Robust resilient control for parametric strict feedback systems with prescribed output and virtual tracking errors

We study the problem of identification and output tracking for uncertain strict-feedback systems where the unknown part of the system depends only on the output. The unknown nonlinear terms in the system description are not linearly parametrized, but it is assumed that the optimal parameters that characterize a neural net based approximation to the nonlinearities lie within a known compact set. The proposed controllers, with full state and derivative information, guarantee the boundedness of all signals in the closed-loop system. Also, at the expense of increased control effort, the output tracking error can be driven to an arbitrarily small neighborhood of the origin arbitrarily fast. Moreover, by specifying an appropriate reference signal, the satisfaction of a relevant persistency of excitation condition is ensured, and hence an adequate identification of the uncertain system is achieved.

In this paper, a recently proposed control design technique, model reference robust control (MRRC), is generalized to provide input–output robust control for a much wider class of SISO systems. A system under consideration may contain not only parametric uncertainties, disturbances, uncertain high-order nonlinearities associated with system output (including stable unmodelled dynamics of the output), but also multiplicative unmodelled dynamics of the input of the system. Input unmodelled dynamics may be unstable and of infinite dimension. Common assumptions such as the order of the system, or bounds on system parameters, or coefficients in size-bounding functions on uncertainties and unmodelled dynamics are not needed in this paper. The a priori information required to apply the proposed design procedure includes the relative degree of the overall system, closed-form expressions of bounding functions, and, for arbitrarily small error in tracking the output of any given reference model, the minimum phase condition. Under the proposed control, the output tracking error can be made arbitrarily small to achieve any specified tracking accuracy. The distinct feature of MRRC is that neither uncertainties nor unmodelled dynamics are required to be small. © 1997 by John Wiley & Sons, Ltd.

This paper proposes a sliding mode tracking control (SMC) approach for a class of state constrained nonlinear systems with prescribed transient and steady-state behavior. The prescribed tracking performance can be characterized by the inequalities on the output tracking error. The proposed SMC is designed based on a two-step backstepping procedure. At the first step, a virtual control scheme is designed by introducing and bounding an integral barrier function, by which the prescribed performance constraint and the system output constraint are satisfied. Then, the SMC is designed by introducing and bounding another integral barrier function, by which the control singularity problem is avoided and the state constraint is satisfied. Theoretical analysis and simulation results verify that the constraints is satisfied and the tracking error converges to an arbitrary small residual set, with convergence rate no less than a prescribed value, exhibiting a maximum overshoot less than a sufficiently small prescribed constant.

This paper design an output tracking controller for a class of uncertain nonlinear systems to address the input quantization and output tracking funnel control problem. By the traditional adaptive control and backstepping technique, an adaptive quantized funnel control scheme is designed. It is shown that the presented controller can ensure that arbitrary closed-loop signals are globally uniformly bounded, and the output tracking error is bounded, and held in the prescribed funnel performance functions. The presented control scheme is checked through the simulation result.

In the process of energy storage clusters participating in automatic generation control (AGC) of power systems, reasonable command power allocation is the key to effective execution of frequency regulation commands. Currently, the traditional AGC command tracking energy storage control strategy is to allocate according to the proportion of energy storage rated power. Due to the difference in power configuration of energy storage capacity in energy storage clusters, this will cause the state of charge (SOC) of small capacity energy storage power stations to reach the boundary first, resulting in limited output and command tracking errors, affecting the frequency regulation effect. This article proposes an energy storage cluster frequency modulation power optimization strategy that takes into account command tracking errors to address the above issues. Firstly, considering the basic process of automatic power generation control, a collaborative control architecture was designed for energy storage clusters to participate in AGC regulation; Then, a multi type energy storage regulation target considering the state of charge of energy storage was constructed. The model construction took into account the constraints of instruction power allocation and energy storage operation. Finally, the Lagrange multiplier method was used to solve the problem and obtain the output allocation of energy storage. The proposed strategy has been verified through simulation analysis to ensure the effective execution of AGC instructions and reduce the instruction tracking error of energy storage clusters participating in AGC regulation.

This paper considers the adaptive neuro-fuzzy control scheme to solve the output tracking problem for a class of strict-feedback nonlinear systems. Both asymmetric output constraints and input saturation are considered. An asymmetric barrier Lyapunov function with time-varying prescribed performance is presented to tackle the output-tracking error constraints. A high-gain observer is employed to relax the requirement of the Lipschitz continuity about the nonlinear dynamics. To avoid the "explosion of complexity", the dynamic surface control (DSC) technique is employed to filter the virtual control signal of each subsystem. To deal with the actuator saturation, an additional auxiliary dynamical system is designed. It is theoretically investigated that the parameter estimation and output tracking error are semi-global uniformly ultimately bounded. Two simulation examples are conducted to verify the presented adaptive fuzzy controller design.

