Unknown Nonlinear Systems Research Articles

Optimal Synchronization Control of Heterogeneous Asymmetric Input-Constrained Unknown Nonlinear MASs via Reinforcement Learning

The asymmetric input-constrained optimal synchronization problem of heterogeneous unknown nonlinear multiagent systems (MASs) is considered in the paper. Intuitively, a state-space transformation is performed such that satisfaction of symmetric input constraints for the transformed system guarantees satisfaction of asymmetric input constraints for the original system. Then, considering that the leader's information is not available to every follower, a novel distributed observer is designed to estimate the leader's state using only exchange of information among neighboring followers. After that, a network of augmented systems is constructed by combining observers and followers dynamics. A nonquadratic cost function is then leveraged for each augmented system (agent) for which its optimization satisfies input constraints and its corresponding constrained Hamilton-Jacobi-Bellman (HJB) equation is solved in a data-based fashion. More specifically, a data-based off-policy reinforcement learning (RL) algorithm is presented to learn the solution to the constrained HJB equation without requiring the complete knowledge of the agents' dynamics. Convergence of the improved RL algorithm to the solution to the constrained HJB equation is also demonstrated. Finally, the correctness and validity of the theoretical results are demonstrated by a simulation example.

Point-to-point consensus tracking control for unknown nonlinear multi-agent systems using data-driven iterative learning

This paper considers the point-to-point consensus tracking control for a class of nonlinear multi-agent systems with completely unknown dynamics, where the consensus is concerned with some given desired points instead of the entire desired trajectory. It is assumed that the multi-agent system executes repetitive coordination tasks in a finite time interval and the iterative learning control is also utilized to design a consensus protocol with learning ability. To deal with the unknown nonlinear agent’s dynamic, the relationship between agent’s output at these given points and agent’s control input is first derived and then a data-based model referring to the agent’s dynamic is established by utilizing the iteration-domain dynamical linearization technique. Then, a data-driven iterative learning protocol is developed by optimizing two performance indexes, which contains a control input updated algorithm, a parameter estimation algorithm and a reset algorithm. The results show that the proposed design can achieve the point-to-point consensus tracking task only by using the I/O data of the agent. Finally, simulation examples are provided to verify the effectiveness of the proposed protocol.

A neural network adaptive interval observer design for nonlinear systems

A design method of neural network adaptive interval observer for the continuous-time unknown nonlinear system is proposed. The bounds of unknown nonlinear functions are described by the state and the input, so that the bounds of the nonlinear function vector are unmeasurable. Therefore, this method can be used to observe systems with higher degree of nonlinearity and any priori knowledge about systems. In this work, the hyper basis function neural network (HBFNN) is presented to estimate the boundary (including lower and upper bounds) of the unknown nonlinear function vector. Furthermore, the non-negativity and stability of the error dynamic system are given, and the convergence and non-negativity are also guaranteed. Compared with the traditional interval observer, the efficiency of the proposed approach is verified through a numerical simulation example.

Broad-learning recurrent Hermite neural control for unknown nonlinear systems

The broad-learning systems (BLS) with advance control theories have been studied, but found to have two disadvantages: one is that the calculations are too complicated and the other is that the convergence time cannot be guaranteed. In order to mitigate the high computational loading, this study proposes a broad-learning Hermite neural network (BHNN), which has the capability of dynamic mapping and reduces the structural complexity of neural network. Meanwhile, a broad-learning recurrent Hermite neural control (BRHNC) system is proposed while maintaining finite-time stability to speed up the tracking error convergence. The proposed BRHNC system comprises two controllers: a recurrent broad controller that utilizes a BHNN to approximate on-line an ideal finite-time controller and a robust exponential controller that ensures system stability through a Lyapunov function. Meanwhile, the BHNN’s full-tuned parameter learning laws are developed to increase the approximating capacity, learning capacity and accuracy using gradient descent method. Finally, simulation and experimental results show that the BRHNC system has good control, tracking and disturbance rejection properties, while the BRHNC system requires no prior knowledge about the system dynamics.

