Unknown Gain Sign Research Articles

Event-Triggered Adaptive Bipartite Containment Control for Stochastic Multiagent Systems

In this article, the adaptive bipartite containment control problem is investigated for stochastic nonlinear multiagent systems (MASs) with an event-triggered mechanism. It is known that the dynamic surface control method suffers from the mismatch between the virtual controller and the filter output. To address this issue, a novel error compensator is designed. Meanwhile, motivated by their universal approximation capability, fuzzy-logic systems (FLSs) are employed to identify the plants’ unknown nonlinear characteristics. To reduce the communication overhead, a distributed event-triggered control scheme is designed based on an estimate of unknown gain sign’s reciprocal. Leveraging the stochastic Lyapunov stability theory and backstepping design technique, it is proved that 1) the output responses of followers converge to a convex hull formed by those of the leaders and their symmetric ones; 2) all signals in the closed-loop system are semiglobally uniformly ultimately bounded in probability (SGUUBP); and 3) there is no Zeno behavior. Finally, simulation results are presented to illustrate the effectiveness of the proposed method.

Prescribed Performance Synchronization Control of Chaotic Systems with Unknown Control Gain Signs

For a class of uncertain nonlinear chaotic systems with unknown control gain signs and saturated input, by means of Nussbaum function, a scheme of finite-time prescribed performance synchronization control is proposed. Here, Nussbaum function is used to eliminate the influence of unknown control gain signs, and fuzzy logic systems are used to estimate unknown functions. Lyapunov theory is used to prove that all synchronization errors converge to a predefined small performance range under the designed control method. Finally, simulation results are provided to illustrate the feasibility of the proposed method.

Novel prescribed performance-tangent barrier Lyapunov function for neural adaptive control of the chaotic PMSM system by backstepping

This paper investigates a neural adaptive output tracking prescribed performance control of the chaotic permanent magnet synchronous motor system with output-constrained, time-delays, parameter perturbations and external disturbances. Firstly, a novel prescribed performance-tangent barrier Lyapunov function is created to tackle the prespecified constraints of tracking error and output. Subsequently, backstepping controllers have been suggested. In specific steps, Chebyshev neural networks and the Nussbaum-type function are exploited to solve unknown nonlinearities and the unknown gain sign. Time-delays are tackled by constructing Lyapunov–Krasovskii functions (LKFs). Meanwhile, the “explosion of complexity” caused by the differentiation of virtual input is removed by plugging tracking differentiator into the controller. Furthermore, it is demonstrated that all the closed-loop signals are ultimate boundedness and predefined constraints are not violated. Finally, simulation studies were performed to confirm the validities and robustness of the raised scheme.

A neural composite dynamic surface control for pure‐feedback systems with unknown control gain signs and full state constraints

SummaryThis paper investigates a composite neural dynamic surface control (DSC) method for a class of pure‐feedback nonlinear systems in the case of unknown control gain signs and full‐state constraints. Neural networks are utilized to approximate the compound unknown functions, and the approximation errors of neural networks are applied in the design of updated adaptation laws. Comparing the proposed composite approximation method with the conventional ones, a faster and better approximation performance result can be obtained. Combining the composite neural networks approximation with the DSC technique, an improved composite neural adaptive control approach is designed for the considered nonlinear system. Then, together with the Lyapunov stability theory, all the variables of the closed‐loop system are semiglobal uniformly ultimately bounded. The infringements of full state constraints can be avoided in the case of unknown control gain signs as well as unknown disturbances. Finally, two simulation examples show the effectiveness and feasibility of the proposed results.

Cooperative Control of Multiple Agents With Unknown High-Frequency Gain Signs Under Unbalanced and Switching Topologies

Existing results on cooperative control of multi-agent systems with unknown control directions require that the underlying topology is either fixed with a strongly connected graph or switching between different strongly connected graphs. Furthermore, in most cases the graph is assumed to be balanced. This paper proposes a new class of nonlinear PI based algorithms to relax these requirements and allow for unbalanced and switching topologies having a jointly strongly connected basis. This is made possible for single-integrator (SI) and double-integrator (DI) agents with non-identical unknown control directions by a suitable selection of the distributed nonlinear PI functions. Moreover, as a special case, the proposed algorithms are applied to strongly connected and fixed graphs. Finally, simulation examples are given to show the validity of our theoretical results.

