Design Of Nonlinear Systems Research Articles

Removing the Feasibility Conditions Imposed on Full-State Constraint Control Design for Discrete-Time Nonlinear Systems

Removing the Feasibility Conditions Imposed on Full-State Constraint Control Design for Discrete-Time Nonlinear Systems

Domain estimation and coupled controller design for high-dimensional nonlinear multi-agent systems

This paper investigates the consensus problem of a class of high-dimensional nonlinear multi-agent systems. The agents are homogeneous and have coupled interactions with their nearby agents. Firstly, we study the consensus of this class of nonlinear multi-agent systems and present some consensus conditions based on the linearization technique. By transforming the consensus problem into a stability problem, we show that there exists a domain such that if all pairs of connected agents stay in the domain, the system will achieve consensus under the consensus conditions. Then, we propose a method to estimate the consensus domain since the accurate description of the domain is still challenging. Moreover, a method of coupled controller design is presented to make the multi-agent systems achieve consensus. At last, two numerical examples and a practical example are used to show the effectiveness of the results proposed in this paper.

Output feedback command filtered fuzzy controller design for uncertain strict-feedback nonlinear systems with unmodeled dynamics and event-triggered strategy

An adaptive control problem is considered for a class of nth-order uncertain nonlinear systems with unmodeled dynamics. Compared with the traditional backstepping method, this article improves the systems performance by introducing command filtered and event-triggered. The former primarily enhances the flexibility of controller design, while the latter employs a variable threshold triggering mechanism to achieve savings in communication resources. Simultaneously, the estimation error is compensated by the introduced hyperbolic tangent function. In addition, fuzzy logic system (FLS) is primarily used for observer design and approximation of unknown functions. The conclusion that the closed-loop signals are bounded is obtained through stability analysis. Finally, the numerical simulation results provide a comparative validation of the effectiveness of the proposed control scheme.

A new approach for dynamic output feedback control design of time-delayed nonlinear systems

This paper introduces a full-order dynamic output-feedback (DOF) controller for discrete-time nonlinear systems with time-varying delays represented by Linear Parameter-Varying (LPV) systems. The controller design is carried out by developing delay-dependent Linear Matrix Inequality based conditions using Lyapunov–Krasovskii stability arguments. A notable characteristic of the proposed approach is that the dynamic controller gains are directly obtained, without the need for variable transformations, equality constraints, or iterative algorithms. This feature sets it apart from many existing approaches in the literature and simplifies the design process. Furthermore, the proposed approach guarantees the local asymptotic stability of the origin of the closed-loop system and provides an estimated admissible initial condition region. The correct operation of the system is ensured once the state trajectories initiated within the admissible initial condition region remain enclosed in the validity domain of the LPV model. Numerical examples are provided to illustrate the potential and effectiveness of the proposed conditions.

Adaptive Prescribed-Time SOSM Controller Design for Nonlinear Systems With Prescribed Performance

Adaptive Prescribed-Time SOSM Controller Design for Nonlinear Systems With Prescribed Performance

Observer Design for Nonlinear Descriptor Systems: A Survey on System Nonlinearities

In general, the construction of observers for nonlinear descriptor systems depends on the solvability of a linear matrix inequality involving system matrices, and it is based on the system’s nonlinearity. Therefore, the type of nonlinearity present in the system heavily affects the observer design process. There are significant developments in the literature for observer design for descriptor systems with various types of nonlinearity. Motivated by this, the current work reviews the literature on observer design for nonlinear descriptor systems with an extensive discussion on the type of nonlinearities that are considered. Here, an analysis and the comparison on the most common nonlinearities is presented, providing a roadmap to all researchers in the field. Furthermore, less common nonlinearities have been identified, presenting under-explored areas within the literature, and can open new domains for future research.

Command filter-based adaptive neural tracking control of nonlinear systems with multiple actuator constraints and disturbances

In this paper, the adaptive practical finite-time tracking control problem for a class of strictly feedback nonlinear systems with multiple actuator constraints is investigated using backstepping techniques and practical finite-time stability theory. The effects of deadband and saturated nonlinear constraints on the controller design of nonlinear systems are addressed by the equivalent transformation method. The problem of complexity explosion due to the derivatives of virtual control signals is solved by using the virtual control signals as inputs to the command filters and using the outputs of the command filters to perform the corresponding control tasks. An adaptive neural network tracking backstepping control strategy based on the command filter technique and the backstepping design algorithm is proposed by approximating an unknown nonlinear function using a neural network. The control strategy ensures the boundedness of all variables in the closed-loop system, and the output tracking error fluctuates in a small region near the origin. Finally, simulations verify the effectiveness of the control strategy designed in this paper.

