Adaptive Control Law Research Articles

Adaptive Output Feedback Control for Constrained Switched Systems with Input Quantization

This paper investigates adaptive output feedback control problem for switched uncertain nonlinear systems with input quantization, unmeasured system states and state constraints. Firstly, fuzzy logic systems are introduced to identify system uncertainties, then the fuzzy based observer is constructed to estimate unavailable states. Secondly, combing the backstepping technique and the barrier Lyapunov function method, an adaptive fuzzy output feedback control law is designed, which guarantees that all signals in the closed-loop system are bounded, the system output tracks the reference signal, and system states satisfy their corresponding constraint conditions. Finally, simulation results further show the good performances of the proposed control scheme.

Adaptive neural dynamics-based speed control strategy for stable retrieval of tethered satellite system

This work proposed a novel adaptive neural dynamics (AND)-based speed control strategy for the stable sub satellite’s retrieval of the tethered satellite system (TSS). The new control scheme is implemented by adjusting the retrieval speed only. An analytical speed function is used to ensure stable retrieval without libration motion overall. A high-efficiency adaptive neural dynamic control law with the retrieval speed as control input is used to eliminate the libration motion. In the control loop, the tension in the tether is monitored and restrained directly. The Lyapunov stability of the control law is proved analytically. The simulation results show the proposed adaptive neural dynamics-based speed control strategy is very effective in keeping a stable retrieval by adjusting the retrieval speed only. The libration motions can be eliminated promptly in a fast manner with limited control input and tension constrain.

Distributed adaptive formation control of multi-agent systems with measurement noises

In this paper, we investigate the distributed adaptive formation control problem of leader-following multi-agent systems where the measurements are subject to noises. A distributed LMS-like algorithm is proposed to estimate the relative position between the followers and the leader. By employing the “certainty equivalence” principle, an adaptive motion controller is designed to achieve the desired formation under dynamically changing interaction topologies. The incompatibility in simultaneously satisfying the persistent excitation condition required by localization estimators and accomplishing the control tasks makes the theoretical analysis challenging. In order to deal with this issue, an excited noise signal is embedded into the control law. We give the upper bounds of both the estimation errors and formation error of the closed-loop multi-agent system under the distributed adaptive control law. Finally, the numerical simulations are provided to demonstrate the effectiveness of our theoretical results.

Fuzzy Adaptive Control Law for Trajectory Tracking Based on a Fuzzy Adaptive Neural PID Controller of a Multi-rotor Unmanned Aerial Vehicle

Fuzzy Adaptive Control Law for Trajectory Tracking Based on a Fuzzy Adaptive Neural PID Controller of a Multi-rotor Unmanned Aerial Vehicle

Adaptive generalized predictive control for dynamic positioning system of ships with model unknown parameters

This paper proposes an adaptive generalized predictive control for dynamic positioning of ships with unknown model parameters and unknown time-varying environmental disturbances. The controlled auto-regressive integrated moving average (CARIMA) model is employed to describe the movements of ships with model parameter and disturbance uncertainties. The recursive least square method with forgetting factor is utilized to design adaptive laws to estimate the CARIMA model parameters online. Considering both the positioning accuracy and the change intensity of control increments, a cost function is constructed. The optimal control increments that minimize the cost function are obtained by using Lagrange multiplier method. Then, the adaptive control law is designed to maintain ship’s position and heading at desired values. Finally, simulation studies in different cases are carried out and simulation results demonstrate the effectiveness of the proposed control scheme.

Adaptive robust control for Pendubot with matched–mismatched uncertainty via constraint-following

AbstractThe study presents an adaptive robust control method for the Pendubot subjects to matched and mismatched uncertainty. First, the control task is formatted as a reduced-dimension equality constraint of the system states. To handle the matched and mismatched uncertainties, an orthogonal decomposition method is employed to make the mismatched part disappear after decomposition. Based on the above, an adaptive robust control law based on constraint-following is devised. By the Lyapunov approach, it is rigorously proven that the proposed approach ensures the uniform boundedness and uniform ultimate boundedness of the closed-loop control system and thus renders approximate constraint-following, regardless of uncertainty. Simulation and experimental results are provided and discussed, demonstrating the good performance of the proposed approach.

