Simple Adaptive Law Research Articles

Trajectory Tracking with Obstacle Avoidance for Nonholonomic Mobile Robots with Diamond-Shaped Velocity Constraints and Output Performance Specifications.

In this paper, we address the trajectory-/target-tracking and obstacle-avoidance problem for nonholonomic mobile robots subjected to diamond-shaped velocity constraints and predefined output performance specifications. The proposed scheme leverages the adaptive performance control to dynamically adjust the user-defined output performance specifications, ensuring compliance with input and safety constraints. A key feature of this approach is the integration of multiple constraints into a single adaptive performance function, governed by a simple adaptive law. Additionally, we introduce a robust velocity estimator with a priori-determined performance attributes to reconstruct the unmeasured trajectory/target velocity. Finally, we validate the effectiveness and robustness of the proposed control scheme, through extensive simulations and a real-world experiment.

Adaptive Gain Tuning Rule for Nonlinear Sliding-Mode Speed Control of Encoderless Three-Phase Permanent Magnet Assisted Synchronous Motor

In this paper, an adaptive gain tuning rule is designed for the nonlinear sliding mode speed control (NSMSC) in order to enhance the dynamic performance and the robustness of the permanent magnet assisted synchronous reluctance motor (PMa-SynRM) with considering the parameter uncertainties. A nonlinear sliding surface whose parameters are altering with time is designed at first. The proposed NSMSC can minimize the settling time without any overshoot via utilizing a low damping ratio at starting along with a high damping ratio as the output approaches the target set-point. In addition, it eliminates the problem of the singularity with the upper bound of an uncertain term that is hard to be measured practically as well as ensures a rapid convergence in finite time, through employing a simple adaptation law. Moreover, for enhancing the system efficiency throughout the constant torque region, the control system utilizes the maximum torque per ampere technique. The nonlinear sliding surface stability is assured via employing Lyapunov stability theory. Furthermore, a simple sliding mode estimator is employed for estimating the system uncertainties. The stability analysis and the experimental results indicate the effectiveness along with feasibility of the proposed speed estimation and the NSMSC approach for a 1.1-kW PMa-SynRM under different speed references, electrical and mechanical parameters disparities, and load disturbance conditions.

Robust Reduced Order Thau Observer With the Adaptive Fault Estimator for the Unmanned Air Vehicles

Developing fault detection and diagnoses algorithms for the unmanned air vehicles such as the quadrotors is challenging since they are intrinsically non-linear, time-varying, unstable, and uncertain. This paper develops a reduced order Thau observer by only considering the uncertain rotational dynamics, which are re-constructed as the dominant linear and non-linear for the design purpose. Therefore, the proposed Thau observer is just third order and can reveal a rotational state estimation error in the presence of the quadrotor faults. This paper also equips the proposed Thau observer with a simple online adaptive fault estimation law, which is able to recognize up to two faulty actuators instantly using the estimated rotational state error. Lyapunov analysis confirms the error convergence in both the Thau observer states and the adaptive fault estimates. In addition, this paper constructs a batch type least-squares projection approach to quantify the magnitude percentages of the actuator failures. Moreover, to show the feasibility of the proposed algorithm, this paper extensively analyses the fault detection and diagnosis results performed in the simulation and real-time environments. Finally, to demonstrate the superiority of the proposed algorithm, it is compared with a recent Kalman filter based quadrotor fault estimation research under the equal conditions.

Fully Distributed Synchronization of Complex Networks With Adaptive Coupling Strengths.

This article considers the fully distributed leaderless synchronization in a complex network by only utilizing local neighboring information to design and tune the coupling strength of each node such that the synchronization problem can be solved without involving any global information of the network. For an undirected network, a fully distributed synchronization algorithm is presented to adjust the coupling strength of each node based on a simple adaptive law. When the topology of a network is directed, two different types of adaptive algorithms are developed to achieve synchronization in a fully distributed manner, where the coupling strength of each node is designed to be either the sum or product of two non-negative scalar functions. The fully distributed leaderless synchronization of a directed network is investigated in a leader-follower framework, where the leader subnetwork is analyzed by using the techniques from constrained Rayleigh quotients and the follower subnetwork is addressed by employing the properties of nonsingular M -matrices. Simulations are given to illustrate the theoretical results.

