Output Tracking Control Research Articles

A new robust output tracking control for discrete-time switched constrained-input systems with uncertainty via a critic-only iteration learning method

In this paper, the control objective is driving the output of a discrete-time switched constrained system with uncertainty to track a desired output of reference by an optimal manner. A new augmented switched system with discounted cost function is constructed based on the switched and reference dynamics, which converts the complex tracking problem to a stabilizing robust control optimization problem. Combining the two stage optimization and iteration learning technique, the overall optimal hybrid policy is first achieved for the constrained switched tracking control. Instead of the general critic-actor structure, only critic neural network (NN) is applied in the algorithm to simply the architecture and manner of implementation. As the main computational burden or load in iteration learning process comes from the information transmissions of tuning NNs, the designed critic-only structure can reduce computational load with less transmissions. Then the convergence of the iteration learning process is demonstrated by theorems and the tracking objective is achieved as the output tracking errors get converged to zero. Finally, the proposed robust tracking control scheme for constrained-input switched systems is applied in the simulation, and the tracking results proved the effectiveness and applicability of the designed method.

MTN optimal control of MIMO non-affine nonlinear time-varying discrete systems for tracking only by output feedback

In practice, many controlled plants are equipped with MIMO non-affine nonlinear systems. The existing methods for tracking control of time-varying nonlinear systems mostly target the systems with special structures or focus only on the control based on neural networks which are unsuitable for real-time control due to their computation complexity. It is thus necessary to find a new approach to real-time tracking control of time-varying nonlinear systems. In this paper, a control scheme based on multi-dimensional Taylor network (MTN) is proposed to achieve the real-time output feedback tracking control of multi-input multi-output (MIMO) non-affine nonlinear time-varying discrete systems relative to the given reference signals with online training. A set of ideal output signals are selected by the given reference signals, the optimal control laws of the system relative to the selected ideal output signals are set by the minimum principle, and the corresponding optimal outputs are taken as the desired output signals. Then, the MTN controller (MTNC) is generated automatically to fit the optimal control laws, and the conjugate gradient (CG) method is employed to train the network parameters offline to obtain the initial parameters of MTNC for online learning. Addressing the time-varying characteristics of the system, the back-propagation (BP) algorithm is implemented to adjust the weight parameters of MTNC for its desired real-time output tracking control by the given reference signals, and the sufficient condition for the stability of the system is identified. Simulation results show that the proposed control scheme is effective and the actual output of the system tracks the given reference signals satisfactorily.

Exponential H ∞ output tracking control for coupled switched systems with states of different dimensions

This paper is concerned with the output tracking control for complex switched systems with non-diffusively delayed coupling. The states' dimensions are different in the coupled switched systems and reference system. On the base of the average dwell time and piecewise Lyapunov functional methods, a delay-dependent exponential stability criterion is derived for the switched systems under the QUAD condition which is less conservative than the Lipschitz condition. The state feedback controller is employed in the design of output tracking, and the tracking performance is guaranteed by solving a linear matrix inequality. Finally, three numerical examples are provided to show the advantage and effectiveness of the proposed theoretical results.

Incremental passivity-based H∞ output tracking control for switched nonlinear systems

This paper is concerned with the problem of H∞ output tracking control for a class of switched nonlinear systems with external disturbances using incremental passivity, even if the problem of H∞ output tracking control for none of subsystems is solvable. First, an incremental passivity concept of switched nonlinear systems without external disturbances is proposed. This incremental passivity property requires each active subsystem is incrementally passive. Then, sufficient conditions to be incrementally passive are given. Second, by resorting to the established incremental passivity theory, a state-dependent switching law and a set of feedback controllers are designed to solve the problem of H∞ output tracking control for a class of switched nonlinear systems with external disturbances. This avoids solving Hamilton-Jacobi (HJ) inequality. Third, a composite state-dependent switching law and the state feedback controllers are designed to solve the H∞ output tracking problem for a class of cascaded switched nonlinear systems with external disturbances. The designed composite switching law allows the driven switched system and the driving switched system switch asynchronously. Finally, two examples are provided to verify the effectiveness of the proposed method.

