Design Of Nonlinear Systems Research Articles

Safe Control Design for Unknown Nonlinear Systems with Koopman-based Fixed-Time Identification

We consider the problem of safe control design for a class of nonlinear, control-affine systems subject to an unknown, additive, nonlinear disturbance. Leveraging recent advancements in the application of Koopman operator theory to the field of system identification and control, we introduce a novel fixed-time identification scheme for the infinitesimal generator of the infinite-dimensional, but notably linear, Koopman dynamical system analogous to the nonlinear system of interest. That is, we derive a parameter adaptation law that allows us to recover the unknown, residual nonlinear dynamics in the system within a finite-time, independent of an initial estimate. We then use properties of fixed-time stability to derive an estimation error bound on the unknown dynamics as an explicit function of time, which allows us to synthesize a safe controller using control barrier function based methods. We conduct a quadrotor-inspired case study in support of our proposed method, in which we show that safe trajectory tracking is achieved despite unknown, nonlinear dynamics.

Domain-aware Control-oriented Neural Models for Autonomous Underwater Vehicles

Conventional physics-based modeling is a time-consuming bottleneck in control design for complex nonlinear systems like autonomous underwater vehicles (AUVs). In contrast, purely data-driven models require a large number of observations and lack operational guarantees for safety-critical systems. Data-driven models leveraging available partially characterized dynamics have potential to provide reliable systems models in a typical data-limited scenario for high value complex systems, thereby avoiding months of expensive expert modeling time. In this work we explore this middle-ground between expert-modeled and pure data-driven modeling. We present control-oriented parametric models with varying levels of domain-awareness that exploit known system structure and prior physics knowledge to create constrained deep neural dynamical system models. We employ universal differential equations to construct data-driven blackbox and graybox representations of the AUV dynamics. In addition, we explore a hybrid formulation that explicitly models the residual error related to imperfect graybox models. We compare the prediction performance of the learned models for different distributions of initial conditions and control inputs to assess their suitability for control.

Vibration control design for nonlinear MIMO wing-plate systems based on operator theory

Vibration control design for nonlinear MIMO wing-plate systems based on operator theory

Vibration control design for nonlinear MIMO wing-plate systems based on operator theory

Vibration control design for nonlinear MIMO wing-plate systems based on operator theory

Consensus of Nonlinear Multiagent Systems With Uncertainties Using Reinforcement Learning Based Sliding Mode Control

This paper investigates distributed control protocols design for uncertain nonlinear multi-agent systems with the goal of achieving the optimal consensus. The critical challenges encountered when designing the optimal distributed control protocols are mainly caused by the internal coupling of agents, uncertainty and nonlinear dynamics. Communication delay among agents makes overcoming these challenges even more difficult. To this end, a novel sliding mode control design method is developed based on the sliding mode control principle and the reinforcement learning technique. The remarkable highlights of the developed method in this paper include the design of distributed sliding mode controllers and the integrated framework of sliding mode control and reinforcement learning, which bring the outcome of successfully learning the composite distributed control protocols for multi-agent systems. Thus, all agents can successfully eliminate the negative impacts brought by system uncertainties and communication delay among agents, and finally follow the leader with a nearly optimal approach. The reachability of sliding mode surfaces and the optimal consensus are rigorously proven and analyzed. Finally, simulation results illustrate the effectiveness of the developed method.

On asymptotic fixed-time controller design for uncertain nonlinear systems with pure state constraints

<abstract><p>This study investigates the problem of asymptotic fixed-time tracking control (AFXTTC) for uncertain nonlinear systems (UNS) subject to pure state constraints. To study this problem, we define asymptotic fixed-time stability (AFXTS) and thus a criterion for determining AFXTS. Dynamic surface control (DSC) is combined with fuzzy logic systems (FLSs) to construct a new adaptive fuzzy asymptotic fixed-time controller. A barrier Lyapunov function (BLF) is introduced to ensure that constraints on all states are satisfied. The proposed criterion is used to analyze the AFXTS of the system, and the effectiveness and superiority of the theoretical analysis results are verified through simulations.</p></abstract>

A High-Gain Observer Design for Nonlinear System with Delayed Measurements: Application to a Quadrotor UAV

The paper deals with the design of a high-gain observer for nonlinear system with delayed output measurements and bounded disturbances. The new structure of the proposed observer exhibits good performance in terms of allowing a higher MAVTD (Maximum Allowable Value of the Time-Delay) compared to the existing works, where the MAVTD is limited due to the high value of the high-gain parameter. Based on the LMI technique and using Lyapunov-Krasovskii function, an explicit relation between MAVTD and the LMI tuning parameters is deduced from the stability analysis of the proposed observer. The efficiency of the proposed structure is illustrated through an application to a Quadrotor UAV and a comparison with standard and cascade high-gain observers is performed.