Finite-Time Disturbance Observer of Nonlinear Systems

In practical applications, for highly nonlinear systems, how to implement control tasks for dynamic systems with uncertain parameters is still a hot research issue. Aiming at the internal parameter fluctuations and external unknown disturbances in nonlinear system, this paper proposes an adaptive dynamic terminal sliding mode control (ADTSMC) based on a finite-time disturbance observer (FTDO) for nonlinear systems. A finite-time disturbance observer is designed to compensate for the unknown uncertainties and a dynamic terminal sliding mode control (DTSMC) method is developed to achieve finite time convergence and weaken system chattering. Moreover, a dual hidden layer recurrent neural network (DHLRNN) estimator is proposed to approximate the sliding mode gain, so that the switching item gain is not overestimated and optimal value is obtained. Finally, simulation experiments of an active power filter model verify the designed ADTSMC method has better steady-state and dynamic-steady compensation effects with at least 1% THD reduction in the presence of nonlinear load and disturbances compared with the simple adaptive DTSMC law.

Robust Passivity-based Sliding Mode Control of a Large Class of Nonlinear Systems Subject to Unmatched Uncertainties: A Robot Manipulator Case Study

The existence of unmatched uncertainties is known as a serious challenge for designing a robust sliding mode control (SMC) law for nonlinear systems. To pass over this obstacle, a novel robust passivity-based sliding mode approach is proposed here for a large class of MIMO nonlinear systems. The design procedure is accomplished in two steps in presence of both matched and unmatched uncertainties. First, an efficient adaptive sliding surface is designed based on the passivity concept. The passivity provides a flexible robust structure for the sliding surface and guarantees the global asymptotic stability of the reduced-order equations of the system as well. Furthermore, simple adaptation laws are obtained to eliminate the effects of uncertainties. Then, the robust controller is formulated using the SMC method. As another important advantage, the proposed approach is relaxed from the upper bound’s constraints of the uncertainties. It is also applied to n-link rigid electrically driven robot manipulator as a widely-used practical nonlinear system. The simulation results show the appropriate tracking performance for the industrial selective compliance assembly robot arm (SCARA) in the presence of noisy external disturbances. Also, an extending case is studied with related research to emphasize the potential of the proposed approach.

Adaptive output regulation for minimum-phase systems with unknown relative degree

In this paper it is shown how to design a stable regulator on the basis of the regulation error only, for a class of minimum-phase unknown linear systems sharing the same high-frequency gain sign and the same upper bound ρ̄ for the relative degree ρ. The order of the regulator is minimal and equal to ρ̄+2p, with p being the number of known frequencies of the biased multi-sinusoidal exogenous signal. The regulator is parameterized by a scalar gain which should be chosen sufficiently high and can be updated on-line by a simple discrete-time adaptation law at every arbitrarily chosen time interval.

Twofold Sliding Controller Design for Uncertain Switched Nonlinear Systems

This paper deals with the problem of controller design for normal nonlinear switched systems with unknown dynamics. The situation assumes that the nonlinear component of the system dynamics is unknown and there are extra uncertain terms and external perturbations affecting the system responses. Unlike previous methods that usually apply artificial neural networks to obtain an approximate model for an unknown dynamics, we use simple adaptive laws to surmount such fluctuations as well as to circumvent the steady state errors in the approaches provided by neural networks or fuzzy logics. No information on the bounds and parameters of the uncertain parts is needed. We design a twofold sliding mode control methodology to stabilize the whole switched system with arbitrary switching signals. To handle the consequences of the inherent chattering, a smooth integral type control signal is constructed. It is proved that once the system states attain the developed sliding manifold, the system becomes insensitive to both the lumped uncertainties and the dynamics of the switched system. The common assumption of a known Lyapunov functions for the subsystems is relaxed and the derived adaptive approach provides nonconservative circumstances for guaranteeing the global stability of the equilibrium state. The theoretical results of this paper are generalized for the canonical nonlinear systems with mismatched uncertainties and a novel adaptive sliding manifold is proposed to suppress the effects of the system mismatching uncertain parts. A comparative computer simulation is developed to examine the effective performance of the introduced controllers.