A linear matrix inequality approach to optimal reset control design for a class of nonlinear systems

AbstractIn this article, the problem of the optimal reset control design for Lipschitz nonlinear systems is addressed. The reset controller includes a base linear controller and a reset law that enforces resets to the controller states. The reset law design is strongly dependent on the appropriate design of the base controller. For this reason, in this article, the base controller and reset law are simultaneously designed. More precisely, an optimal dynamic output feedback is considered as the base controller which minimizes the upper bound of a quadratic performance index, and a reset law is used to improve the transient response of the closed‐loop system. This design is done in a full offline procedure. The problem is transformed into a set of linear matrix inequalities (LMIs), and the reset controller is obtained by solving an offline LMI optimization problem. Finally, two examples are presented to illustrate the effectiveness and validity of the proposed method.

Secure memory adaptive event‐triggered filter design of nonlinear network system under hybrid network attacks with application to tunnel diode circuit

AbstractThis article investigates the problem of secure memory adaptive event‐triggered filter design for nonlinear network systems under hybrid network attacks. First, the introduction of memory adaptive event‐triggered mechanism and numerical quantization is employed to enhance system performance, optimize network channel utilization, and prevent network congestion. Second, we consider the impact of deceptive attacks and DoS attacks occurring in the network channel on data transmission, which form the hybrid network attacks studied in this article. Subsequently, based on the established error model, we derive sufficient conditions for the mean‐square exponential stability of the system under a given performance index using Lyapunov–Krasovskii function and linear matrix inequality (LMI) techniques. Furthermore, the filter parameters are determined using the LMI method. Finally, we illustrate the feasibility and generality of the conclusions through numerical simulation examples and a tunnel diode circuit system.

Adaptive predefined time neural filtered control design for an uncertain nonlinear system and application to flight control

The paper studies the control problem of an uncertain nonlinear system with tracking error constraint, unknown nonlinear functions and unknown control input gains. An asymmetric barrier Lyapunov function composed with predefined time prescribed performance function is constructed to ensure tracking error enters into the predefined asymmetric constraint in a given time. Then radial basis function neural network is adopted to approximate unknown functions. To reduce computation load, minimal-learning parameter technique is applied. Meanwhile, adaptive method is used to solve actuator faults and the unknown control input gains. Moreover, an adaptive neural control strategy is designed in the framework of backstepping method. An adaptive fixed time filter is developed for avoiding the “explosion of complexity” problem, where the convergence speed of the filter error is improved compared with fixed time filter. It is proved that all signals of the closed-loop system are bounded and tracking error is kept in its constraint boundary. At the end, compared numerical simulations and application simulation of a hypersonic vehicle are demonstrated to verify the efficiency of the designed control scheme.

Disorder-resistant fusion estimator design for nonlinear stochastic systems in the presence of measurement quantization

In this paper, we thoroughly study a new nonlinear disorder-resistant fusion estimation problem under both packet disorder and measurement quantization. Packet disorder, which occurs due mainly to random transmission delays (RTDs), are characterized via a series of integer-valued functions and random variables obeying certain distributions. Sensor measurements are logarithmically quantized before entering designated communication networks. The upper bounds on the filtering error covariances are acquired and later minimized by appropriately designing gain parameters of both local and fusion estimators. For fusion estimation, all local estimates and filtering covariances are integrated at a fusion center through the well-known federated criterion. Moreover, the fusion performance is examined by means of assessing the resistance of the designed estimator against the RTD-induced disorder. Simulation examples are presented to illustrate the applicability of the proposed disorder-resistant fusion estimator.

Fixed-Time Observer-Based Output Feedback Control for Nonlinear Systems With Full-State Constraints

This brief investigates the problem of fixed-time state observer-based output feedback control design for nonlinear systems with full-state constraints. First, a fixed-time state observer is constructed to estimate the unknown states, which can accurately estimate the system states within a fixed settling time. Then, by combining the integral barrier Lyapunov function with the backstepping method, the full-state constraints are realized after the fixed time. Meanwhile, the proposed control strategy can directly constrain the states rather than impose constraints on errors, which reduces the conservativeness of the constraint satisfaction condition. The proposed control method ensures that all signals in the closed-loop system are bounded and symmetric state constraints are strictly maintained after the fixed settling time. Finally, simulation results prove the effectiveness of the proposed method.

Game-Based Backstepping Design for Strict-Feedback Nonlinear Multi-Agent Systems Based on Reinforcement Learning.

In this article, the game-based backstepping control method is proposed for the high-order nonlinear multi-agent system with unknown dynamic and input saturation. Reinforcement learning (RL) is employed to get the saddle point solution of the tracking game between each agent and the reference signal for achieving robust control. Specifically, the approximate optimal solution of the established Hamilton-Jacobi-Isaacs (HJI) equation is obtained by policy iteration for each subsystem, and the single network adaptive critic (SNAC) architecture is used to reduce the computational burden. In addition, based on the separation operation of the error term from the derivative of the value function, we achieve the different proportions of the two agents in the game to realize the regulation of the final equilibrium point. Different from the general use of the neural network for system identification, the unknown nonlinear dynamic term is approximated based on the state difference obtained by the command filter. Furthermore, a sufficient condition is established to guarantee that the whole system and each subsystem included are uniformly ultimately bounded. Finally, simulation results are given to show the effectiveness of the proposed method.

