Adaptive Control Problem Research Articles

Smooth adaptive finite-time tracking for uncertain time-varying systems

This paper addresses the adaptive finite-time tracking control problem of strict-feedback nonlinear systems, where the control coefficient and the model parameters are time-varying and unknown. Based on the so-called congelation of variables method, a novel fractional-power adaptive update law is designed to achieve finite-time practical tracking in the presence of unknown time-varying coefficient/parameters. The virtual and actual control inputs of the proposed finite-time controller are designed in a smooth sign-function-like form complemented by a smooth sign-function-like filter, which allows for circumventing the singularity issues and the chattering phenomenon caused by non-smooth terms in classical finite-time controllers and filters. The tracking error proves to be bounded and converges to a desired compact set in finite time. Simulations of two practical examples are presented and show the effectiveness of the proposed algorithm.

Distributed adaptive finite-time fault-tolerant cooperative control of heterogeneous multi-agent systems with saturation and disturbances

In this paper, the issue of distributed adaptive finite-time fault-tolerant cooperative control (FT-FTCC) problem is investigated for multiple unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) with unknown parameter uncertainties, actuator faults, input saturation and external disturbances. Starting from the dynamic models of the UAVs and UGVs, an unified control model is presented. Then, a sliding-mode estimator is presented to estimate the position of the leader for the followers which only uses the information from neighbours. Next, a distributed adaptive FT-FTCC scheme, which can also deal with the uncertainties, actuator faults, input saturation and disturbances, is proposed by utilising disturbance observers and neural networks. Based on Lyapunov function approach, the tracking errors of all followers subject to the pre-defined desired positions are uniformly ultimately bounded. Finally, simulations are given to validate the efficiency of the developed FT-FTCC scheme.

Approximation-based adaptive two-bit-triggered bipartite tracking control for nonlinear networked MASs subject to periodic disturbances

PurposeThis paper aims to investigate the problem of adaptive bipartite tracking control in nonlinear networked multi-agent systems (MASs) under the influence of periodic disturbances. It considers both cooperative and competitive relationships among agents within the MASs.Design/methodology/approachIn response to the inherent limitations of practical systems regarding transmission resources, this paper introduces a novel approach. It addresses both control signal transmission and triggering conditions, presenting a two-bit-triggered control method aimed at conserving system transmission resources. Additionally, a command filter is incorporated to address the problem of complexity explosion. Furthermore, to model the uncertain nonlinear dynamics affected by time-varying periodic disturbances, this paper combines Fourier series expansion and radial basis function neural networks. Finally, the effectiveness of the proposed methodology is demonstrated through simulation results.FindingsBased on neural networks and command filter control method, an adaptive two-bit-triggered bipartite control strategy for nonlinear networked MASs is proposed.Originality/valueThe proposed control strategy effectively addresses the challenges of limited transmission resources, nonlinear dynamics and periodic disturbances in networked MASs. It guarantees the boundedness of all signals within the closed-loop system while also ensuring effective bipartite tracking performance.

Fuzzy adaptive asynchronous sampled-data consensus control for nonlinear multi-agent systems under DoS attacks

This article investigates the problem of fuzzy adaptive resilient asynchronous sampled-data consensus control (SDCC) for a class of uncertain nonlinear strict-feedback multi-agent systems (MASs) under denial-of-service (DoS) attacks and with a directed graph. Firstly, the upper bounds on the sampling intervals and a distributed sampled-data observer are proposed to estimate the leader's output and its high-order derivatives under DoS attacks. Then, the sufficient conditions to ensure the asymptotic convergence of the designed distributed sampled-data observer are established. Based on the distributed sampled-data observer and backstepping control design technique, a distributed fuzzy adaptive resilient control algorithm is developed. It is proved that the proposed control scheme can guarantee that the controlled MASs are stable, and the consensus errors converge to a small neighbourhood of zero. Finally, a simulation example on heterogeneous vehicular platoons verifies the feasibility of the proposed control scheme.