Coordinated control of stability and economy of distributed drive electric vehicle based on Lyapunov adaptive theory

In order to solve the problem of poor coordinated control between handling stability and economy of distributed drive electric vehicles, a model reference adaptive yaw moment controller based on Lyapunov stability theory and a quadratic programing wheel torque distribution controller considering energy loss of motors are proposed. A hierarchical control strategy is adopted. The upper controller is a model reference adaptive yaw moment controller based on Lyapunov stability theory. The adaptive control law is obtained by solving the Lyapunov function, and the stability of the model reference adaptive control system is proved. The upper controller provides additional yaw moment in real time according to the vehicle state, which can ensure the handling stability of the vehicle. The lower controller adopts the quadratic programing wheel torque distribution controller considering the energy loss of the motor to realize the real-time torque distribution to the wheel. Moreover, the weight distribution of stability and economy is dynamically coordinated based on the phase portrait. The double lane changing condition and fishhook steering condition are selected, and the simulation test of the proposed control method is carried out on the CarSim/Simulink joint simulation platform. The simulation results under the above two road conditions show that the vehicle has good handling stability when using Lyapunov adaptive control method. In addition, the coordinated decision control strategy can effectively reduce the load and energy loss of hub motor.

Spatiotemporal adaptive state feedback control of a linear parabolic partial differential equation

AbstractThis article deals with the issue of asymptotic stabilization for a linear parabolic partial differential equation (PDE) with an unknown space‐varying reaction coefficient and multiple local piecewise uniform control. Clearly, the unknown reaction coefficient belongs to a function space. Hence, the fundamental difficulty for such issue lies in the lack of a conceptually simple but effective parameter identification technique in a function space. By the Lyapunov technique combined with a variant of Poincaré‐Wirtinger inequality, an update law is derived for estimate of the unknown reaction coefficient in a function space. Then a spatiotemporal adaptive state feedback control law is constructed such that the estimate of the unknown coefficient is bounded and the closed‐loop PDE is asymptotically stable in the sense of spatial norm if a sufficient condition given in terms of space‐time varying linear matrix inequalities (LMIs) is fulfilled for the estimated coefficient and the control gains. Both analytical and numerical approaches are proposed to construct a feasible solution to the space‐time varying LMI problem. With the aid of the semigroup theory, the well‐posedness and regularity of the closed‐loop PDE is also analyzed. Moreover, two extensions of the proposed adaptive control scheme are discussed: the PDE in ‐D space and the PDE with unknown diffusion and reaction coefficients. Finally, numerical simulation results are presented to support the proposed spatiotemporal adaptive control design.

Nonlinear Adaptive Fuzzy Control Design for Wheeled Mobile Robots with Using the Skew Symmetrical Property

This research presents a nonlinear adaptive fuzzy control method as an analytical design and a simple control structure for the trajectory tracking problem in wheeled mobile robots with skew symmetrical property. For this trajectory tracking problem in wheeled mobile robots, it is not easy to find an analytical adaptive fuzzy control solution due to the complicated error dynamics between the controlled wheeled mobile robots and desired trajectories. For deriving the analytical adaptive fuzzy control law of this trajectory tracking problem, a filter link is firstly adopted to find the solvable error dynamics, then the research is based on the skew symmetrical property of the transformed error dynamics. This proposed nonlinear adaptive fuzzy control solution has the advantages of low computational resource consumption and elimination of modeling uncertainties. From the results for tracking two simulation scenarios (an S type trajectory and a square trajectory), the proposed nonlinear adaptive fuzzy control method demonstrates a satisfactory trajectory tracking performance for the trajectory tracking problem in wheeled mobile robots with huge modeling uncertainties and outperforms the existing H2 control method.

Reinforcement learning based-adaptive tracking control for a class of semi-markov non-Lipschitz uncertain system with unmatched disturbances

A reinforcement learning based-adaptive tracking control method has been proposed for a class of semi-markov non-Lipschitz uncertain system with unmatched disturbances. Not only does the considered system contain unknown nonlinear functions and multisource disturbances, but parameter matrix in the system varies with the semi-Markov progress, which create difficulties in the design of the controller. Firstly, to handle the non-Lipschitz nonlinear terms, an adaptive control law based on reinforcement learning has been designed. Secondly, according to the reinforcement learning result, an adaptive disturbance observer has been constructed to offset the adverse influence generated by the multiple disturbances in the considered system. Finally, aiming at the parameter matrixes in the system varying with semi-Markov progress, a novel adaptive tracking controller integrating the reinforcement learning approximation, the adaptive disturbance observer and the tracking control law, has been proposed. With the given adaptive tracking control law based on reinforcement learning, through the Lyapunov direct method, it has been proven that the closed-loop system are stable and convergent and the tracking errors are ultimately uniformly bounded. In addition, several numerical experiments are provided to illustrate the feasibility and effectiveness of the proposed reinforcement learning based adaptive tracking control law.

