Class Of Affine Nonlinear Systems Research Articles

Zero-Sum Differential Game-Based Fault-Tolerant Control for a Class of Affine Nonlinear Systems.

This article proposes a zero-sum differential game-based control scheme for a class of affine nonlinear control systems with actuator faults, including loss of control, loss of effectiveness, and bias faults. In the control design, the bias faults and the control signal are chosen as the two opposite sides. The Nash equilibrium is achieved while the optimal control signal and the upper bound of bias faults can be derived from the Hamilton-Jacobi-Isaacs (HJI) equation. An adaptive dynamic programming (ADP) method is employed to estimate the weight of the critic network. The developed zero-sum differential game-based control scheme can ensure the system stability and optimal performance. Two simulation results on a numerical system and a rigid spacecraft model illustrate the effectiveness of the proposed control scheme.

Neuroadaptive Tracking Control of Affine Nonlinear Systems Using Echo State Networks Embedded With Multiclustered Structure and Intrinsic Plasticity.

In this article, we present an echo state network (ESN)-based tracking control approach for a class of affine nonlinear systems. Different from the most existing neural-network (NN)-based control methods that are focused on the feedforward NN, the proposed method adopts a bioinspired recurrent NN fusing with multiple cluster and intrinsic plasticity (IP) to deal with modeling uncertainties and coupling nonlinearities in the systems. The key features of this work can be summarized as follows: 1) the proposed control is built upon the ESN embedded with multiclustered reservoir inspired from the hierarchically clustered organizations of cortical connections in mammalian brains; 2) the developed neuroadaptive control scheme utilizes unsupervised learning rules inspired from the neural plasticity mechanism of the individual neuron in nervous systems, called IP; 3) a multiclustered reservoir with IP is integrated into the algorithm to enhance the approximation performance of NN; and 4) the multiclustered reservoir is constructed offline and is task-independent, rendering the proposed method less expensive in computation. The effectiveness of the method is also confirmed by comparison with the existing neuroadaptive methods via numerical simulations, demonstrating that better tracking precision is achieved by the proposed method.

Reinforcement Learning-Based Adaptive Optimal Control for Nonlinear Systems With Asymmetric Hysteresis.

This article investigates the adaptive optimal tracking problem for a class of nonlinear affine systems with asymmetric Prandtl-Ishlinskii (PI) hysteresis nonlinearities based on actor-critic (A-C) learning mechanisms. Considering the huge obstacles arising from the uncertainty of hysteresis nonlinearity in actuators, we develop a scheme for the conflict between the construction of Hamilton functions and hysteresis nonlinearity. The actuator hysteresis forces the input into a hysteresis delay, thus preventing the Hamilton function from getting the current moment's input instantly and thus making optimization impossible. In the first step, an inverse model is constructed to compensate for the hysteresis model with a shift factor. In the second step, we compensate for the control input by designing a feedback controller and incorporating the estimation and approximation errors into the Hamilton error. Optimal control, the other part of the actual control input, is obtained by taking partial derivatives of the Hamiltonian function after the nonlinearities have been circumvented. At the end, a simulation is given to validate the developed solution.

Adaptive Inverse Nonlinear Optimal Control Based on Finite-Time Concurrent Learning and Semidefinite Programming.

This article investigates the problem of inverse optimal control (IOC) for a class of nonlinear affine systems. An adaptive IOC approach is proposed to recover the cost functional using only the system state data, which integrates the finite-time concurrent learning (FTCL) technique and the semidefinite programming (SDP) technique. First, an identifier neural network (NN) is employed to approximate the unknown nonlinear control policy, and an FTCL-based update law is proposed to estimate the weights of the identifier NN online, which removes the traditional persistent excitation (PE) condition. Moreover, the finite-time convergence as well as the uniformly ultimately boundness (UUB) of estimation error of the identifier NN weights are analysed according to whether or not there exists the identifier NN approximation error. Then, with the help of a value NN for approximating the value function, an SDP problem with a quadratic objective function can be set up for determining the weighting matrices of the cost functional. Finally, simulation results are presented to validate the proposed method.

Homogeneous systems stabilization based on convex embedding

The paper develops control algorithms for a class of affine nonlinear systems using the so-called canonical homogeneous representation. It is demonstrated that such a representation exists for any homogeneous vector field bounded on the unit sphere. It is shown that canonical homogeneous representation is useful for LMI-based control design and stability analysis of nonlinear systems. Theoretical results are supported by numerical examples.