Robust Adaptive Sampled-Data Control Scheme for a Class of Uncertain Nonlinear Systems

In this paper, a simple robust adaptive sampled-data control law is addressed for a class of uncertain continuous-time systems. For achieving this goal, firstly, the regulation problem and $$ H_{\infty } $$ control designs would be formulated in the uncertain continuous-time systems via including a sampler and data-hold circuits. Then, a robust adaptive digital control law will be derived by using the discrete-time Lyapunov’s stability theory. The results are numerically implemented in two nonlinear uncertain systems. The simulations show the effectiveness of the proposed robust adaptive digital control method compared with the other techniques.

Adaptive sliding mode control based on a combined state/disturbance observer for the disturbance rejection control of PMSM

An improved adaptive sliding mode controller (ASMC) based on a combined state/disturbance observer (CSO) is proposed for the high-performance control of permanent magnet synchronous motor (PMSM). In order to estimate the unknown state and the disturbance including the parameter uncertainty and the external disturbance, the CSO is proposed. Different from the extended state observer (ESO) or generalized ESO (GESO), the CSO uses the linear combination of the extended high-order states to construct the new estimation. The CSO resolves the contradiction between the estimation accuracy and the noise insensitivity, so it is more applicable to time-varying disturbances. Then, the CSO and the ASMC are integrated in the PMSM speed controller by the feed-forward compensation to enhance the system robustness. A simple nonlinear adaptive law is presented to solve the unknown upper bound of the estimation error and minimize the chattering. The theoretical analysis shows that the global stability of the closed-loop system is strictly guaranteed. The simulation and experimental results are presented to demonstrate the effectiveness of the proposed control method.

Simple adaptive trajectory tracking control of underactuated autonomous underwater vehicles under LOS range and angle constraints

In this study, the authors propose a simple adaptive trajectory tracking control scheme for underactuated autonomous underwater vehicles (AUVs) subject to unknown dynamic parameters and disturbances under asymmetric time-varying line-of-sight (LOS) range and angle constraints. A simple error mapping function is constructed to transform the LOS range and angle constraint problems of AUVs trajectory tracking into the problem of the boundedness of transform variable, such that any constraint boundaries of LOS range and angle can be handled. The compounded uncertain item caused by the unknown dynamic parameters and disturbances is transformed into a linear parametric form with only three unknown parameters called virtual parameters. Based on the above, a simple adaptive trajectory tracking control law is developed using dynamic surface control technique, where the adaptive laws online provide the estimations of virtual parameters. As a result, the proposed trajectory tracking control scheme is simple to compute and easy to implement in engineering applications. Strict stability analysis indicates that the designed control law makes AUVs track the desired trajectory within the LOS range and angle constraints and guarantees the boundedness of all signals of the closed-loop control system. Simulation results and comparison verify the effectiveness of the designed control scheme.

Swarm Optimized Simple Adaptive Controller for Spacecraft Proximity Operations Trajectory Tracking

Abstract Adaptive control design allows for the management of systems with time varying or unknown dynamics. Despite their versatility, few well defned design techniques exist for some classes of adaptive controller. Without analytical techniques it is difcult to prove the efcacy of an adaptive controller design. One solution to this issue is the application of parametric search techniques to adaptive controller design. This paper explores the application of diferential evolution on the simple adaptive control law formulation and compares its solution to one found using particle swarm optimization. Afterwards, variations on these techniques, namely the selection particle swarm optimization and self-adaptive diferential evolution, are implemented and their results compared. The final swarm-optimized controller is compared to a classical Linear Quadratic Regulator (LQR) controller, and a manually designed simple adaptive controller for precision trajectory tracking control of spacecraft proximity operations. Parametric search techniques are able to determine controller parameters that produce a superior control response. Swarm-optimization techniques determine controllers with parameters drastically different from manually designed efforts.