Gaussian inference for data-driven state-feedback design of nonlinear systems

Data-driven control of nonlinear systems with rigorous guarantees is a challenging problem as it usually calls for nonconvex optimization and often requires the knowledge of the true basis functions of the unknown system dynamics. To tackle these drawbacks, this work is based on a data-driven polynomial representation of general nonlinear systems exploiting Taylor polynomials. Thereby, we design state-feedback laws that render a known equilibrium globally asymptotically stable while operating with respect to a desired quadratic performance criterion. The calculation of the polynomial state feedback boils down to a sum-of-squares optimization problem, and hence to computationally tractable linear matrix inequalities. Moreover, we examine state-input data in presence of Gaussian noise by Bayesian inference to overcome the conservatism of deterministic noise characterizations from recent data-driven control approaches for Gaussian noise.

LMI-Based H∞ Observer Design for Nonlinear Lipschitz System

The problem of circle criterion-based H∞ observer design for nonlinear systems is addressed in this article. An LMI-based observer is developed for the nonlinear Lipschitz systems with linear outputs under the presence of noise/disturbances. The proposed LMI condition is obtained by using reformulated Lipschitz property, standard Young's relation and a newly defined positive definite matrix multiplier. The inclusion of the matrix multiplier adds additional numbers of decision variables in the LMI, which provides extra degrees of freedom from a feasibility point of view. Further, the performance of the proposed observer is validated using numerical examples.

Data-based control design for nonlinear systems with recurrent neural network-based controllers

This paper addresses the design of controllers for systems modelled as recurrent neural networks (RNNs). A novel data-based procedure for the design of RNN-based regulators is proposed, guaranteeing closed-loop stability properties and desired performances, conferred by virtual reference feedback tuning. The approach is tested on a realistic nonlinear system.

Adaptive observer for a nonlinear system with partially unknown state matrix and delayed measurements

Problem of an adaptive state observer design for nonlinear system with unknown time-varying parameters and under condition of delayed measurements is considered. State observation problem was raised by many researchers (see for example Sanx et al. (2019)). In this paper the results proposed in Bobtsov et al. (2021b), Bobtsov et al. (2021a), Bobtsov et al. (2022a), Bobtsov et al. (2022b) are developed. The problem is solved under assumption that the state matrix can be represented as sum of known and unknown parts. The output vector is measured with a known constant delay. An adaptive observer which reconstructs unmeasured state and unknown time-varying parameter is proposed.

Global adaptive event-triggered output feedback controller design for high-order nonlinear systems

This article focuses on the adaptive event-triggered output feedback stabilization problem for a class of high-order systems with uncertain output function. Firstly, an adaptive event-triggered mechanism with a dynamic gain is designed for the nominal system. Then the gain is employed into the observer and event-triggered controller to dominate the nonlinearities. Thirdly, it is proved that all system states converge to zero and the Zeno-behavior is excluded. Finally, a numerical example reveals the effectiveness of the proposed event-triggered control strategy.

Output feedback neural adaptive control design for nonlinear time-delay systems

This paper addresses the adaptive output feedback control design problem for a class of nonlinear systems with unknown state time delays by combining the dynamic gain and neural network. A novel reduced-order dynamic gain observer is introduced to estimate the unmeasured system states. Radial basis function neural networks (RBF NNs) are used to approximate unknown functions. An adaptive NN output feedback controller is designed based on the backstepping technique. By arranging the proper Lyapunov–Krasovskii functional, we prove that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. Finally, a physical example and a numerical example are given to prove the effectiveness of the proposed control scheme.

Dissipative state observer design for nonlinear time-delay systems

This paper is concerned with the design of dissipative state observers for a family of time-delay nonlinear systems. The Dissipativity method, proposed by one of the authors for delay-free nonlinear systems, is extended here to a class of time-delay nonlinear systems. The design method consists in decomposing the time-delay estimation error dynamics into a time-delay linear subsystem and a time-varying memoryless nonlinearity, connected in a negative feedback loop. By using some storage functionals, both delay-independent and delay-dependent dissipativity criteria are derived in order to guarantee the exponential convergence property of the observer. The exponential stability of the estimation error is then ensured, assuming that the nonlinearity is dissipative with respect to a quadratic supply rate and the linear part is designed, through the observer gains, to be dissipative with respect to a complementary supply rate. The design conditions are formulated in terms of tractable bilinear (BMI’s) or linear matrix inequalities (LMI’s). An interesting advantage is that the proposed dissipative design extends and generalizes under a unified framework several methods available in the literature, since a wide diversity of nonlinearities can be considered. Numerical examples are provided to demonstrate the effectiveness of the theoretical results.

Virtual Sensor Design for Linear and Nonlinear Dynamic Systems

Abstract: The problem of virtual sensors design in linear and nonlinear systems is studied. The problems is solved in three steps: at the first step, the linear model invariant with respect to the disturbance is designed; at the second step, a possibility to take into account the nonlinear term and to estimate the given variable is checked; finally, stability of the observer is achieved. The relations allowing to design virtual sensor of minimal dimension estimating prescribed component of the state vector of the system are obtained. The theoretical results are illustrated by practical example.