Distributed two-channel dynamic event-triggered adaptive finite-time fault-tolerant containment control for multi-leader UAV formations

This paper addresses the distributed adaptive finite-time containment control problem in multi-leader UAV formations with actuator failures, limited communication, and external disturbances. A two-channel dynamic event-triggered strategy based on adaptive and sliding mode control is proposed as a containment control scheme, which solves the contradiction between the need to include containment error in the continuous term of the sliding mode surface in the adaptive law and the discontinuity of the communication between neighboring subsystems (follower UAVs) by constructing intermediate variables. Unlike the traditional event triggering condition that can only be applied to asymptotically convergent systems, the dynamic triggering condition designed in this paper, based on auxiliary variables, hyperbolic tangent function, and adaptive techniques, realizes finite-time convergence during the adjustment of the system and sets a more reasonable lower limit for the triggering thresholds, thus further reducing the communication frequency and ensuring the finite-time convergence of the system. The stability of the closed-loop system can be proved by the Lyapunov theorem. Zeno behavior can be avoided. The simulation results verify the effectiveness of the developed control algorithm.

ADP-based adaptive control of ship course tracking system with prescribed performance

In this paper, an adaptive dynamic programing (ADP)-based adaptive control problem is studied for the ship course tracking system with prescribed performance. Firstly, the complex sea conditions will bring difficulty to ship course tracking when unmanned ship sailing on sea. In order to overcome this difficulty, a prescribed performance feedforward term is designed in the controller to improve the course tracking ability of ship. Secondly, by defining a cost function, an ADP technology is exploited to achieve an optimal control of ship course tracking system. Finally, the stability of the closed loop system is turned out by Lyapunov stability theory and all signals are uniformly ultimately bounded (UUB). Simulation results validate the effectiveness of the proposed method.

Adaptive visual servoing control for uncalibrated robot manipulator with uncertain dead-zone constraint

This paper addresses the adaptive visual tracking control problem of an uncalibrated camera robot system with unknown dead-zone inputs. The uncertainties include camera extrinsic and intrinsic parameters, robot dynamic parameters, and feature depth parameters. The control achieves a better performance by establishing a smooth inverse model of the dead-zone input, which eliminates the nonlinear effect of the actuator constraint. A novel adaptive control scheme is presented which does not require a priori knowledge of the parameter intervals of dead-zone model, to update the parameter values online. Furthermore, adaptive laws are provided to estimate the uncertainties that exist both in robot and in camera models. Meanwhile, in order to avoid the singularity of the image Jacobian matrix, a projection algorithm is also introduced. Subsequently, a novel robust adaptive controller together with dead-zone compensation is established so that the tracking error image space converges to the origin. Simulations and experimental studies are conducted to verify the effectiveness of the proposed method.

Predefined-time adaptive fuzzy control for nonlinear output constraint systems with unknown backlash-like hysteresis via command filtering

In this article, the predefined-time adaptive fuzzy control problem for strict-feedback nonlinear systems with asymmetric time-varying output constraint and unknown backlash-like input hysteresis is considered. An innovative predefined-time adaptive control method, in which utilises unified barrier function (UBF) to deal with the output constraint problem and adopts a differential equation to represent the unknown backlash-like hysteresis, is presented by combining a novel command filter with backstepping technology. Fuzzy logic systems (FLSs) are employed to estimate the unknown nonlinearities. Moreover, by designing appropriate parameters, the constructed control strategy ensures that all signals are predefined-time bound and the tracking error stays in a small neighbourhood adjacent zero. Ultimately, two simulation examples are given to prove the effectiveness of the presented control algorithm.

Mixed-Zero-Sum-Game-Based Memory Event-Triggered Cooperative Control of Heterogeneous MASs Against DoS Attacks.