Stratified Adaptive Finite-Time Tracking Control for Nonlinear Uncertain Generalized Vehicle Systems and Its Application

We present a stratified adaptive finite-time tracking control (SAFTTC) system, and apply the methodology to trajectory tracking of nonlinear uncertain generalized vehicles. The modeling approach separates vehicle pose dynamics and actuator dynamics into indirect and direct modes, respectively. To track the reference trajectory of the task, an adaptive finite-time virtual reference trajectory (AFTVRT) generator is designed to converge to a first switching surface. The output generated by the AFTVRT is a virtual reference that must then be tracked by the direct modes. Direct mode tracking of the AFTVRT output is achieved by a second, AFTTC, which is designed to converge to a second switching surface. Simple adaptive laws for AFTVRT and AFTTC learn the upper bounds of both the indirect mode and direct mode uncertainties, and convergence to both switching surfaces is with linear dynamics and fractional order of tracking errors. Stability of the closed-loop system is ensured by the Lyapunov stability theory. An application for tracking a pair of nested, interlocking circular trajectories by an omnidirectional autonomous ground vehicle also confirms effectiveness and robustness of the proposed adaptive control system. In the absence of adaptive learning, the system is unable to track the trajectory.

Adaptive-Fuzzy Control Compensation Design for Direct Adaptive Fuzzy Control

For direct adaptive fuzzy control of perturbed uncertain nonlinear systems, proportional-integral-derivative control compensation usually has to be used to guarantee $H_{{{\infty }}}$ tracking performance or $L_{2}$ -gain property of the closed-loop system. One common problem is that the control compensation often introduces unwanted high gain at the control input. This paper proves that classical direct adaptive fuzzy control with adaptive-fuzzy control compensation not only is capable of solving the problem of high gain, but also can guarantee $L_{2}$ -gain property of the closed-loop system. A sliding-surface-based adaptive fuzzy control is designed for control compensation. By using a class of triangular membership functions nearest to the origin and a simple adaptive law, the adaptive fuzzy control term is converted to an equivalence control term, which is used to facilitate stability analysis. Moreover, the system output can track not only the constant-period periodic signals but also the constant signal. Compared with previous direct adaptive fuzzy control approaches that can guarantee $H_{{{\infty }}}$ tracking performance or $L_{2}$ -gain property, in addition to the $L_{2}$ -gain property of common tracking error rather than modified tracking error, the major advantages of our approach are that the assumptions on control gain function are relaxed and a less conservative control design on robustness is achieved. Simulation results are given to demonstrate the effectiveness of the proposed approach.

Indirect adaptive robust control of nonlinear systems with time‐varying parameters in a strict feedback form

SummaryWithout any prior knowledge of the physical bounds of unknown parameters and uncertain nonlinearities, an indirect adaptive robust controller is constructed for uncertain nonlinear time‐varying systems in a strict‐feedback form. Firstly, an adaptive strong robust controller is derived based on the command filtered adaptive backstepping approach. This controller not only can guarantee the boundedness of the closed‐loop system signals in the presence of time‐varying (TV) parameters and uncertain nonlinearities but also obviate the need to compute analytic derivatives of virtual control functions. Thus, the problem of “explosion of terms” in the standard adaptive backstepping technique is avoided. Through introduction of a simple adaptation law on the upper bound of uncertainties, a smooth robust control term is used to realize the disturbance attenuation. Afterwards, based on the nonlinear X‐swapping techniques, a modular approach in which the controller and the identifier can be designed separately is exploited. A novel algorithm is proposed to estimate the TV parameters accurately. By adopting the variation trend of the covariance matrix as an indicator of the driving signals' persistent excitation level, this online parameter estimation law is switched between a modified least‐squares algorithm and a gradient algorithm based on fixed σ‐modification. Finally, a series of properties on the asymptotic stability and the global uniform ultimate boundedness of the closed‐loop system is established. Simulation results verify the effectiveness of the suggested method.