Adaptive delay dependent sliding mode fault-tolerant controller design for nonlinear systems with unknown time-varying input and state delays

This paper presents a novel adaptive delay-dependent fault-tolerant sliding mode control (SMC) strategy for the class of nonlinear Lipschitz systems with time-varying unknown delays in system states and inputs. A modified integral sliding surface (ISS) based on which the SMC approach is developed using a linear matrix inequality. Lyapunov-Krasovskii stability theory is employed to guarantee asymptotic stability of the closed-loop system such that system states starting from any arbitrary initial conditions with time-varying delays reach the predefined sliding surface in a finite time. It is also proved that states stay on the surface for all subsequent time, and the effects of the actuator’s faults are simultaneously attenuated. Adaptive tuning laws are used to adjust controller parameters and estimate actuators’ faults. The controllers’ structures are more straightforward than the most existing recent fault-tolerant control methods. Simulation results of practical nonlinear inverted pendulum system verified the outstanding merits and capabilities of the proposed scheme in the presence of actuators’ faults and multiple delays in the system states and inputs.

Novel command-filtered Nussbaum design for continuous-time nonlinear dynamical systems with multiple unknown high-frequency gains

Novel command-filtered Nussbaum design for continuous-time nonlinear dynamical systems with multiple unknown high-frequency gains

Design assessments of complex systems based on design oriented modelling and uncertainty analysis

In the design of nonlinear complex systems, the output responses of a complex system subject to demanding loading conditions need to be assessed before the system can be used in practice. Current assessment approaches (including physical model based analysis, Finite Element (FE) simulation and similitude experiments) are often time-consuming and problematic. The objective of this study is to develop a novel data-driven approach to predict the output responses, as well as their uncertainties, of a complex system for the aim of design assessment. The results can be used to decide whether redesign of the complex system is required to avoid damage for actual use. To achieve this goal, a novel design-oriented data driven modelling approach has been developed based on the FROLS (Forward Regression Orthogonal Least Squares) algorithm and K-fold cross validation. In this approach, the NARX (Nonlinear AutoRegressive with eXogenous input) model of the system is identified and validated. After that, the Monte Carlo Simulation (MCS) method is applied to quantify the uncertainties of the NARX model coefficients. Subject to specified inputs, the model coefficients’ uncertainties are propagated to the model predicted output responses for design assessments. Finally, the proposed approach is verified by a case study on the design assessment of a Chinese Space Station Scientific Experiment Rack (CSS-SER). The results indicate the efficiency of the proposed approach and its potential to be applied to solve many engineering design problems.

Fuzzy Control of Nonlinear Strict-Feedback Systems With Full-State Constraints: A New Barrier Function Approach

This article is concerned with adaptive fuzzy control design of nonlinear strict-feedback systems, in which system functions are unknown and system states are subjected to some constant constraints. The main control issue is to design an adaptive fuzzy controller such that the system output follows the reference signal, meanwhile, all the state variables abide by their constrained requirements. Differing from the existing way to build barrier function, the constructed virtual control signal is employed to build the barrier function. Furthermore, a backstepping-based adaptive fuzzy control design process is presented in this article. Compared to the control schemes in the existing literature on full-state constrained systems, the current control scheme has the following advantages: 1) the built virtual control signals in this article are ensured to satisfy corresponding state constraints, rather than assuming that they do, as in the existing articles; 2) the choice of initial values is independent of the norm of the virtual control signal. So, the conservatism of initial value selection is considerably reduced. It is shown that the proposed adaptive fuzzy controller not only ensures perfect tracking performance, but also ensures that all the states abide by the preassigned state constraints during the operation. At last, simulation study further verifies the efficacy of the proposed control strategy.

Command filter‐based adaptive neural network controller design for uncertain nonsmooth nonlinear systems with output constraint

SummaryThis paper investigates the command filter‐based adaptive neural network tracking control problem for uncertain nonsmooth nonlinear systems. First, an integral barrier Lyapunov function is introduced to deal with the symmetric output constraint and make the output comply with prescribed restrictions. Second, by the Filippov's differential inclusion theory and approximation theorem, the considered nonsmooth nonlinear system is converted to an equivalent smooth nonlinear system. Third, the Levant's differentiator is used to deal with the “explosion of complexity” problem. An error compensation mechanism is established to attenuate the effect of the filtering error on control performance. Then, an adaptive neural network controller is set up by resorting to the backstepping technique. It is strictly mathematically proved that the tracking error can converge to an arbitrarily small neighborhood of the origin and all the signals in the closed‐loop system are semi‐globally uniformly ultimately bounded. Finally, a numerical example and an application example of the robotic manipulator system are provided to demonstrate the availability of the proposed control strategy.