, uncertainties, and both input and state couplings. The basic idea to deal with such problems is to remove the input couplings, then estimating all other issues in an online manner followed be a rejection process. This challenge is presented in this research paper, where a decoupling control scheme is proposed based on the decoupler matrix and the Improved Active Disturbance Rejection Control (IADRC) paradigm. A theoretical analysis based on Hurwitz criterion followed by numerical simulations on a general industrial nonlinear, uncertain and highly coupled Multi-input Multi-Output (MIMO) system proved the validity of the proposed scheme in controlling such kinds of systems. Performance comparisons with the Conventional ADRC (CADRC) based decoupling control scheme are also included.

Neural Adaptive Fault Tolerant Control of Nonlinear Fractional Order Systems Via Terminal Sliding Mode Approach

This article proposes an adaptive neural output tracking control scheme for a class of nonlinear fractional order (FO) systems in the presence of unknown actuator faults. By means of backstepping terminal sliding mode (SM) control technique, an adaptive fractional state-feedback control law is extracted to achieve finite time stability along with output tracking for an uncertain faulty FO system. The unknown nonlinear terms are approximated by radial-basis function neural network (RBFNN) with unknown approximation error upper bound. Using convergence in finite time and fractional Lyapunov stability theorems, the finite time stability and tracking achievement are proved. Finally, the proposed fault tolerant control (FTC) approach is validated with numerical simulations on two fractional models including fractional Genesio–Tesi and fractional Duffing's oscillator systems.

MTN Optimal Tracking Control of SISO Nonlinear Time-Varying Discrete-Time Systems without Mechanism Models

Nonlinear time-varying systems without mechanism models are common in application. They cannot be controlled directly by the traditional control methods based on precise mathematical models. Intelligent control is unsuitable for real-time control due to its computation complexity. For that sake, a multidimensional Taylor network (MTN) based output tracking control scheme, which consists of two MTNs, one as an identifier and the other as a controller, is proposed for SISO nonlinear time-varying discrete-time systems with no mechanism models. A MTN identifier is constructed to build the offline model of the system, and a set of initial parameters for online learning of the identifier is obtained. Then, an ideal output signal is selected relative to the given reference signal. Based on the system identification model, Pontryagin minimum principle is introduced to obtain the numerical solution of the optimal control law for the system relative to the given ideal output signal, with the corresponding optimal output taken as the desired output signal. A MTN controller is generated automatically to fit the numerical solution of the optimal control law using the conjugate gradient (CG) method, and a set of initial parameters for online learning of the controller is obtained. An adaptive back propagation (BP) algorithm is developed to adjust the parameters of the identifier and controller in real time, and the convergence for the proposed learning algorithm is verified. Simulation results show that the proposed scheme is valid.

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.

Adaptive Backstepping-Based Neural Tracking Control for MIMO Nonlinear Switched Systems Subject to Input Delays.

This brief proposes a new neural-network (NN)-based adaptive output tracking control scheme for a class of disturbed multiple-input multiple-output uncertain nonlinear switched systems with input delays. By combining the universal approximation ability of radial basis function NNs and adaptive backstepping recursive design with an improved multiple Lyapunov function (MLF) scheme, a novel adaptive neural output tracking controller design method is presented for the switched system. The feature of the developed design is that different coordinate transformations are adopted to overcome the conservativeness caused by adopting a common coordinate transformation for all subsystems. It is shown that all the variables of the resulting closed-loop system are semiglobally uniformly ultimately bounded under a class of switching signals in the presence of MLF and that the system output can follow the desired reference signal. To demonstrate the practicability of the obtained result, an adaptive neural output tracking controller is designed for a mass-spring-damper system.

Optimal Sliding Mode Robust Control for Fractional-Order Systems with Application to Permanent Magnet Synchronous Motor Tracking Control

This paper presents an optimal sliding mode output tracking control scheme for a class of fractional-order uncertain systems. Firstly, an augmented fractional-order system, composed of the original system and the external system, is constructed to transform the optimal output tracking issue into the design problem of linear quadratic regulator. The optimal tracking control problem for the nominal augmented fractional-order system is then studied. Secondly, the fractional-integral sliding mode controller is introduced to robustify the augmented fractional-order system, which satisfy the matching conditions. As a result, the original system output can track the external system output trajectory effectively even the uncertainties exist. Finally, the developed design techniques are applied to the tracking control of fractional-order permanent magnet synchronous motor. The simulation results demonstrate the validity of this approach.