Distributed prescribed performance control for consensus output tracking of nonlinear semi-strict feedback systems using finite-time disturbance observers

ABSTRACTThe distributed consensus output tracking problem is dealt with for a class of nonlinear semi-strict feedback systems in the presence of mismatched nonlinear uncertainties, external disturbances and uncertain nonlinear virtual control coefficients of the subsystems. The systems are under a directed communication graph, where the leader node is the root. The controller is designed in a backstepping manner, and the dynamic surface technique is adopted to avoid direct differentiation. At each step of virtual controller design, a prescribed performance controller is constructed to achieve prescribed transient performance so that the system states remain in the feasible domain. Then each virtual controller is enhanced by a finite-time disturbance observer which estimates the disturbance term in a finite-time. The properties of the control system are analysed theoretically. It is clarified that the prescribed performance control technique ensures that the system signals stay in the feasible domain, whereas sufficiently small ultimate control errors can be achieved by the finite-time disturbance observers. Finally, the performance of the proposed methods is confirmed by numerical studies.

Experience replay–based output feedback Q‐learning scheme for optimal output tracking control of discrete‐time linear systems

SummaryThis paper focuses on solving the adaptive optimal tracking control problem for discrete‐time linear systems with unknown system dynamics using output feedback. A Q‐learning‐based optimal adaptive control scheme is presented to learn the feedback and feedforward control parameters of the optimal tracking control law. The optimal feedback parameters are learned using the proposed output feedback Q‐learning Bellman equation, whereas the estimation of the optimal feedforward control parameters is achieved using an adaptive algorithm that guarantees convergence to zero of the tracking error. The proposed method has the advantage that it is not affected by the exploration noise bias problem and does not require a discounting factor, relieving the two bottlenecks in the past works in achieving stability guarantee and optimal asymptotic tracking. Furthermore, the proposed scheme employs the experience replay technique for data‐driven learning, which is data efficient and relaxes the persistence of excitation requirement in learning the feedback control parameters. It is shown that the learned feedback control parameters converge to the optimal solution of the Riccati equation and the feedforward control parameters converge to the solution of the Sylvester equation. Simulation studies on two practical systems have been carried out to show the effectiveness of the proposed scheme.

Output tracking with disturbance attenuation for cascade control systems subject to network constraint

AbstractIn this paper, we investigate the output tracking control and disturbance attenuation for a class of cascade control systems subject to network‐induced delays. In order to indicate the time‐varying characteristics and uncertainty of network‐induced delays, a switched system approach is applied to the cascade architecture. This leads to the simultaneous design of controllers and switching signals in terms of the network transmission. Unlike the traditional cascade control design approach, which needs to first tune the secondary controller and then the primary one, we can provide a simultaneous design method of the double‐loop controllers and switching signals to make the networked cascade control system achieve the output tracking performance with disturbance attenuation. Finally, two examples are proposed to demonstrate the feasibility and the effectiveness of the approach.

Output Feedback-Based Output Tracking Control with Adaptive Output Predictive Feedforward for Multiple-Input–Multiple-Output Systems

This paper proposes a two-degree-of-freedom adaptive output feedback control system design scheme with an adaptive output predictive feedforward for multiple-input–multiple-output (MIMO) LTI system...

Observer-based improved Composite Nonlinear Feedback control for output tracking of time-varying references in descriptor systems with actuator saturation

In this paper, an observer-based improved Composite Nonlinear Feedback (CNF) controller is proposed for output tracking of general time-varying reference signals in descriptor systems subject to actuator saturation. Different parts of the proposed control law are designed based on the reconstructed states by a full-order descriptor observer. Algebraic constraints in descriptor systems can significantly complicate design procedures of the observer and the controller. Moreover, considering the actuator saturation constraint, adds additional complexity to the tracking problem. On the other hand, the proposed improved CNF controller’s performance is also challenged in presence of external disturbances. The effect of external disturbances, along with the previous mentioned constraints, needs extremely intricate calculations for investigating the solvability of the tracking problem. Furthermore, due to the nonlinearity of the closed-loop system, steady-state analysis is also needed to show the uniformly ultimately boundedness of the tracking error in presence of external disturbances. In this regard, precise mathematical operations are performed through a theorem, which investigates the tracking goal for three different cases of the saturation function. Finally, the theoretical achievements are verified by computer simulations through numerical and practical examples.