Learning‐based robust control methodologies under information constraints

Learning‐based robust control methodologies under information constraints

Adaptive consensus control for a class of nonlinear multi-agent systems with unknown time delays and external disturbances

This paper investigates a class of unknown nonlinear multi-agent systems with unknown time delays and external disturbances. The external disturbance considered in this paper is completely unknown, and the accurate mathematical expression cannot be obtained. To eliminate the external disturbance, a disturbance observer is constructed by the Disturbance-Observer-Based-Control (DOBC) method. By utilizing Young’s inequality scaling technique, the problem of time delay is solved. By assuming that the communication graph among the agents is directed and connected, a novel distributed adaptive consensus control protocol is established based on the relative output information to achieve the goal of consensus control. Furthermore, the stability of the multi-agent system is analyzed by selecting an appropriate Lyapunov function; it is certified that with the proposed control protocol, all signals are guaranteed to be globally uniformly bounded, and the considered multi-agent systems can reach consensus even in the presence of time delay and external disturbance. Finally, two simulation examples are given to support the proposed control strategy.

Security data-driven iterative learning control for unknown nonlinear systems with hybrid attacks and fading measurements

To achieve the stabilization objective of a class of nonlinear systems with unknown dynamics, this paper studies the security data-driven control problem under iterative learning schemes, where the faded channels are suffering from randomly hybrid attacks. The networked attacks try to obstruct the data transmission by injecting the false data. The plant is transformed into a dynamic data-model with the iteration-related linearization method. Then, two data-driven control methods, including a compensation scheme multiplied by increasing gains, are designed by using incomplete I/O signals. The effectiveness of the algorithms and the influence brought by stochastic issues are analyzed theoretically. Finally, a numerical simulation and a tracking example of agricultural vehicles illustrate the validity of the design.

Stabilizing regions of PID controller for a class of unknown nonlinear non‐affine discrete‐time systems

AbstractBased on the technology of dynamic linearization, the stability regions of PID, PI, PD, and P type controllers are investigated for a class of unknown nonlinear non‐affine discrete‐time systems. An equivalent data model to the unknown nonlinear system is established first through the dynamic linearization technique. Then based on the established data model, the determination of the structure of PID/PI controller has been given by rigorous theoretical derivation. The closed‐loop system is shown to be asymptotically stable for the PID, PI controllers, and the output/input signals of the closed loop system are bounded for the PD and P type controllers with the method of contraction mapping principle. An example of nonlinear non‐affine discrete‐time systems is used to demonstrate its correspondingly stability regions.

Robust tracking control design for fractional-order interval type-2 fuzzy systems

This paper is concerned with an uncertainty and disturbance estimator-based tracking control problem for a class of interval type-2 fractional-order Takagi-Sugeno fuzzy systems subject to time-varying delays. The footprints of the uncertainty of the underlying fuzzy systems are taken into account to capture and model different levels of uncertainties. The uncertainty and disturbance estimator is used to promote the tracking behavior of rejecting disturbance in the control system. First, by applying the Lyapunov approach, we focus on the examination of stability and performance of the fractional-order tracking error system. Next, unknown system uncertainties, external disturbances and nonlinearities are accurately estimated via an appropriate filter design. Particularly, the proposed control technique does not require any prior knowledge about above said unknown factors and it only requires the bandwidth information about the low-pass filter. Then, four numerical examples with simulation results are presented in the end, to show the potential of the theoretical results of the proposed control method.

Optimal plug-and-control of unknown nonlinear systems

Modeling and control design are typically subsequent but independent activities. Optimal control is traditionally developed on the basis of explicit models. While this usually yields good results for linear systems, the same is not as true for nonlinear ones, for which explicit solutions can be found only for few cases. In practice, in most cases receding horizon controls based on linear approximations are used. In this paper, we propose a procedure which delivers in one step both a model and an optimal receding horizon control algorithm, without requiring a linearization. Our procedure relies essentially on a system identification by a suitable class of functions which offers universal approximation properties that can be directly incorporated in the control algorithm. Using directional forgetting we show that an adaptive extension can be realized. Measurements and simulations based on a standard automotive control problem are presented to confirm the validity of our proposal.