This article studies the problem of memory event-triggered cooperative adaptive control of heterogeneous nonlinear multiagent systems (MASs) under denial-of-service (DoS) attacks based on the multiplayer mixed zero-sum (ZS) game strategy. First, a neural-network-based reinforcement learning scheme is structured to obtain the Nash equilibrium solution of the proposed multiplayer mixed ZS game scheme. Then, a memory-based event-triggered mechanism considering the historical data is proposed. This effectively avoids incorrect triggering information caused by unknown external factors. Moreover, thanks to the idea of switching topology, the mixed ZS game problem under the influence of node-based DoS attacks is solved efficiently. In accordance with the Lyapunov stability theory, it is proved that all signals of heterogeneous MASs are bounded, all heterogeneous followers can track the trajectory of the leader during the no-attack period, the attacked follower can achieve stabilization control during the attack period, and the remaining nonattacked followers can achieve cooperative control during the attack period. Finally, the effectiveness of the designed memory-event-triggered-based mixed ZS game cooperative control strategy is tested by the given simulation results.

Solving Multi-Objective Optimal Control Problems Using a Multiresolution Approach

This paper presents an adaptive multiresolution strategy for multi-objective optimal control problems. The optimal control problem is solved using a direct approach, with individualistic grid adaptation facilitated by a local error analysis at element boundaries. Multiple objectives are considered using a dominance-based approach applying both local and global search methods to a collaborative population of unique solutions. These aspects are simultaneously incorporated via a novel application of evolutionary algorithms for adaptive optimal control problems. Together, this avoids the need for a priori specification of the quantity and temporal location of element boundaries and the set of scalarization weights defining the multi-objective descent directions. Solution fidelity can thus increase concurrently with the exploration of the design space, which leads to increased numerical efficiency while propagating and maintaining population diversity. The benefits of the proposed approach over traditional uniform-grid implementations are demonstrated. Results show that the multiresolution approach is capable of striking an effective balance between solution fidelity, population diversity, and computational cost unachievable using uniform grids.

Quantization-Based Adaptive Fuzzy Consensus for Multiagent Systems Under Sensor Deception Attacks: A Novel Compensation Mechanism.

This study mainly investigates the adaptive leader-following consensus tracking control problem for a class of nonlinear multiagent systems (MASs) subjected to unknown control directions, external disturbances, and sensor deception attacks. To start with, an equivalent MAS with known control directions is obtained by introducing a linear state transformation. For the purpose of estimating the unavailable system states caused by malicious attacks, a quantization-based fuzzy state observer is designed, and the fuzzy-logic system (FLS) is utilized to approximate nonlinear functions. Moreover, a dynamic uniform quantizer with scaling function is established to reduce information transmission. With the help of coordinate transformation and available compromised states, a novel compensation mechanism is designed to offset the influence of filter errors while avoiding the problem of "explosion of complexity" in the backstepping design process. In addition, the Nussbaum-type function is considered to eliminate the design obstacle of unknown control gains resulting from the attacks. Under the constructed consensus protocol, it is proved theoretically that the consensus tracking error converges to an adjustable small neighborhood of the origin, and all signals in the closed-loop system are bounded. Finally, the feasibility of the provided secure control scheme is verified through two simulation examples.

Adaptive control of nonlinear time-varying systems with unknown parameters and model uncertainties

This paper investigates the adaptive control problem for nonlinear time-varying systems with unknown parameters and model uncertainties. A novel class of switching functions is designed, and its construction method is detailed, along with a proof of the continuity of its n−1 order derivatives. Two simple examples are provided to illustrate how the proposed congelation of variables method handles unknown high-frequency time-varying parameters in both the feedback and input paths. A new neural network control scheme is then developed, integrating an adaptive neural network controller with a robust controller. The smooth transition between these two controllers is ensured by the novel switching function, which guarantees global system stability. Furthermore, by combining the congelation of variables method with adaptive backstepping, a new adaptive tracking control scheme is proposed. This scheme effectively handles unknown high-frequency time-varying parameters while achieving asymptotic tracking of arbitrary reference signals. Simulation results show that the proposed novel adaptive control method delivers superior control accuracy while reducing energy consumption: it achieves an order of magnitude improvement over the traditional adaptive robust control method and two orders of magnitude improvement over the conventional sliding mode control method.