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.

Output tracking control of delayed switched systems via state-dependent switching and dynamic output feedback

This paper investigates the problem of output tracking control for a class of delayed switched linear systems via state-dependent switching and dynamic output feedback control. A state-dependent switching rule and the switching regions are proposed. Then the stability and tracking performance analysis are proposed based on single Lyapunov function technique, respectively. The design problem of dynamic output feedback controllers can be solved efficiently by using linear matrix inequalities (LMIs) toolbox. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.

Adaptive Fuzzy Control With High-Order Barrier Lyapunov Functions for High-Order Uncertain Nonlinear Systems With Full-State Constraints.

This paper focuses on the practical output tracking control for a category of high-order uncertain nonlinear systems with full-state constraints. A high-order tan-type barrier Lyapunov function (BLF) is constructed to handle the full-state constraints of the control systems. By the BLF and combining a backstepping design technique, an adding a power integrator, and a fuzzy control, the proposed approach can control high-order uncertain nonlinear system with full-state constraints. A novel controller is designed to ensure that the tracking errors approach to an arbitrarily small neighborhood of zero, and the constraints on system states are not violated. The numerical example demonstrates effectiveness of the proposed control method.

A Robust Iterative Learning Switching Controller for following Virtual Constraints: Application to a Hybrid Neuroprosthesis

Abstract In this paper, a robust iterative learning switching controller that uses optimal virtual constraint is designed for a hybrid walking exoskeleton that uses functional electrical stimulation and a powered exoskeleton. The synthesis of iterative learning control with sliding-mode control improves tracking performance and accuracy. The motivation for designing this switching controller was to obtain joint torques either from functional electrical stimulation or electric motor. A generalized switching controller is utilized to switch based on the stimulated muscle fatigue state. For achieving stability in walking cycle, the controller is used to force the system to follow the designed virtual constraints. The combination of sequential quadratic programming and genetic-particle swarm optimization algorithm is used for deriving the virtual constraints. The effectiveness of the new iterative learning control for output tracking is verified in a simple model of walking (3-link) that has active actuation at the hip joints.

A Local Separation Principle via Dynamic Approximate Feedback and Observer Linearization for a Class of Nonlinear Systems

A separation principle for a class of nonlinear systems inspired by the techniques of feedback linearization and observer design with linear error dynamics is discussed. The output feedback construction combines strategies for approximate feedback linearization and observer design, which are of interest per se , yielding a dynamic control law that ensures a linear, spectrally assignable, behavior from the certainty equivalence input mismatch to the extended state of the system and the observer. The first ingredient, namely the approximate feedback linearization strategy, can be applied, under mild conditions, also to nonlinear systems that are linearly uncontrollable—or that do not possess a well-defined relative degree in the case of a given output function—yet providing a chain of integrators of length equal to the dimension of the state in the transformed coordinates. Interestingly, a systematically designed nonlinear inner loop enables the use of linear design techniques, $\text{e.g.}$ , pole placement. The observer design, on the other hand, employs an additional dynamic extension that allows us to assign the local dynamic behavior of the error dynamics independently from its zeros, differently from the classic high-gain observer design. The paper is concluded by presenting several numerical simulations, including an output tracking control problem for the Ball and Beam model that does not possess a well-defined relative degree.