Fuzzy Adaptive Prescribed Performance Tracking Control for Uncertain Nonlinear Systems With Unknown Control Gain Signs

This work addresses fuzzy adaptive tracking control of uncertain nonlinear systems with unknown control gain signs. Nussbaum functions are used to eliminate the effect of unknown control directions (i.e. unknown control gain signs). In order to make tracking errors approach a predefined neighborhood, two controllers are developed by the aid of fuzzy adaptive prescribed performance control (PPC) technique. The controlled system is transformed to an equivalent one by using appropriate transformation function. Under the proposed tracking controllers without accurate initial errors, the boundedness of all involved variables is guaranteed. Moreover, the tracking errors can remain within the small prescribed performance bounds (PPBs). Finally, simulation results show the effectiveness of the proposed methods.

Adaptive iterative learning protocol design for nonlinear multi-agent systems with unknown control direction

This paper investigates a new adaptive iterative learning control protocol design for uncertain nonlinear multi-agent systems with unknown gain signs. Based on Nussbaum gain, adaptive iterative learning control protocols are designed for each follower agent and the adaptive laws depend on the information available from the agents in the neighbourhood. The proper protocols guarantee each follower agent track the leader perfectly on the finite time interval and the Nussbaum-type item can seek control direction adaptively. Furthermore, the formation problem is studied as an extension. Finally, simulation examples are given to demonstrate the effectiveness of the proposed method in this article.

Distributed Adaptive FBC of Uncertain Nonaffine Multiagent Systems Preceded by Unknown Input Nonlinearities With Unknown Gain Sign

An adaptive filtered backstepping control (FBC) is proposed for cooperative tracking control of uncertain nonaffine nonlinear multiagent systems preceded by input nonlinearities with unknown gain sign. The input nonlinearities can be backlash-like hysteresis and dead-zone. The gains of input nonlinearities are unknown nonlinear functions with unknown sign. To cope with unknown nonlinearities neural networks based on universal approximation theorem are utilized. The weights of neural networks are derived based on appropriate adaptive rules. Using the proposed adaptive FBC desirable steady-state and transient response can be achieved. Based on Lyapunov synthesis approach all the adaptive laws are extracted. It is proved that all the signals in the closed-loop network are semi-globally uniformly ultimately bounded and the outputs of the agents track the leader’s output asymptotically. Simulation results demonstrate the applicability and effectiveness of the proposed method.

Adaptive Neural Prescribed Performance DSC for Non-affine SISO Nonlinear Systems with External Disturbances

Explosion of complexity and undesirable transient response of systems, are two major problems that conventional backstepping methods suffer from it. Furthermore, lack of information about the system and undesirable external disturbances are other problems that have been addressed in this paper. Therefore, an adaptive neural controller is designed to consider the proposed problems in this paper. The presented controller is constructed for the class of single-input, single-output (SISO) non-affine strict feedback systems with unknown gain signs and a neural network is employed to approximate unknown functions. By applying dynamic surface control (DSC) and prescribed performance functions, two major problems of an explosion in terms and the transient response of the system will be solved, respectively. Nussbaum functions are also utilized to address the problem of unknown gain signs. The proposed controller guarantees that all the closed-loop signals are semi-globally, uniformly ultimately bounded (SGUUB). Finally, in order to show the feasibility of this approach, a simulation example is provided.

Consensus in Networks of Agents With Unknown High-Frequency Gain Signs and Switching Topology

The agreement control problem of single and double-integrator agents with unknown and nonidentical control directions is addressed in this note under switching network topology. Distributed nonlinear PI control laws are proposed which ensure asymptotic consensus among the agents based on a new boundedness lemma and a generalized version of Barbalat's lemma for uniformly piecewise right continuous functions. Theoretical results are verified by simulation studies.