Distributed adaptive event-triggered finite-time fault-tolerant containment control for multi-UAVs with input constraints and actuator failures

This article investigates the distributed adaptive finite-time containment control problem for multi-UAVs with input constraints, actuator failures, communication limitations, and external disturbances. First, a new smoothing function is used to smooth the asymmetric input constraint signals so that the input constraint and actuator fault control problem can be transformed into a variable gain control problem. Subsequently, a new Nussbaum function is proposed to solve the variable gain control problem. A new adaptive event-triggered strategy is designed to solve the communication limitation problem, and the trigger threshold has the characteristic of adaptive adjustment that can be dynamically decreased. In response to external disturbances, an adaptive law is designed to estimate and compensate for the boundaries of disturbances. It follows from the analysis based on Lyapunov theory that under the proposed controller, the followers will converge to the convex envelope formed by the leaders in a finite time, and Zeno-free is achieved. Simulation results are provided to verify the effectiveness of the developed adaptive event-triggered finite-time fault-tolerant containment control laws.

Distributed Adaptive Formation Control for Fractional-Order Multi-Agent Systems with Actuator Failures and Switching Topologies

In this paper, a class of distributed adaptive formation control problems are investigated for second-order nonlinear fractional-order multi-agent systems with actuator failures and switching topologies. To address these challenges, two adaptive coupling gains based on agents’ position and velocity are incorporated into the control protocol. Using the Lyapunov method along with graph theory and matrix analysis, sufficient conditions for system stability are derived in the presence of actuator failures and switching topologies. The effectiveness of the proposed control protocol is demonstrated through numerical simulations, which show its capability to maintain stable formation control under these challenging conditions.

Fuzzy adaptive fixed-time control for output-constrained uncertain nonstrict-feedback time-delay systems

This paper deals with the problem of fuzzy adaptive fixed-time control for a class of uncertain nonlinear nonstrict feedback systems with time delays and output constraints. The negative effects of time delays on system performance and stability are overcome by introducing a new Barrier Lyapunov–Krasovskii (BLK) function and an innovative inequality. In addition, the singularity problem that arises in the process of deriving the control and adaptive laws, is solved by the proposed BLK function. The controller is designed in the backstepping framework which ensures that the system output does not violate predefined constraints. The proposed controller needs less information from the system and therefore has less implementation complexity than previous references, which leads to a more straightforward implementation. A fuzzy system approximation is utilized to overcome the uncertainties of the model. It is guaranteed that all closed-loop system signals converge to small neighborhoods around zero in a fixed time. Finally, an example is presented to verify that the proposed method achieves the control objectives.

Adaptive fuzzy fixed-time control for uncertain switched nonlinear systems with non-symmetrical dead-zone

This paper addresses fuzzy adaptive fixed-time tracking control problem for uncertain switched nonlinear systems with non-symmetrical dead-zone, even if the tracking control problem for subsystems is not solvable. A fixed-time stability criterion for switched nonlinear systems using MLF(multiple Lyapunov functions) method is presented. Then, it is applied to fixed-time tracking control of uncertain strict-feedback switched nonlinear systems. The design methods of fuzzy adaptive feedback controllers and a state-dependent switching law are given to achieve the boundedness of all the signals of the resulting closed-loop system and the fixed-time output tracking control. Nonsymmetrical dead-zone model is used to estimate an adaptive factor through less parameters, which related to fixed-time tracking control for the uncertain switched nonlinear systems. Two examples are given to verify the effectiveness of the proposed design method.