Adaptive Event-Triggered Near-Optimal Tracking Control for Unknown Continuous-Time Nonlinear Systems

This paper studies the event-triggered optimal tracking control (ETOTC) problem of continuous-time (CT) unknown nonlinear systems. In order to solve the ETOTC problem, an augmented system composed of the error system dynamics and the reference dynamics is used to introduce a new discounted performance index function (DPIF). A novel event-triggered (ET) adaptive dynamic programming (ADP) method is developed to solve the ET Hamilton-Jacobi-Bellman equation (HJBE). The presented method is implemented via an identifier-critic architecture, which consists of two neural networks (NNs): an identifier NN is applied to estimate the unknown system dynamics, and a critic NN is constructed to obtain the approximate solution of the ET HJBE. The augmented closed-loop system and the critic estimation error are proved to be ultimately uniformly bounded (UUB) by the Lyapunov direct method. Finally, two simulations illustrate the effectiveness of the developed method.

Adaptive Constrained Control of Unknown Strict Feedback Nonlinear Systems With Dead Zone Input

To tackle the problem of unknown strict feedback nonlinear control systems with dead zone input and pre-assigned tracking control, a novel adaptive tracking control strategy is proposed based on immune function, active disturbance rejection control and pre-assigned funnel constraint. For unknown information in the control system, the immune function and the extended state observer are utilized to estimate the unknown information of control systems. By combining with the Lyapunov function, the funnel control is introduced to design the controller, it is employed to guarantee the tracking error within pre-assigned funnel boundary. The adaptive controller is designed on the basis of the rapid changing rate of hyperbolic tangent function, the command filtering resolves the repeating derivations problem of the backstepping method. The stability analysis demonstrates the boundedness of all the closed-loop signals. A simulation example shows the effectiveness of the proposed control strategy.

Distributed control of nonlinear systems with unknown time-varying control coefficients: A novel Nussbaum function approach

In this paper, distributed control of uncertain multi-agent systems (MAS) with completely unknown nonlinearities, unknown time-varying control coefficients and multiple unknown control directions is investigated. Firstly, a new theorem with a series of novel Nussbaum functions are presented, which solve the outstanding problem in control of nonlinear systems with unknown time-varying control coefficients and unknown signs. Secondly, global consensus of MAS with unknown time-varying control coefficients and unknown system nonlinearities under directed graph is firstly achieved, and the transient tracking performance is also guaranteed. Thirdly, a novel filter is proposed for each agent which does not require a prior knowledge of time derivative of leader. Finally, simulation results show the effectiveness of the proposed control schemes.

Modelling and System Identification of a Nonlinear Microreactor: a Dual Youla Approach

We present a reduced order nonlinear model of a microreactor which is suitable for control. We show that a nonlinear dual Youla structure provides a useful parameterisation that can be identified with data generated in closed loop. We show that the unknown nonlinear system can be represented by a combination of a nominal linear model and a nonlinearity whose identified parameters have a nonlinear ARX (NARX) structure.

Approximate Reachability for Koopman Systems Using Mixed Monotonicity

We present a data-driven method for computing reachable sets for unknown nonlinear dynamical systems using a Koopman operator based approach. We find mixed-monotone decompositions for a class of Koopman lifted dynamics. The mixed-monotone system can be further embedded to a higher-dimensional dynamical model which is propagated in time deterministically. This allows us to find over-approximations of forward reachable sets that do not suffer from the curse of dimensionality. The proposed method can account for unknown nonlinear dynamics and allow a calculation of the conservative approximations of the reachable sets to a prefixed degree of accuracy in a computationally inexpensive manner. We demonstrate the efficacy of the proposed algorithm using an illustrative example with an unknown, nonlinear dynamical model, and compare it to CORA, a well-known existing method.

Suboptimal Control of Unknown Second-Order Nonlinear Systems With Guaranteed Global Convergence

A suboptimal active disturbance rejection controller (S-ADRC) is proposed for second-order systems with unknown time-varying nonlinear dynamics. The output-feedback controller guarantees a global convergence to the vicinity of an optimal solution by means of dynamic control gains, based on the estimated main and extended state variables obtained through a high-gain observer. Three numerical examples compare the performance of the proposed control scheme applied to linear and nonlinear systems with that of a fixed-gain conventional ADRC as well as several model-based optimal and suboptimal controllers.