Attitude path design and adaptive robust tracking control of a remote sensing satellite in various imaging modes

This paper addresses the attitude path design of a remote sensing satellite in various imaging modes. The novel path design algorithm is based on local polynomial regression, which produces a smooth attitude path by receiving the size and timing of maneuvers in each axis according to the desired imaging mode. This algorithm is described for stereo and snapshot modes in an imaging operation. The adaptive robust tracking control (ARTC) law is designed using quaternion algebra to perform the required maneuvers in an attitude path. The ARTC structure includes a sliding mode strategy, a projection-based adaptive model compensation, and a linear feedback term. Suitable conditions for imaging in each mode and the time of taking the image are determined by defining and evaluating the attitude control indices. These indices are defined by the half-cone error along the payload line of sight and relative performance error as a jitter with a 3-sigma confidence level. Despite the challenges in the path design, such as smoothness, system agility, and finite time realization of indices, in a conventional stereo imaging mode, taking an image in the nadir-pointing attitude is neglected. As a result, our work provides suitable conditions for taking the image in this attitude with an interval of 1.2 s. Finally, numerical simulations and verification are performed using multidisciplinary simulation, indicating the effectiveness of the proposed algorithm and model-based ARTC law.

Distributed Adaptive Control with Momentum for Synchronization of Linear Agents

This paper studies the problem of learning-based adaptive state feedback control for networks of heterogeneous agents with input and matched uncertainties. We propose a control strategy that guarantees that the closed-loop synchronization error of all agents in the network is bounded. Adaptive control laws are designed via matching conditions to approximate the dynamics of each agent, which are partially unknown. Uncertainty parameters in the model are suppressed using adaptive optimal modification theory. Moreover, a momentum-based technique is also introduced in our framework for improving the convergence behavior of the adaptive control law parameters computation. Finally, a simulation example for Cooperative Adaptive Cruise Control (CCAC) is presented to validate the effectiveness of the control scheme. Numerical examples show that momentum-based techniques reach the bounded error set faster than gradient-based techniques.

Adaptive Bearing-Only Control of Multiple Euler-Lagrange Systems for Static Geometric Formation⋆

This paper studies the formation control problem of multi-agent systems each of which the dynamics are modeled by the Euler-Lagrange equation with unknown parameters. The objective of each agent is to develop a control law using the bearing information with respect to its neighbors, such that the multi-agent system forms a static geometric formation defined by the bearing constraints among agents. An adaptive dynamic control law with a leader-following type is proposed such that the objective can be achieved in the presence of unknown systems’ parameters. Finally, simulation examples are presented to illustrate the effectiveness and feasibility of the main results.

Dynamic Leader-Following Bipartite Consensus of Multiple Uncertain Euler-Lagrange Systems Under Deception Attacks

In this brief, we mainly focus on the problem of leader-following (LF) bipartite consensus of multiple uncertain Euler-Lagrange systems (ELSs) under the influence of deception attacks. In contrast to existing results, we consider the exosystem with an auxiliary system in this brief, of which auxiliary system is dynamic, and both exosystem and auxiliary system can greatly enrich the reference signal and make our control scheme more flexible. However, due to the presence of deception attacks and the dynamic auxiliary system, we are confronted with the question of whether the system can properly achieve LF bipartite consensus despite the effects of both previously mentioned. To solve this problem, we define a so-called dynamic leader-following problem, where the tracking error is bounded and decays to zero in a dynamic manner. Finally, we design an adaptive distributed control law with a filter to remove the effect of deception attacks, which is combined with the existing results to solve the LF bipartite consensus problem.

Fixed-Time Fault-Tolerant Formation Control for a Cooperative Heterogeneous Multiagent System With Prescribed Performance

This article investigates the fixed-time fault-tolerant formation control problem of a leader–follower heterogeneous multiagent system (HMAS), including multiple unmanned aerial vehicles (UAVs) and multiple unmanned ground vehicles (UGVs) under loss of effectiveness actuator faults and disturbances. Different from the existing fixed-time formation results, to realize the special application, a finite-time performance function (FTPF) is considered, which can guarantee that formation error converges to a prescribed arbitrarily small region within a known time. Then, based on sliding mode control and bi-limit homogeneity, distributed and decentralized fixed-time formation control algorithms are constructed for the HMAS in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$x$ </tex-math></inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$y$ </tex-math></inline-formula> axis and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$z$ </tex-math></inline-formula> axis, respectively, which can steer the whole system achieving target formation configuration within a scheduled time. In addition, based on local state information, adaptive online updating strategies for unknown actuator efficiency factors and lumped uncertainties are proposed. Then, under the online updating parameters, two novel distributed and decentralized adaptive fault-tolerant formation control laws are presented using practical fixed-time stability theory, which not only achieves stable formation tracking with finite-time prescribed behavioral metrics but also ensures that the formation errors are uniformly bounded within a settling time. Finally, the effectiveness of the developed control schemes is verified by simulation examples.