Distributed-Observer-Based Distributed Control Law for Affine Nonlinear Systems and Its Application on Interconnected Cruise Control of Intelligent Vehicles

Distributed-observer-based distributed control law for interconnected systems has become the research focus in recent years. This paper extends this study from linear systems to a class of affine nonlinear systems. Before this, distributed observer for nonlinear systems with control inputs has not been studied, as well as the distributed-observer-based distributed control law. To fill this gap, we overcome the difficulty of proving joint observability for distributed nonlinear observer by an original analysis method based on maximum invariant distribution. In addition, the influence of model mismatch on distributed observer and distributed controller is also investigated and analyzed in detail. By analyzing the complex coupling relationship between observer dynamics, control input, and model mismatch, we successfully deal with the dissatisfaction of separation principle and prove the stability of observer error systems and closed-loop systems. The results show both the error dynamics of distributed observer and the system states of closed-loop system formed by the observer-based distributed control law can converge to an arbitrarily small invariant set around the origin. In addition to the original work in distributed-observer-based distributed control law, this paper also contributes to the design of distributed observer. Firstly, the proposed design method is also applicable to distributed observer of autonomous systems. Compared to the existing results, our method admits weaker assumptions. Specifically, one could find an approximate system to meet the assumptions required by designing distributed observer when the underlying system fails to meet the requirements. At last, the automated highway system is employed to verify the results.

Prescribed Performance Adaptive Fuzzy Control for Affine Nonlinear Systems With State Constraints

This article considers the problem of prescribed performance control for a class of affine nonlinear systems with state constraints. Fuzzy logic systems (FLSs) are employed to cope with unknown nonlinear functions. In addition, an additive transformation and one-to-one mapping method are introduced to handle the control problem of nonlinear systems with full-state constraints. Then, based on adaptive backstepping control, we develop a new prescribed performance adaptive fuzzy control method, which not only makes the tracking error be constrained within the prescribed range but also ensures the other state variables do not violate the predefined constraints. The simulation example verify the feasibility of the control method.

Robust adaptive iterative learning control for nonrepetitive systems with iteration-varying parameters and initial state

This paper explores how to construct an adaptive iteration learning control (AILC) mechanism for a class of discrete-time nonrepetitive systems subject to iteration-varying unknown parameters and unidentical initial condition. Firstly, for the linear discrete-time nonrepetitive systems, by minimizing the discrepancy of the real system outputs from the estimated system outputs, a gradient-type adaptation law is designed to estimate the system lower triangular parameter matrix and the system initial state. Especially, the current parametric estimation is updated by virtue of the input-output data and the previous estimation. Secondly, an AILC mechanism is constructed based on the estimated system lower triangular parameter matrix, where the control input algorithm and the adaptation law are scheduled in an interactive mode. Thirdly, the boundedness of the estimation error between the real system matrix and the estimation one is derived by means of vector norm theory. Based on the boundedness of the estimation error, the robust condition of the proposed AILC is given. Finally, the proposed AILC is investigated for a class of nonlinear affine systems and the corresponding results are captured. Simulation results illustrate the validity and effectiveness of the proposed AILC schemes.

Inverse Optimal Control Via Diagonal Stabilization Applied to Attitude Tracking of a Reusable Launch Vehicle

In this work, a novel strategy for the inverse optimal control of a class of affine nonlinear systems is proposed. The proposed strategy involves translation of the infinite horizon nonlinear optimal control problem into a Diagonal stability problem, followed by the formulation of a set of criteria for the synthesis of a stabilizing feedback control law. Hence, the proposed controller design methodology is refered to as inverse optimal control via diagonal stabilization. Besides providing a closed-form solution, the methodology also possesses the added advantage of inherent robustness, on account of adequate stability margins. Most importantly, the methodology ensures an estimate of the associated domain of attraction, which is a highly desirable feature especially in the case of crucial and stringent aerospace applications. The proposed methodology is applied for the re-entry control of a reusable launch vehicle which provides a full envelope optimality-based design philosophy. For this, the control-oriented attitude model based on the three-degree-of-freedom dynamic model is utilized. The resulting control law possess desirable features of guaranteed estimate of stability domain, assured design flexibility, and inherent robustness. Simulation results verify the validity of these theoretically proven facets in terms of the efficacy and robustness of the proposed controller.

Robust PI-Based Non-Singular Terminal Synergetic Control for Nonlinear Systems via Hybrid Nonlinear Disturbance Observer

This paper proposes a novel robust proportional integral non-singular terminal synergetic control (PI-NTSC) for a class of affine nonlinear systems. To counteract the effects of the disturbances, a hybrid nonlinear disturbance observer (HNDOB) scheme is proposed to estimate the matched and mismatched disturbances. A novel proportional integral non-singular terminal synergetic control (PI-NTSC) is proposed for a class of affine nth-order systems. The stability of the PI-NTSC approach is proven using the Lyapunov stability theory. Its effectiveness and applicability is evaluated through simulations of a four-bar linkage mechanism and a servo-hydraulic system. The proposed HNDOB-based PI-NTSC is characterized by a finite time convergence rate, simple implementation, better disturbance rejection ability to both matched and mismatched uncertainties, and chattering free dynamics compared to conventional sliding mode control.