Data-Driven Abstraction and Model Invalidation for Unknown Systems With Bounded Jacobians

In this paper, we consider data-driven abstraction and model invalidation problems for unknown nonlinear discrete-time dynamical systems with bounded Jacobians, where only prior noisy sampled data of the systems, instead of mathematical models, are available. First, we introduce a novel non-parametric learning approach to over-approximate the unknown model/dynamics with upper and lower functions, i.e., to find model abstractions, under the assumption of known bounded Jacobians. Notably, the resulting data-driven models can be mathematically proven to be equal to or more accurate than componentwise Lipschitz continuity-based methods. Further, we show that the resulting data-driven model can be used to determine its (in)compatibility with a newly observed length-T output trajectory, i.e., to (in)validate models, using a tractable feasible check. Finally, we propose a method to estimate the Jacobian bounds if they are not known or given.

A Framework for Prescribed-Time Control Design via Time-Scale Transformation

This letter presents a unified framework for the design of prescribed-time controllers under time-varying input and state constraints for normal-form unknown nonlinear systems with uncertain input gain. The proposed approach is based on a time-domain mapping method by which any infinite-time system can be corresponded to a prescribed-time system and vice versa. It is shown that the design of a constrained nonasymptotic prescribed-time controller can be reduced to the asymptotic control design for an associated constrained infinite-time system. Fa\`a di Bruno's formula and Bell polynomials are used for a constructive representation of the associated infinite-time system. The presented results are not confined to a particular mapping function, which adds to the flexibility of the proposed scheme. It is shown that necessary and sufficient conditions on the uniform (practical) prescribed-time stability and attractivity can be obtained as corollaries of the main result.

Passivity and Immersion (P&I) Approach With Gaussian Process for Stabilization and Control of Nonlinear Systems

The virtual derivatives computation and successive derivations of virtual inputs in an adaptive backstepping controller cause the explosion of complexity. Moreover, the feedback linearization has poor robustness features and necessitates exact estimation of the feedback control law’s coefficients. Due to measurement noise, the model-based estimation techniques for identifying uncertainties result in inaccurate gradient and Hessian calculations. Such limitations lead to model and measurement uncertainties that prevent effective stabilization and control of nonlinear systems. Machine learning-based data-driven approaches offer effective tools for identifying dynamical systems and uncertainties with minimal prior knowledge of the model structure. Therefore, the contribution of this research is two-fold: First, the general controller design theory is proposed which utilizes the idea of an invariant target manifold giving rise to a non-degenerate two form, through which the definition of certain passive outputs and storage functions leads to a generation of control law for stabilizing the system. Since the above concepts are linked with the Immersion and Invariance (I&I) design policy and the passivity theory of controller design, the proposed methodology is labeled as the "Passivity and Immersion (P&I) based approach". Second, the proposed P&I approach is integrated with a Bayesian nonparametric approach, particularly the Gaussian Process for stabilization and control of the partially unknown nonlinear systems. The effectiveness of the proposed methodologies has been evaluated on an inverted pendulum using MATLAB in the presence of input-output uncertainties.

A novel bipartite consensus tracking scheme for unknown nonlinear multi-agent systems: Theoretical analysis and applications

This article proposes a novel distributed data-driven bipartite consensus tracking scheme for bipartite consensus tracking problems of multi-agent systems with bounded disturbances and coopetition networks. The proposed scheme only uses the input/output data of each agent without requiring the agents’ dynamics. We obtain the equivalent dynamic linearization data model for a controlled plant using the dynamic linearization technique based on the pseudo partial derivative. Considering the cooperative and competitive interactions among agents, the proposed method ensures that agents with adversarial relationships implement bipartite consensus tracking tasks even if only a subset of agents can access the information from the virtual leader. Moreover, the strict proof process of convergence properties reveals that the tracking error coverages to a small range around the origin. We also establish a set of software and hardware platform to demonstrate the effectiveness of the proposed distributed data-driven bipartite consensus tracking method.