Prescribed-Time Observer Design for Nonlinear Triangular Systems With Delayed Measurements

Prescribed-Time Observer Design for Nonlinear Triangular Systems With Delayed Measurements

A New Event-Triggered Adaptive Fixed-Time Control Design for Uncertain Nonlinear Systems.

This article investigates the problem of dynamic memory event-triggered (DMET) fixed-time tracking control within time-varying asymmetric constraints for nonaffine nonstrict-feedback uncertain nonlinear systems with unmodeled dynamics and unknown disturbances. The existing dynamic event-triggered control methods cannot handle the nonlinear systems with unmodeled dynamics and nonaffine inputs, which greatly limits the applicability of the strategy. To this end, a novel DMET adaptive fuzzy fixed-time control protocol is constructed based on the idea of command filtered backstepping, in which a new dynamic signal function is established to deal with the unmodeled dynamics and an improved DMET mechanism (DMETM) is designed to solve the problem of nonaffine inputs. It is proved that the newly DMET control strategy ensures the tracking error converges to an arbitrarily small compact set in a fixed time and all the signals of the closed-loop systems are bounded. The effectiveness of the proposed approach is demonstrated by two simulation examples.

Practice-oriented controller design of a simple nonlinear system

The paper analyses and illustrates the design of a constrained gain scheduling for a simple non-linear hydraulic system based on automatic-reset controller. The main objective is to explain the basics of gain-scheduling control in a simple way so that it can be understood by computer programmers working in the field of automatic control. The study is based on small deviations from the selected operating points that allow the use of linear design methods. In contrast to linearization-based design methods, where the control action is calculated by integrating small control increments, the new control output is obtained by adding the calculated small increments to the operating point values. Another innovative aspect is the introduction of a gain-scheduled automatic-reset controller. This is the oldest and the simplest control solution including a disturbance observer based on ultra-local models and accurate even in steady-states.

Event-Driven Reduced-Order Fault Detection Filter Design for Nonlinear Systems With Complex Communication Channel

Event-Driven Reduced-Order Fault Detection Filter Design for Nonlinear Systems With Complex Communication Channel

Nested extended state observer design for uncertain nonlinear systems under time‐varying disturbance

AbstractWith rising demands on system performance and reliability in engineering practice, researchers are increasingly interested in disturbance rejection control, of which state and disturbance observation is the essential element. The extended state observer (ESO, or extended high‐gain observer) is extensively utilized to compensate disturbance, nevertheless, the neglect of lumped disturbance's first derivative and peak phenomenon in classical ESO design impose obstacles to further promotion. In this article, nested ESO (NestedESO) is proposed to estimate states and disturbance simultaneously for general uncertain nonlinear systems under time‐varying disturbance. In NestedESO framework, low‐gain generalized ESO is implemented to obtain a rough estimation of lumped disturbance in the first stage. Then, a novel proportion‐filter‐derivative disturbance estimation refinement mechanism is introduced to provide accurate disturbance estimation. With refined disturbance estimation, modified Luenburger observer is put forward to reconstruct state. Besides, extension to sampled‐data systems is investigated to adapt the networked signal transmission scenario. Numerical examples are given to illustrate the validity and effectiveness of the proposed method.

Output feedback and adaptive output feedback control design for input-affine nonlinear systems based on Riemannian metrics

This paper deals with output feedback and adaptive output feedback control design for input-affine nonlinear systems on the basis of Riemannian metrics. Firstly, an observer for the considered class of nonlinear systems is proposed. Then, it is shown that by combining the introduced observer with state-feedback controllers in a suitable way, output tracking can be achieved. Moreover, the obtained results are extended to be used for adaptive output feedback stabilization of uncertain nonlinear systems. The introduced adaptive controller is more general than the existing adaptive output feedback ones because it does not assume any constraint on the structure of the system and the parametric uncertainty. Simulation results are presented to verify the effectiveness of the proposed control methods.

Improved prescribed performance fuzzy control for nonlinear multiagent systems with actuator faults and dual input saturations

This paper conducts the distributed adaptive prescribed performance fuzzy control design for nonlinear multiagent systems (MASs) subjected to actuator faults and dual input saturations. A unified smooth characterizing function is constructed to approximate a practical input saturations model. Then, with the aid of the mean-value theorem, Nussbaum-type function and boundary estimation method, the distributed saturated fault-tolerant controllers are devised to deal with actuator faults and dual input saturations. In order to achieve excellent tracking performance of followers, an improved prescribed performance control method with a tight constraint region is proposed. Different from most existing control methods, the proposed method not only ensures that the tracking error rapidly converges to the specified area within a predetermined time, but also achieves transient performance without obvious overshoot. Stability analysis proves that the consensus tracking error converges to an arbitrary small specified area within a preset time and all signals of the overall controlled systems are semi-globally uniformly ultimately bounded (SUUB). Eventually, the comprehensive simulation results validate the feasibility and superiority of the control strategy.