Neuro-adaptive backstepping control of SISO non-affine systems with unknown gain sign

This paper presents two neuro-adaptive controllers for a class of uncertain single-input, single-output (SISO) nonlinear non-affine systems with unknown gain sign. The first approach is state feedback controller, so that a neuro-adaptive state-feedback controller is constructed based on the backstepping technique. The second approach is an observer-based controller and K-filters are designed to estimate the system states. The proposed method relaxes a priori knowledge of control gain sign and therefore by utilizing the Nussbaum-type functions this problem is addressed. In these methods, neural networks are employed to approximate the unknown nonlinear functions. The proposed adaptive control schemes guarantee that all the closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB). Finally, the theoretical results are numerically verified through simulation examples. Simulation results show the effectiveness of the proposed methods.

Adaptive Control of Nonlinear Systems with Hysteresis and Unknown Control Direction

An adaptive backstepping controller is proposed for a class of nonlinear systems with hysteresis and unknown control direction. As the unknown gain sign is combined with multi-valued non-smooth hysteresis together, it is more challengeable to mitigate hysteresis effects and meanwhile guarantee stability of the dynamic systems. In this paper, Bouc-Wen model is adopted to describe the hysteresis. Then RBF neural networks are applied to approximate the unknown functions. The unknown control direction is solved by Nussbaum function. The adaptive backstepping controller is developed using prescribed performance function to confine the error to a predefined residual set. It is proved that all the closed-loop signals are bounded and the tracking error converges to an arbitrarily small field. Finally, the simulation result shows the feasibility of the control scheme.

Adaptive fuzzy output-feedback dynamic surface control of MIMO switched nonlinear systems with unknown gain signs

This paper investigates the problem of adaptive fuzzy tracking control for a class of multi-input–multi-output (MIMO) switched uncertain nonlinear systems with unknown gain signs and unmeasurable states. Fuzzy logic systems are used to approximate the unknown nonlinear functions, a fuzzy MIMO switched observer is designed to estimate the unmeasurable states. The Nussbaum-type functions are utilized to handle the unknown gain signs of the system under study. A switched-dynamic-surface-based adaptive fuzzy control approach is then established by exploiting the average dwell time method and backstepping and the dynamic surface control technique, which constructs multiple switched first-order filters to overcome the multiple “explosion of complexity” problem when applying the backstepping recursive design scheme. Also, the proposed approach extends the classical dynamic surface control technique from its original non-switched nonlinear version to a switched nonlinear version. It is proved that all the signals in the closed-loop system are semiglobal uniformly ultimately boundedness under a class of switching signals with average dwell time, and the tracking errors converge to a small neighborhood of the origin. A mass–spring–damper system with controller switching as a practical example is provided to demonstrate the effectiveness of the proposed design method.

Observer‐based direct adaptive fuzzy control for single‐input single‐output non‐linear systems with unknown gain sign

This study presents an observer-based direct adaptive fuzzy control for a class of uncertain single-input single-output non-linear systems with unknown gain sign. A state observer is designed to estimate the unmeasured state, the direct adaptive fuzzy controller is designed in the presence of only system output is available for measurement, and the parameter adaptive laws are updated by fuzzy basis functions rather than by its filtering. A robust controller is designed to compensate for the lumped errors, and a Nussbaum gain function is incorporated in the robust controller to estimate the unknown gain sign. The proposed scheme guarantees that all of the signals in the resulting closed-loop systems are bounded and that the tracking errors converge asymptotically to zero. A simulation example is used to demonstrate the effectiveness of the proposed scheme.

Observer-based indirect adaptive fuzzy control for SISO nonlinear systems with unknown gain sign

This paper develops an observer-based indirect adaptive fuzzy control scheme for a class of single-input single-output (SISO) nonlinear systems. The considered systems have unknown nonlinear functions, unknown control gain sign, and unmeasurable state variables. In this study, fuzzy systems are utilized to approximate unknown nonlinear functions, and a fuzzy adaptive state observer is designed to estimate the unmeasured state. A robust controller is used to compensate for the lumped errors, and the Nussbaum gain function is incorporated in the robust controller to estimate the unknown gain sign. Based on the strictly positive real Lyapunov design approach, the parameter adaptive laws are designed by the fuzzy basis functions rather than by its filtering. It is proved that all the signals in the closed-loop systems are bounded and that the tracking error converges asymptotically to zero. A simulation example is used to demonstrate the effectiveness of the proposed scheme.