Parameter Identification of Chaotic and Hyper-Chaotic Systems Using Synchronization-Based Parameter Observer

A technique is introduced for identifying uncertain and/or unknown parameters of chaotic and hyper-chaotic systems via using a synchronization-based parameter observer. The proposed technique is based on designing a state feedback controller and then solving for the unknown parameters using some simple parameter adaptive laws that require access to some or all of the states depending on the dynamical model of the systems. Two detailed cases utilizing chaotic and hyper-chaotic systems are used to exemplify the proposed observer when partial identification of the unknown parameters is considered, where the results demonstrated the effectiveness of the proposed method via comparing it with other methods reported in the literature, Furthermore, the feasibility of the designed observer on unknown-structure model and complex-variable model are verified through the theoretical analyses and simulation results, and the advantages and limitations of the synchronization-based parameter observer approach are discussed in detail.

A Nonlinear Sliding Mode Controller for IPMSM Drives with an Adaptive Gain Tuning Rule

This paper presents a nonlinear sliding mode control (SMC) scheme with a variable damping ratio for interior permanent magnet synchronous motors (IPMSMs). First, a nonlinear sliding surface whose parameters change continuously with time is designed. Actually, the proposed SMC has the ability to reduce the settling time without an overshoot by giving a low damping ratio at the initial time and a high damping ratio as the output reaches the desired setpoint. At the same time, it enables a fast convergence in finite time and eliminates the singularity problem with the upper bound of an uncertain term, which cannot be measured in practice, by using a simple adaptation law. To improve the efficiency of a system in the constant torque region, the control system incorporates the maximum torque per ampere (MTPA) algorithm. The stability of the nonlinear sliding surface is guaranteed by Lyapunov stability theory. Moreover, a simple sliding mode observer is used to estimate the load torque and system uncertainties. The effectiveness of the proposed nonlinear SMC scheme is verified using comparative experimental results of the linear SMC scheme when the speed reference and load torque change under system uncertainties. From these experimental results, the proposed nonlinear SMC method reveals a faster transient response, smaller steady-state speed error, and less sensitivity to system uncertainties than the linear SMC method.

Single-approximation-based adaptive control of a class of nonlinear time-delay systems

This paper presents a simple adaptive control approach for uncertain strict-feedback nonlinear systems with unknown time-varying delays. All nonlinear functions and time delays in the systems are assumed to be unknown. Compared with the existing works, the contribution of this study is the design of a simple adaptive control law using single function approximator, without the implementation of virtual controllers derived from the backstepping design procedure. Unlike the existing backstepping methods, virtual controllers are only used as intermediate signals for designing the actual control. Therefore, the proposed control scheme is simpler than the existing methods for strict-feedback time-delay systems because the problems of using multiple approximators and calculating virtual controllers are eliminated. In addition, it is shown that all signals in the closed-loop system are uniformly ultimately bounded.

Adaptive mechanism for synchronization of chaotic oscillators with interval time-delays

This paper addresses the adaptive feedback controller design for the synchronization of chaotic systems with interval time-delays in their state vectors by exploiting a lower and an upper bound on time-delays. Simple control and adaptation laws are developed for chaos synchronization, and linear matrix inequalities (LMIs) are derived to ensure asymptotic convergence of the synchronization error between the master–slave systems, using the proposed feedback control strategy, by employing a novel treatment of Lyapunov–Krasovskii functional. Further, the proposed strategy is strengthened by exploiting \(L_2 \) stability against disturbances and perturbations and corresponding LMIs for robust adaptive controller synthesis are derived. Furthermore, a novel delay-range-dependent robust adaptive synchronization control approach for dealing with locally Lipschitz non-delayed and delayed nonlinearities in the dynamics of chaotic oscillators is provided by employing an additional adaptation law for the nonlinearities. A numerical simulation example is provided to illustrate effectiveness of the proposed synchronization approach.

Adaptive Synchronization of Fractional Neural Networks with Unknown Parameters and Time Delays

In this paper, the parameters identification and synchronization problem of fractional-order neural networks with time delays are investigated. Based on some analytical techniques and an adaptive control method, a simple adaptive synchronization controller and parameter update laws are designed to synchronize two uncertain complex networks with time delays. Besides, the system parameters in the uncertain network can be identified in the process of synchronization. To demonstrate the validity of the proposed method, several illustrative examples are presented.