Optimal state estimation and fault diagnosis for a class of nonlinear systems

This study proposes a scheme for state estimation and, consequently, fault diagnosis in nonlinear systems. Initially, an optimal nonlinear observer is designed for nonlinear systems subject to an actuator or plant fault. By utilizing Lyapunov &#x02BC s direct method, the observer is proved to be optimal with respect to a performance function, including the magnitude of the observer gain and the convergence time. The observer gain is obtained by using approximation of Hamilton-Jacobi-Bellman &#x0028 HJB &#x0029 equation. The approximation is determined via an online trained neural network &#x0028 NN &#x0029 . Next a class of affine nonlinear systems is considered which is subject to unknown disturbances in addition to fault signals. In this case, for each fault the original system is transformed to a new form in which the proposed optimal observer can be applied for state estimation and fault detection and isolation &#x0028 FDI &#x0029 . Simulation results of a singlelink flexible joint robot &#x0028 SLFJR &#x0029 electric drive system show the effectiveness of the proposed methodology.

An Analysis of IRL-Based Optimal Tracking Control of Unknown Nonlinear Systems with Constrained Input

In this paper, a comparison is addressed between two methods, that is, the optimal tracking control methods of unknown nonlinear systems with and without constrained input. Firstly, the optimal tracking problem for a class of affine nonlinear system is formulated. The tracking cost functions are also defined, both for the two methods. The two methods are proved to be equivalent as the actuator bound is large enough. Integral reinforcement learning (IRL) algorithm is employed to solve the optimal tracking problem by using only system data. To facilitate the implementation of the IRL algorithm, the actor-critic neural network technique and the least squares method are employed in approximating the unknown weights iteratively. In the simulation, a detailed comparison is given to demonstrate the relationship between the two methods in the aspects of control input and tracking cost value.

Design of Modified Repetitive Controller for T–S Fuzzy Systems

A repetitive controller contains a pure-delay positive-feedback loop that makes it difficult to stabilize a strictly proper system. A low-pass filter is inserted in a repetitive controller to relax the stability condition of the modified repetitive-control system at the cost of degrading the tracking performance. In this study, a modified repetitive-control approach is developed, which reaches a balance between the stability and tracking performance for a class of affine nonlinear systems based on the Takagi–Sugeno fuzzy model. First, a 2D model is established to adjust continuous control and discrete learning actions preferentially induced by exploiting the 2D property in a repetitive-control process. Then, the Lyapunov stability theory and 2D system theory are used to derive a sufficient stability condition in the form of linear matrix inequalities to design parallel-distributed-compensation-based state-feedback controllers. Finally, an application-oriented example is used, and a comparison is performed to show that an extra variable is introduced such that the developed method has a better tracking performance.

Inverse optimal control of a class of affine nonlinear systems

This paper proposes a systematic formulation of inverse optimal control (IOC) law based on a rather straightforward reduction of control Lyapunov function (CLF), applicable to a class of second-order nonlinear systems affine in the input. This method exploits the additional design degrees of freedom resulting from the non-uniqueness of the state dependent coefficient (SDC) formulation, which is widely used in pseudo-linear control techniques. The applicability of the proposed approach necessitates an apparently effortless SDC formulation satisfying an SDC matrix criterion in terms of the structure and characteristics of the state matrix, [Formula: see text]. Subsequently, a sufficient condition for the global asymptotic stability (g.a.s) of the closed-loop system is established. The SDC formulations conforming to the sufficient condition ensure the existence and determination of a smooth radially unbounded polynomial CLF of the form [Formula: see text], while offering a benevolent choice for the gain matrix [Formula: see text], in the CLF. The direct relationship between the gain matrix [Formula: see text] and state weighing matrix [Formula: see text] ensures optimization of an equivalent [Formula: see text]. This feature enables one to rightfully choose the gain matrix [Formula: see text] as per the performance requisites of the system. Finally, the application of the proposed methodology for the speed control of a permanent magnet synchronous motor validates the efficacy and design flexibility of the methodology.

Design of robust <i>H</i><SUB align="right">∞ fuzzy output feedback controller for affine nonlinear systems: fuzzy Lyapunov function approach

In this paper, we propose a new systematic approach based on non-quadratic Lyapunov function and technique of introducing slack matrices, for a class of affine nonlinear systems with disturbance. To achieve the goal, first, the affine nonlinear system is represented via Takagi-Sugeno (T-S) fuzzy bilinear model. Subsequently, the robust H∞ controller is designed based on parallel distributed compensation (PDC) scheme. Then, the stability conditions are derived in terms of linear matrix inequalities (LMIs) by utilising Lyapunov function. Moreover, some slack matrices are proposed to reduce the conservativeness of the LMI stability conditions. Finally, for illustrating the merits and verifying the effectiveness of the proposed approach, the application of an isothermal continuous stirred tank reactor (CSTR) for Van de Vusse reactor is discussed in details.