Observer-based adaptive robust control of nonlinear nonaffine systems with unknown gain sign

In this paper, a direct adaptive robust controller for a class of SISO nonaffine nonlinear systems is presented. The existence of an ideal controller is proved based on the Implicit Function Theorem. Since the Implicit Function Theorem only guarantees the existence of the controller and does not provide a way to construct it, a neural network is employed to approximate the unknown ideal controller. In addition, an observer is designed to estimate the system states because all the states may not be available for measurements. In this method, a priori knowledge about the sign of control gain is not required and, in order to cope with unknown control direction, the Nussbaum-type technique is used. Moreover, only one adaptive parameter is needed to be updated and also a robust term is used in the control signal to reduce the effect of external disturbances and approximation errors. Furthermore, the stability analysis for the closed-loop system is presented based on the Lyapunov stability method. Theoretical results are illustrated through a simulation example. These simulations show the effectiveness of the proposed method.

Asymptotic tracking control of uncertain nonlinear systems with unknown actuator nonlinearity and unknown gain signs

Two adaptive control schemes for a class of uncertain nonlinear systems preceded by actuator nonlinearity are presented. We consider two possible input nonlinearities, that is, backlash-like hysteresis and symmetric dead-zone, which can be simultaneously dealt with by using the proposed compensation controllers. The knowledge on the signs of the unknown plant parameters and the parameters in the input nonlinearity models is not required. Only the boundedness of the reference signal is assumed. The Nussbaum gain approach is employed to remove the assumption on the control gain sign. The first scheme is based on the backstepping technique. The final step of the recursive design is crucial for the closed-loop stability. In the second scheme, a direct adaptive control law is designed. The controller has a simple structure and only one adaptation parameter is updated. In both controllers, it is shown that asymptotic tracking is ensured. Two numerical examples are provided to show the effectiveness of the theoretical results.

Adaptive neural tracking control of pure-feedback nonlinear systems with unknown gain signs and unmodeled dynamics

In this paper, robust adaptive control is proposed for a class of pure-feedback nonlinear systems with unmodeled dynamics and unknown gain signs using radial basis function neural networks (RBFNNs). Dynamic uncertainties are dealt with using a dynamic signal. The unknown virtual gain signs are solved using the Nussbaum functions. Using mean value theorem and Young's inequality, only one learning parameter needs to be tuned online at each step of recursion. It is proved that the proposed design scheme can guarantee semi-global uniform ultimate boundedness (SGUUB) of all signals in the closed-loop system. Simulation results demonstrate the effectiveness of the proposed approach.

Adaptive neural control of non-affine pure-feedback non-linear systems with input nonlinearity and perturbed uncertainties

In this article, two robust adaptive control schemes are investigated for a class of completely non-affine pure-feedback non-linear systems with input non-linearity and perturbed uncertainties using radial basis function neural networks (RBFNNs). Based on the dynamic surface control (DSC) technique and using the quadratic Lyapunov function, the explosion of complexity in the traditional backstepping design is avoided when the gain signs are known. In addition, the unknown virtual gain signs are dealt with using the Nussbaum functions. Using the mean value theorem and Young's inequality, only one learning parameter needs to be tuned online at each step of recursion. It is proved that the proposed design method is able to guarantee semi-global uniform ultimate boundedness (SGUUB) of all signals in the closed-loop system. Simulation results verify the effectiveness of the proposed approach.

Adaptive actuator failure compensation with unknown control gain signs

This study deals with the problem of adaptive control for a class of non-linear systems with parameterisable time-varying actuator failures. An adaptive output-feedback actuator failure compensation scheme is proposed based on the backstepping technique and the Nussbaum gain approach. The assumption on the control gain signs is removed. The boundedness of all the closed-loop signals and the asymptotic output tracking are guaranteed in spite of the unknown actuator failures. Finally, an example is given to show the effectiveness of the proposed design method.