Constraint relaxation for design of binaural reproduction controller applying output tracking control

Constraint relaxation for design of binaural reproduction controller applying output tracking control

A Riemannian Geometric Approach to Output Tracking for Nonholonomic Systems

The problem of designing coordinate-invariant output tracking control laws for nonholonomic mechanical systems is addressed. The velocity constrained Euler-Lagrange equations of motion are expressed through a constrained affine connection which is compatible with the kinetic energy Riemannian metric. This formalism is used in designing an output tracking control law via backstepping, which is shown to guarantee exponential stability when the initial distance between the output and reference trajectory is within injectivity radius of the output manifold. In particular this enables almost-global tracking when the output manifold is a rank-1 symmetric space. The control law is intrinsic to the Riemannian structure, and is explicitly constructed. The control law is applied to the problem of tracking the reduced attitude of a rigid body with a nonholonomic velocity constraint. Numerical simulations illustrating the tracking performance are presented.

Adaptive Neural Network Finite-Time Control for Multi-Input and Multi-Output Nonlinear Systems With Positive Powers of Odd Rational Numbers.

This article investigates the adaptive neural network (NN) finite-time output tracking control problem for a class of multi-input and multi-output (MIMO) uncertain nonlinear systems whose powers are positive odd rational numbers. Such designs adopt NNs to approximate unknown continuous system functions, and a controller is constructed by combining backstepping design and adding a power integrator technique. By constructing new iterative Lyapunov functions and using finite-time stability theory, the closed-loop stability has been achieved, which further verifies that the entire system possesses semiglobal practical finite-time stability (SGPFS), and the tracking errors converge to a small neighborhood of the origin within finite time. Finally, a simulation example is given to elaborate the effectiveness and superiority of the developed.

Event-based output tracking control for fuzzy networked control systems with network-induced delays

This paper investigates the problem of event-based output tracking control with network-induced time-varying delays for nonlinear networked control systems (NCSs) approximated by interval type-2 (IT2) fuzzy systems. The membership functions (MFs) with upper and lower bounds are utilized to capture the uncertainties in the nonlinear systems. A novel IT2 fuzzy controller is designed, where the premise variables and MFs are asynchronous and different from those of the fuzzy systems. It is shown that the proposed adaptive event-based control mechanism for IT2 fuzzy NCSs is effective to reduce the utilization of limited network resources. Finally, simulation examples are applied to show the advantages of the presented approach.

Experimental study of robust output‐based continuous sliding‐modes controllers for Van der Pol oscillator

Robust output tracking control of Van der Pol oscillator is an important practical problem from an application point of view. Output feedback-based robust tracking control strategies are proposed in this work for that purpose. First, a high-order sliding-mode observer is used to estimate the oscillator states from the measurable output and to identify some types of disturbances. Then, five different continuous sliding-modes controllers (Continuous-SMCs) are provided to robustly track a desired time-varying trajectory, exponentially or in a finite time, for the Van der Pol oscillator despite the presence of external disturbances. The closed-loop stability for each Continuous-SMC is given based on input-to-state stability properties. Finally, experimental validations are also provided to show the feasibility of the proposed controllers in real time.

Research on Variable Cycle Engine Control Based on Model Reference Adaptive Sliding Mode Control Method

As to solve the problem of multivariable output tracking control of variable cycle engine under system uncertainties and external disturbances, an augmented model reference adaptive sliding mode control method based on LQR method was developed. Firstly, the model is augmented and the reference state is provided to the controller by designing the reference model using the optimal LQR method. Then, based on the state tracking sliding mode control method, the adaptive law is derived based on the strict stability condition of Lyapunov function to estimate the upper bound of the system perturbation matrix and the upper bound of the external disturbances. Finally, the controller achieves the asymptotic zero tracking error of the system under the conditions of uncertainty and external disturbance. The simulation results showed that the LQR-based augmented model reference adaptive sliding mode control method can solve the problem that the traditional sliding mode control method needs to specify the reference state in advance and improve the control performance of the variable cycle engine control with system uncertainties and external disturbance. The tracking of the control command is effectively achieved and the steady-state and dynamic performance are improved. The steady-state control errors under different conditions are less than 0.1%, the system overshoot is less than 0.5%, and the adjustment time is less than 1s, which conformed to the requirements of the aero engine control system technology.