Design of robust H_ fuzzy output feedback controller for affine nonlinear systems: Fuzzy Lyapunov function approach

In this paper, we propose a new systematic approach based on non-quadratic Lyapunov function and technique of introducing slack matrices, for a class of affine nonlinear systems with disturbance. To achieve the goal, first, the affine nonlinear system is represented via Takagi-Sugeno (T-S) fuzzy bilinear model. Subsequently, the robust H∞ controller is designed based on parallel distributed compensation (PDC) scheme. Then, the stability conditions are derived in terms of linear matrix inequalities (LMIs) by utilising Lyapunov function. Moreover, some slack matrices are proposed to reduce the conservativeness of the LMI stability conditions. Finally, for illustrating the merits and verifying the effectiveness of the proposed approach, the application of an isothermal continuous stirred tank reactor (CSTR) for Van de Vusse reactor is discussed in details.

Convergence of iterative learning control for SISO nonrepetitive systems subject to iteration-dependent uncertainties

This paper studies the robust convergence properties of iterative learning control (ILC) for single-input, single-output (SISO), nonrepetitive systems subject to iteration-dependent uncertainties that arise in not only initial states and external disturbances but also plant models. Given an extended relative degree condition, it is possible to propose necessary and sufficient (NAS) conditions for robust ILC convergence. The tracking error bound is shown to depend continuously on the bounds of the iteration-dependent uncertainties. When the iteration-dependent uncertainties are bounded, NAS conditions exist to guarantee bounded system trajectories and output tracking error. If the iteration-dependent uncertainties converge, then NAS conditions ensure bounded system trajectories and zero output tracking error. The results are also extended to a class of affine nonlinear systems satisfying a Lipschitz condition. Simulation tests on a representative batch process demonstrate the validity of the obtained robust ILC convergence results.

Composite Learning Fuzzy Control of Uncertain Nonlinear Systems

Function approximation accuracy and computational cost are two major concerns in approximation-based adaptive fuzzy control. In this paper, a model reference composite learning fuzzy control strategy is proposed for a class of affine nonlinear systems with functional uncertainties. In the proposed approach, a modified modeling error that utilizes data recorded online is defined as a prediction error, a linear filter is applied to estimate time derivatives of plant states, and both the tracking error and the prediction error are exploited to update parametric estimates. It is proven that the closed-loop system achieves semiglobal practical exponential stability by an interval-excitation condition which is much weaker than a persistent-excitation condition. Compared with a concurrent learning approach that has the same aim as this study, the computational cost of the proposed approach is significantly reduced for the guarantee of accurate function approximation. An illustrative example of aircraft wing rock control has been provided to verify effectiveness of the proposed control strategy.

Online fault compensation control based on policy iteration algorithm for a class of affine non‐linear systems with actuator failures

In this study, a novel online fault compensation control scheme based on policy iteration (PI) algorithm is developed for a class of affine non-linear systems with actuator failures. The control scheme consists of a PI algorithm and a fault compensator. For fault-free dynamic models, the PI algorithm is developed to solve the Hamilton–Jacobi–Bellman equation by constructing a critic neural network, and then the approximate optimal control policy can be derived directly. Alternatively, the actuator failure is reconstructed adaptively to achieve online fault compensation without the fault detection and isolation mechanism. The closed-loop system is proved to be asymptotically stable via Lyapunov's direct method. Two numerical simulation examples are given to demonstrate the effectiveness of the proposed fault compensation control scheme.

Fault reconstruction in a class of nonlinear systems using inversion-based filter

The article presents an approach for fault reconstruction in nonlinear systems. In addition to straightforward detection, fault reconstruction is also highly beneficial in directly isolating the faults by revealing which component is faulty. Initially an inversion-based fault reconstruction filter is introduced for nonlinear systems subject to an actuator or plant fault. If the system has fixed relative order with respect to the fault signal, the filter will reproduce the fault at its output. Then, a class of affine nonlinear systems is considered which is subject to unknown disturbances in addition to fault signals. In this case, for each fault the original system is transformed to a new form in which the proposed inversion-based filter can be applied for fault reconstruction. The transformation is done via a novel formulation on the observability concept in differential geometry. Reproducing the fault in the presence of unknown disturbances is main advantage of the proposed approach. To illustrate the effectiveness of the proposed methodology, simulation results are provided.