Non-vanishing Uncertainties Research Articles

Disturbance Observer-Based Prescribed-Time Tracking Control of Nonlinear Systems With Non-Vanishing Uncertainties

Disturbance Observer-Based Prescribed-Time Tracking Control of Nonlinear Systems With Non-Vanishing Uncertainties

Practical Prescribed Time Tracking Control With Bounded Time-Varying Gain Under Non-Vanishing Uncertainties

Practical Prescribed Time Tracking Control With Bounded Time-Varying Gain Under Non-Vanishing Uncertainties

Prescribed-Time Tracking With Guaranteed Performance for a Class of Self-Switching Systems Under Unknown Control Directions.

This article investigates the problem of prescribed-time tracking control for a class of self-switching systems subject to nonvanishing/nonparametric uncertainties and unknown control directions. Due to the existence of the unknown inherent nonlinear dynamics and the undetectable actuation faults, the resultant control gain of the system becomes unknown and time varying, making the control impact on the system uncertain and the prescribed-time control synthesis nontrivial. The underlying problem becomes further complex as the switching is arbitrary and unknown. To circumvent the aforementioned difficulties, the following major steps are employed. First, by integrating a novel time-varying feedback gain and performance function into the control synthesis, the nonvanishing uncertainties are completely rejected and the transient performance is guaranteed. Second, to facilitate the stability analysis under arbitrarily switching, the concept of the constraining function is introduced and incorporated into a skillfully chosen common Lyapunov function. Third, to deal with the uncertain control gain, a new Nussbaum-related lemma is derived. The proposed control is shown to be capable of ensuring that the tracking error not only evolves within the prescribed bound during all the operation time but also converges to zero at the rate of convergence that can be preassigned as fast as desired, in the presence of self-switching dynamics and unknown control directions. Both theoretical analysis and numerical simulation confirm the effectiveness of the proposed method.

Prescribed-Time Tracking Control of MIMO Nonlinear Systems With Nonvanishing Uncertainties

It is highly desirable yet challenging to achieve zero-error tracking within a given short time period for uncertain multi-input multi-output (MIMO) nonlinear systems. Previous results are primarily state-regulation oriented and are valid only for single-input single-output (SISO) linear systems or nonlinear systems in normal-form. This note presents a tracking control solution for high-order MIMO nonlinear systems in strict-feedback-like form. The proposed control is able to achieve precise tracking within the prescribed time irrespective of initial conditions in the presence of mismatched uncertainties and non-vanishing disturbances.

Adaptive asymptotic tracking control for autonomous underwater vehicles with non-vanishing uncertainties and input saturation

This article provides an adaptive asymptotic backstepping-based tracking control algorithm for autonomous underwater vehicles (AUVs) under the situation of non-vanishing uncertainties and input saturation. Firstly, the adaptive asymptotic control algorithm is developed to compensate the non-vanishing uncertainties. And then, virtual control stabilizing functions are reconstructed to improve the system performance by virtue of variable substitutions. Next, the hyperbolic tangent function is applied to handle the unknown input saturation problem. Based on the Lyapunov stability theory, the asymptotic stability of AUVs is proven. Finally, simulation results illustrate that the control strategy can effectively inhibit the effect of unknown model dynamics on the system.

Asymptotic containment control of uncertain multi-agent systems with partially unknown non-identical control directions

This paper investigates the precise containment control problem for nonlinear multi-agent systems (MAS) subject to non-vanishing uncertainties and unknown non-identical control directions under directed communication topology. Due to the existence of the inherent non-vanishing/non-parametric uncertainties and unknown control directions, the precise (zero-error) containment control synthesis becomes nontrivial. The underlying problem becomes even complicated if the convergence rate is required to be pre-specified. This work aims at circumventing the aforementioned difficulties to derive a precise containment control solution. The salient features behind the derived algorithms are: i) the non-vanishing uncertainties are completely rejected; ii) the containment error is regulated to zero at prescribed convergence rate, in spite of the non-vanishing uncertainties and unknown non-identical control directions; and iii) the full-state containment rather than output containment is achieved. A simulation example is given to confirm the effectiveness of the proposed method.

Active Disturbance Rejection Formation Tracking Control for Uncertain Nonlinear Multi-Agent Systems With Switching Topology via Dynamic Event-Triggered Extended State Observer

In this paper, the time-varying formation tracking (TVFT) control problem is concerned for multi-agent systems (MASs). The primary objective is to achieve asymptotical convergence for formation tracking error subject to nonparametric and nonvanishing uncertainties. Firstly, in order to estimate lumped unmodeled dynamics and external disturbances, an event- triggered fuzzy extended state observer (FESO) inspired by our previous works is established for follower group, in which efficient nonlinear observation pattern and convenient linear numerical tractability are integrated. For rationally scheduling transmission, a dynamic event-triggered mechanism is applied to form adaptively regulating strategy. Secondly, a distributed TVFT control law is developed by utilizing neighborhood formation tracking errors. Different from conventional disturbance-tolerant methodologies, total disturbance compensation is introduced to attenuate uncertainty influence in real time. Consequently, active disturbance rejection formation tracking control architecture is systematically constructed for uncertain MASs. Moreover, considering switching topology, the controller design algorithm is presented by piecewise Lyapunov analysis. Finally, the effectiveness and advantages of the proposed event-triggered FESO-based active disturbance rejection control protocol is illustrated by an numerical example on unmanned aerial vehicle swarm system.