Tracking Control for Nonlinear Minimum Phase Systems

In this paper, we proposed the robust output tracking control scheme for a class of MIMO nonlinear dynamical systems using output feedback linearization method. Because the states of zero dynamics are not accessible, we consider these states as bounded uncertainties(or disturbances) under the assumption that zero dynamics is stable(or nonlinear minimum phase) and also we have no priori knowledge concerning the magnitude of these uncertainties. A second order sliding mode control method is used to establish the desired output tracking controller. It is shown that the outputs of the closed-loop system asymptotically track given output trajectories despite the uncertainties while maintaining the boundedness of all signals inside the loop. From the computer simulation results for the numerical example, we prove the validity of the proposed control algorithm.

Output Tracking Control for Networked Systems: A Model-Based Prediction Approach

This paper studies the problem of output tracking for networked control systems with network-induced delay, packet disorder, and packet dropout. The round-trip time (RTT) delay is redefined to describe these communication constraints in a unified way. By including the output tracking error as an additional state, the output tracking problem is converted into the stabilization problem of an augmented system. Based on the observer of the original state increment and the feedback of the output tracking error, a model-based networked predictive output tracking control (NPOTC) scheme is proposed to actively compensate for the random RTT delay. The closed-loop stability is proved to be independent of the RTT delay, and the separation principle for the design of the observer-based state feedback controller is still held in the NPOTC system. A two-stage controller design procedure is presented, which not only guarantees the stability of the closed-loop NPOTC system but also achieves the same output tracking performance as that of the local control system for time-varying reference signals. Both numerical simulations and practical experiments on an Internet-based servo motor system illustrate the effectiveness of the proposed method.

Nonlinear dynamics and station-keeping control of a rotating tethered satellite system in halo orbits

The dynamics of a rotating tethered satellite system (TSS) in the vicinity of libration points are highly nonlinear and inherently unstable. In order to fulfill the station-keep control of the rotating TSS along halo orbits, a nonlinear output tracking control scheme based on the θ–D technique is proposed. Compared with the popular time-variant linear quadratic regulator (LQR) controller, this approach overcomes some limitations such as on-line computations of the algebraic Riccati equation. Besides, the obtained nonlinear suboptimal controller is in a closed form and easy to implement. Numerical simulations show that the TTS trajectories track the periodic reference orbit with low energy consumption in the presence of both tether and initial injection errors. The axis of rotation can keep pointing to an inertial specific object to fulfill an observation mission. In addition, the thrusts required by the controller are in an acceptable range and can be implemented through some low-thrust propulsion devices.

Nonfragile Output Tracking Control of Hypersonic Air-Breathing Vehicles With an LPV Model

This paper presents a novel nonfragile output tracking control scheme for flexible hypersonic air-breathing vehicles (HAVs). This problem is challenging due to the complex interactions between the aerodynamics, the propulsion system, and the structural dynamics. By utilizing the curve-fit and the least-squares methods, a new model for HAVs is established, and then converted into a linear parameter-varying system, in which the scheduling variables depend on a handful of meaningful states and parameters. With a specified reference model, a tracking error model is also proposed. The nonfragile output tracking controller is designed, which guarantees the tracking error dynamics to be robustly stable. Finally, simulation results are presented to show the effectiveness of the proposed control design scheme.

Adaptive neural decentralized control for strict feedback nonlinear interconnected systems via backstepping

An approximation based adaptive neural decentralized output tracking control scheme for a class of large-scale unknown nonlinear systems with strict-feedback interconnected subsystems with unknown nonlinear interconnections is developed in this paper. Within this scheme, radial basis function RBF neural networks are used to approximate the unknown nonlinear functions of the subsystems. An adaptive neural controller is designed based on the recursive backstepping procedure and the minimal learning parameter technique. The proposed decentralized control scheme has the following features. First, the controller singularity problem in some of the existing adaptive control schemes with feedback linearization is avoided. Second, the numbers of adaptive parameters required for each subsystem are not more than the order of this subsystem. Lyapunov stability method is used to prove that the proposed adaptive neural control scheme guarantees that all signals in the closed-loop system are uniformly ultimately bounded, while tracking errors converge to a small neighborhood of the origin. The simulation example of a two-spring interconnected inverted pendulum is presented to verify the effectiveness of the proposed scheme.