Global Asymptotic Position and Heading Tracking for Multirotors Using Tuning Function-Based Adaptive Hybrid Feedback

This letter considers the problem of global asymptotic position and heading tracking for multirotors. We propose a hybrid adaptive feedback control law that globally asymptotically tracks a position and heading reference in the presence of unknown constant disturbances in both the translational and rotational dynamics. By employing a tuning function-based backstepping approach, the number of parameter estimates are minimized. Moreover, we propose a novel control law for the translational subsystem, which leads to a simpler virtual control law when backstepping. Global asymptotic heading tracking is achieved through a novel construction of the desired rotation matrix. The theory is verified through experiments on a quadrotor.

MIMO fuzzy adaptive control systems based on fuzzy semi-tensor product

&lt;abstract&gt;&lt;p&gt;Based on fuzzy semi-tensor product (STP) algorithms and fuzzy relation matrix (FRM) models, the design of an adaptive fuzzy controller was proposed in this paper for the multivariable nonlinear systems with uncertainty. The controlled multi-input-and-multi-output (MIMO) plants were expressed and processed first by FRM models and fuzzy STP operations, and then the indirect adaptive fuzzy control laws were designed. The tracking property of the FRM models was proved for the control objective of MIMO systems. The effectiveness of the novel matrix expression was verified by simulations of the tracking control on a two-link rigid robot manipulator. Results in simulation tests show that the proposed design of adaptive FRM control is efficient for nonlinear multivariables. Therefore, the proposed indirect fuzzy adaptive controllers can be extended to general matrix expression for MIMO nonlinear systems with fuzzy STP algorithms and FRM models and online approximate unknown parameters, according to required accuracy.&lt;/p&gt;&lt;/abstract&gt;

Nussbaum Gain-Based Cone Angle Constrained Fault-Tolerant Attitude Control with Time-Varying Inertia

This paper proposes a robust adaptive attitude control law for handling a class of actuator faults in the presence of various challenges, such as time-varying inertia, attitude constraints, and input saturation. The proposed approach uses cone angles to represent orientation errors, which are constrained within a performance function to ensure desired transient and steady-state behaviour during reference tracking. Input saturation is approximated using a smooth hyperbolic tangent function. The Nussbaum gain technique is used to handle the unknown control coefficients, which guarantees uniformly ultimately bounded stability in the presence of uncertainties and disturbances. The paper also proposes a norm-based disturbance approximation to estimate the total uncertainty during the Lyapunov analysis. Numerical simulations demonstrate the effectiveness of the proposed control law.

A Novel Exploration-Exploitation-Based Adaptive Law for Intelligent Model-Free Control Approaches.

Model-free control approaches require advanced exploration-exploitation policies to achieve practical tasks such as learning to bipedal robot walk in unstructured environments. In this article, we first construct a comprehensive exploration-exploitation policy that carries quality knowledge about the long-term predictor and the control policy, and the control signal of the model-free algorithms. Therefore, the developed model-free algorithm continues exploration by adjusting its unknown parameters until the desired learning and control are accomplished. Second, we provide an utterly model-free adaptive law enriched with the exploration-exploitation policy and derived step-by-step using the exact analogy of the model-based solution. The obtained adaptive control law considers the control signal saturation and the control signal (input) delay. Performed Lyapunov stability analysis ensures the convergence of the adaptive law that can also be used for intelligent control approaches. Third, we implement the adaptive algorithm in real time on a challenging benchmark system: a fourth-order, coupled dynamics, input saturated, and time-delayed underactuated manipulator. The results show that the proposed adaptive algorithm explores larger state-action spaces and treats the vanishing gradient problem in both learning and control. Also, we notice from the results that the learning and control properties of the adaptive algorithm are optimized as required.

Attitude Tracking Control of Uncertain Flexible Spacecraft Systems Subject to External Disturbances*

In this paper, we consider the attitude tracking and disturbance rejection problem of uncertain flexible spacecrafts. Compared with existing works, we consider two types of uncertainties of flexible spacecrafts, that is, the uncertain parameters of the inertial matrix, and the unknown external disturbance with unbounded energy. Inspired by the internal model principle, we design a class of dynamic compensators and some auxiliary dynamic systems to compensate the external disturbance. Then, by introducing a series of coordinate transformations, we convert the attitude tracking and disturbance rejection problem into an adaptive regulation problem of an augmented system. Finally, we design the adaptive control law and show that attitude tracking of uncertain flexible spacecrafts can be achieved in the presence of unknown disturbances. The effectiveness and robustness of the controller are illustrated by some numerical simulations.