Finite-time integral control for a class of nonlinear planar systems with non-vanishing uncertainties

This paper considers the problem of globally regulating a class of planar nonlinear systems perturbed by various non-vanishing uncertainties including constant step disturbances, exogenous time-varying disturbances with unknown magnitudes, and modeling uncertainties with unknown system parameters. A new integral controller consisting of a nonlinear integral dynamic and a semi-linear control law is constructed to drive the states of the uncertain systems to the origin in a finite time. This is achieved by three major mechanisms: (i) for the purpose of finite-time convergence, a lower-order integral dynamic is first constructed; (ii) by revamping the technique of adding a power integrator, a semi-linear control law containing a linear corrective term is proposed to handle the various forms of uncertainties; and (iii) a new inequality is established to provide an effective estimating tool for the selection of a suitable control gain to guarantee finite-time stability.

Robust Synchronization of Class Chaotic Systems Using Novel Time-Varying Gain Disturbance Observer-Based Sliding Mode Control

For synchronization of a class of chaotic systems in the presence of nonvanishing uncertainties, a novel time-varying gain observer-based sliding mode control is proposed. First, a novel time-varying gain disturbance observer (TVGDO) is developed to estimate the uncertainties. Then, by using the output of TVGDO to modify sliding mode control (SMC), a new TVGDO-based SMC scheme is developed. Although the observation and control precision of conventional fixed gain disturbance observer-based control (FGDOC) for chaotic systems can be guaranteed by a high observer gain, the undesirable spike problem may be caused by the high gain if the initial values of estimate and true states are not equal. The most attractive feature of this work is that the newly proposed TVGDO can eliminate the spike problem by developing a time-varying gain scheme. Finally, the effectiveness of the proposed method is demonstrated by the numerical simulation.

Practical tracking control of perturbed uncertain nonaffine systems with full state constraints

In this paper, we study the practical tracking control problem for a class of pure-feedback systems subject to full states asymmetric and time-varying constraints, non-vanishing uncertainties and external disturbances. A new robust control scheme is proposed to deal with state constraints. Unlike some existing results for practical tracking control, the proposed method does not involve any switching and is able to deal with asymmetric and time varying state constraints without the need for feasibility conditions. Furthermore, with proper choice of scaling function, three different tracking control results (i.e., ultimately uniformly bounded tracking, practical tracking and asymptotic tracking) can be achieved. Simulation verification further confirms the effectiveness of the proposed approach.

Velocity-Observer-Based Distributed Finite-Time Attitude Tracking Control for Multiple Uncertain Rigid Spacecraft

This article addresses the distributed finite-time attitude tracking control problem for a group of uncertain rigid spacecraft in the presence of unavailable angular velocity under the directed topology condition. First, a finite-time adaptive neural network observer is proposed for each follower to estimate its own unavailable angular velocity. Unlike existing velocity-observer-based design methods, the proposed one does not need the exact knowledge of the system model, and works well for the systems with both vanishing and nonvanishing uncertainties. Further, another finite-time observer is provided to obtain the precise angular velocity information of the dynamic leader in a distributed manner. Based on these two observers and adding a power integrator technique, a continuous distributed finite-time control scheme with only attitude measurements is finally established. A rigorous theoretical proof shows that the entire finite-time stability of the combined observer–controller closed-loop system is ensured. Simulation results illustrate the benefits and effectiveness of the developed control scheme.

Local stabilization for a class of nonlinear impulsive switched system with non-vanishing uncertainties under a norm-bounded control input

Local stabilization for a class of nonlinear impulsive switched system with non-vanishing uncertainties under a norm-bounded control input

A general approach to precise tracking of nonlinear systems subject to non-vanishing uncertainties

In this work we introduce a new and systematic methodology for precise tracking control of normal-form nonlinear systems subject to non-vanishing/non-parametric uncertainties. We propose a general solution to achieving robust tracking with a rate of convergence that can be pre-assigned as fast as desired (e.g. super exponential or even closer to a pre-specified finite time). The key design tool is the utilization of a time-varying feedback gain through a time-varying scaling function that satisfies certain conditions. Our method also features with complete rejection (rather than partial attenuation) of uncertainties/disturbances and regulation of the tracking error to zero. A generic and analytical procedure to construct the time-varying rate function is provided, extending and generalizing the existing results in the literature.

Zero-error tracking control with pre-assignable convergence mode for nonlinear systems under nonvanishing uncertainties and unknown control direction

This work addresses the tracking control problem for a class of high-order multi-input multi-output (MIMO) nonlinear systems with unknown control direction and nonparametric uncertainties. By integrating a matrix (rather than scalar) rate transformation with Nussbaum gain, we develop an accelerated robust adaptive control that exhibits several attractive features: (1) it is able to achieve full-state zero-error tracking despite unknown control direction and non-vanishing uncertainties; (2) with the proposed control scheme, the whole tracking process seamlessly consists of the first phase of steering the tracking error into an adjustable small residual region with accelerated convergence rate and the second phase of further driving the error to zero; (3) before reaching the residual region, each component of the tracking error is forced to decay at an accelerated rate that can be pre-assigned; and (4) the resultant control action is continuous differentiable everywhere without involving excessively large initial driving effort.