Adaptive neural inverse optimal control for uncertain switched nonlinear systems: an improved predefined-time method

For the first time, this paper introduces an improved predefined-time inverse optimal method to address the adaptive tracking control problem of a class of uncertain switched nonlinear systems. The proposed approach enables the system to achieve optimal performance without resorting to the HJB equation. Firstly, we design two-time constants to improve the traditional predefined-time lemma. The improved predefined-time lemma exhibits faster convergence. Subsequently, to realise the design of a predefined-time inverse optimal controller, a specific form of the auxiliary controller is designed using Sontag functions and nonsingular functions. Furthermore, the stability of the system and the optimality of the inverse are proven through the use of a common Lyapunov function method, ensuring that tracking errors converge to the neighbourhood of zero within the predefined time. Finally, the rationality of the proposed control structure is demonstrated through the example results.

Reinforcement learning-based adaptive event-triggered control of multi-agent systems with time-varying dead-zone

In this paper, a novel reinforcement learning (RL)-based adaptive event-triggered control problem is studied for non-affine multi-agent systems (MASs) with time-varying dead-zone. The purpose is to design an efficient event-triggered mechanism to achieve optimal control of MASs. Compared with the existing results, an improved smooth event-triggered mechanism is proposed, which not only overcomes the design difficulties caused by discontinuous trigger signals, but also reduces the waste of communication resources. In order to achieve optimal event-triggered control, RL algorithm of the identifier-critic-actor structure based on fuzzy logic systems (FLSs) is applied to estimate system dynamics, evaluate control performance, and execute control behavior, respectively. In addition, considering time-varying dead-zone in non-affine MASs brings obstacles to controller design, which makes system applications more generalized. Through Lyapunov theory, it is proved that the optimal control performance can be achieved and the tracking error converges to a small neighborhood of the origin. Finally, simulation proves the feasibility of the proposed method.

Finite-time adaptive fuzzy event-triggered control for nonlinear time-delay system with input quantization via command filter

This paper investigates the problem of finite-time adaptive fuzzy event-triggered control for a class of uncertain nonlinear systems with input quantization. The nonlinear systems under consideration contain unmodeled dynamics and time-varying delays. Fuzzy logic systems are used to handle unknown nonlinear terms. Additionally, finite-time filters are introduced to solve the problem of “explosion of complexity” as well as to ensure that the derivative of the virtual controller can be approximated in finite time. The Lyapunov–Krasovskii function is used to handle time-varying delays. The hysteresis quantizer is used to ensure adequate precision when there is a low transmission rate requirement. The control strategy combines event-triggered mechanisms and quantization technology to ensure that all signals of the closed-loop system remain bounded in finite time. Finally, two examples are included to demonstrate the effectiveness of the proposed controller.

ADP-based online compensation hierarchical sliding-mode control for partially unknown switched nonlinear systems with actuator failures

This article investigates an adaptive dynamic programming-based online compensation hierarchical sliding-mode control problem for a class of partially unknown switched nonlinear systems with actuator failures and uncertain perturbations under an identifier-critic neural networks architecture. Firstly, by introducing a cost function related to hierarchical sliding-mode surfaces for the nominal system, the original control problem is equivalently converted into an optimal control problem. To obtain this optimal control policy, the Hamilton–Jacobi–Bellman equation is solved through an adaptive dynamic programming method. Compared with conventional adaptive dynamic programming methods, the identifier-critic network architecture not only overcomes the limitation on the unknown internal dynamic but also eliminates the approximation error arising from the actor network. The weights in the critic network are tuned via the gradient descent approach and the experience replay technology, such that the persistence of excitation condition can be relaxed. Then, a compensation term containing hierarchical sliding-mode surfaces is used to offset uncertain actuator failures without the fault detection and isolation unit. Based on the Lyapunov stability theory, all states of the closed-loop nonlinear system are stable in the sense of uniformly ultimately boundedness. Finally, numerical and practical examples are given to demonstrate the effectiveness of our presented online compensation control strategy.