Stability of adaptive control for time-varying systems (TVS) is surveyed and then a powerful mathematical tool-martingale hyperconvergence theorem-is presented which can be successfully applied to analyze the convergence of various identification algorithms and adaptive control algorithms for TVS. It makes an important advance in the study of the convergence and stability problems of TVS. The analysis indicates that the output tracking error given by adaptive control based on the projection algorithm is consistently bounded. The authors state that this is the best convergence result in the area of adaptive control for time-varying systems up to now.

In a new inversion-based iterative learning algorithm for a class of nonminimum-phase systems the least-squares method is used to estimate the system parameters after each repetitive trial. The output tracking error and the identified system model are used through stable inversion to find the feedforward input, together with the desired state trajectories, for the next trial. A robust controller is used in each trial to ensure the stability of the systems and the output tracking error convergence. Sufficient conditions for learning control convergence are provided. Simulation studies on systems with gain uncertainty and time constant uncertainty are also presented. Simulation results demonstrate that the proposed learning control scheme is effective in reproducing the desired trajectories.

This research utilizes the repetitive control approach in morphing a high-speed cam mechanism so that its output displacement tracks the desired output trajectory. The main objective is to reduce the output tracking error, which is the difference between the actual and desired output displacements of the output mass. A 3-degree of freedom mathematical model is used to analyze and represent the cam follower system. The output tracking error in cam follower systems is generally caused by errors in cam profile manufacturing, variation in the speed of the driving motor and the dynamics of the cam follower system. Theoretical and experimental results show that the output tracking error is greatly reduced after repetitive control has been applied to the system. As a result, the actual output displacement tracks the desired output displacement very closely.

In this article, a new self-tuning control adaptive system utilizing output tracking error in identification and control instead of the plant output is presented. The output tracking error that is used in the proposed controller works based on the difference between the plant output and its desired value. Thus, in the controller design instead of direct use of model reference of conventional self-tuning controller, another model reference is used for the output tracking error. In contrast to the conventional self-tuning controller, in this approach, dynamic of disturbance does not need to be known a priori and the performance of the control system including robustness against the external disturbance is outstandingly superior to the conventional method. Furthermore, the suggested control structure is simpler with fewer computations and complications. Simulation results demonstrate practicality and effectiveness of the proposed approach in controlling linear systems and locally in nonlinear ones.

Mechatronic positioning servo system is a typical nonlinear system, and also usually exist many uncertainties. The nonlinear and uncertainties make the conventional controller not yield to the required system performance. Aiming at unknown dynamic friction parameters and unknown load characteristic, a adaptive friction compensation is designed for the servo system.The design of the controller is simplified by using a dynamic filter and an adaptive robust controller is designed to improve the system steady state accuracy and the robustness respectively. The output tracking error is proved to converge to a small neighborhood around zero and the performance of system tracking error can be guaranteed by appropriately choosing design parameters and introducing an initializing technique. Simulation and experiment results are shown to effectively inhibit the disadvantageous influence of friction and lay the foundation for improvement of dynamic performance of servo system.

Prediction of Heliostat Tracking Errors Using an Adaptive Neuro-Fuzzy Inference System

This paper studies the tracking control problem for underactuated surface vessel with unknown time-varying disturbances. To avoid the controller singularity problem, the constraints on output tracking errors of underactuated surface vessel are enforced in the control design. With the help of error transformation functions, the constrained tracking control of the vessel is converted into the stabilization of the transformed error systems. To compensate for the effect of the external disturbances, disturbance observers are presented to estimate the unknown time-varying disturbances. Subsequently, disturbance-observer-based tracking control is developed to steer the vessel along a desired reference trajectory with guaranteeing the tracking errors within certain predefined bounds. The performance of the proposed tracking control is demonstrated through simulation results.

In this paper, an adaptive optimal predictive control method based on improved prescriptive performance is proposed for the path tracking control of an underactuated two‐wheeled mobile robot. The system is challenging to control due to its underactuated characteristics and nonlinear dynamics behavior. To improve the robustness of the system under uncertainty and reduce the jitter phenomenon, a new control strategy is designed by combining the improved prescribed performance control with adaptive optimal predictive control. The method ensures that the system output can satisfy the prescribed performance requirements within a specific time range and recover the stable operation faster under certain disturbances through the design of reasonable soft‐constraint performance indexes. In addition, a rigorous stability analysis of the control system is carried out to demonstrate the boundedness of the error function and the transient and steady‐state performances specified by the output tracking error. Simulation results show that the proposed control method can significantly improve the stability and control accuracy of the system under disturbances.

In this study, the authors address the problem of output tracking for single-input and single-output (SISO) parametric strict-feedback (PSF) non-linear systems in the presence of uncertain parameters under adaptive sampled-data control. The main contributions of this work are twofold: (i) the authors develop a systematic design procedure for adaptive sampled-data controller by combining the backstepping technique with two kinds of discretisation approaches; and (ii) they also provide a theoretical analysis for the performance of sampled-data controller, which shows that the proposed adaptive sampled-data controller can regulate the tracking error to any given neighbourhood of the origin and the state of the sampled-data closed-loop system is bounded. Finally, an illustrative example is given to demonstrate the effectiveness of the presented method.