Local exponential stabilization for a class of uncertain nonlinear impulsive periodic switched systems with norm-bounded input

This paper investigates stabilization for a class of uncertain nonlinear impulsive periodic switched systems under a norm-bounded control input. The proposed approach studies stabilization criteria locally where the nonlinear dynamics satisfy the Lipschitz condition only on a subspace containing the origin, not on $$\mathbb {R}^{n}$$ . This makes the proposed approach applicable in most practical cases where the region of validity is limited due to physical issues. In presence of different resources of non-vanishing uncertainties, the main objective is to find a stabilizing control signal such that not only trajectories exponentially converge to a sufficient small ultimate bound, but also have the largest region of attraction. To this, for a more general model, we first propose several sufficient conditions using the common Lyapunov function approach. The proposed strategy allows the Lyapunov function to increase in some intervals, which is suitable when some of the subsystems are unstable and uncontrollable. We then apply these conditions to the targeted system, and the sufficient criteria are extracted in the forms of linear and bilinear matrix inequalities. To achieve the main goal, an optimization problem is also formulated which is solvable using augmented Lagrangian methods. Finally, some illustrative examples are presented to demonstrate the proposed approach.

Robust Adaptive Fault-Tolerant PID Control of MIMO Nonlinear Systems With Unknown Control Direction

This paper shows that the structurally simple and computationally inexpensive PID control, popular with single-input single-output (SISO) linear time-invariant systems, can be generalized and extended to control nonlinear multi-input multi-output (MIMO) systems with nonparametric uncertainties and actuation failures. By utilizing the Nussbaum-type function and the matrix decomposition technique, nonsquare systems with unknown control direction are also considered. Furthermore, with the proposed analytic algorithms for adaptively tuning PID gains, the resultant PID control can be made robust, adaptive, and fault-tolerant, and applicable to nonlinear systems with nonvanishing uncertainties and unexpected actuation faults. Both theoretical analysis and numerical simulation verify the effectiveness and benefits of the design.

Robust adaptive path following of underactuated ships

Robust path following is an issue of vital practical importance to the ship industry. In this paper, a nonlinear robust adaptive control strategy is developed to force an underactuated surface ship to follow a predefined path at a desired speed, despite the presence of environmental disturbances induced by wave, wind and ocean-current. The proposed controller is scalable and is designed using Lyapunov's direct method and the popular backstepping and parameter projection techniques. Along the way of proving closed-loop stability, we obtain a new stability result for nonlinear cascade systems with non-vanishing uncertainties. Interestingly, it is shown in this paper that our developed control strategy is easily extendible to situations of practical importance such as parking and point-to-point navigation. Numerical simulations using the real data of a monohull ship are provided to illustrate the effectiveness of the proposed methodology for path following of underactuated ships.

State- and output-feedback robust path-following controllers for underactuated ships using Serret–Frenet frame

This paper develops state- and output-feedback controllers that force an underactuated surface ship to follow a predefined path at a constant forward speed controlled by the main thruster system under the presence of environmental disturbances induced by wave, wind and ocean-current. The proposed controllers are designed using Lyapunov’s direct method and the popular backstepping. The unmeasured sway and yaw velocities are estimated by introducing a new nonlinear passive observer. A stability result for nonlinear cascade systems with nonvanishing uncertainties is introduced to analyze closed-loop stability. Numerical simulations using the real data of a monohull ship are provided to illustrate the effectiveness of the proposed methodology for path following of underactuated ships.

Robust near-optimal output feedback control of non-linear systems

This work proposes a robust near-optimal non-linear output feedback controller design for a broad class of non-linear systems with time-varying bounded uncertain variables. Both vanishing and non-vanishing uncertainties are considered. Under the assumptions of input-to-state stable (ISS) inverse dynamics and vanishing uncertainty, a robust dynamic output feedback controller is constructed through combination of a high-gain observer with a robust optimal state feedback controller synthesized via Lyapunov's direct method and the inverse optimal approach. The controller enforces exponential stability and robust asymptotic output tracking with arbitrary degree of attenuation of the effect of the uncertain variables on the output of the closed-loop system, for initial conditions and uncertainty in arbitrarily large compact sets, provided that the observer gain is sufficiently large. Utilizing the inverse optimal control approach and singular perturbation techniques, the controller is shown to be near-optimal in the sense that its performance can be made arbitrarily close to the optimal performance of the robust optimal state feedback controller on the infinite time-interval by selecting the observer gain to be sufficiently large. For systems with non-vanishing uncertainties, the same controller is shown to ensure boundedness of the states, uncertainty attenuation and near-optimality on a finite time-interval. The developed controller is successfully applied to a chemical reactor example.