Addressing asymptotic stability of tracking control in nonlinear systems subjected to embedded unscented Kalman filter dynamics under actuator saturation

Learning‐based robust control methodologies under information constraints

Emerging approaches for nonlinear parameter varying systems

Tracking control and dynamic regulation of time-varying delay nonlinear systems with actuator saturation via multi-dimensional Taylor networks

This paper investigates the issue of event-triggered adaptive saturated fault-tolerant control (ESFC) for uncertain nonlinear systems with time-varying full state constraints (TFSCs), actuator saturation and faults as well as unknown control direction. A bounded function with an auxiliary variable is constructed by utilizing a novel dynamics of the auxiliary system, which contributes to reducing the adverse impact of actuator saturation. Different from the previous backstepping-based event-triggered control methods such specifications by either using fuzzy approximation or by employing neural approximation techniques, this paper skillfully addresses the unknown nonlinearities, actuator saturation and faults without involving any approximation structures, and thus, we proposes the ESFC on the basis of low-complexity design framework as contributing to communication and computational resource reduction. A rigorous theoretical analysis shows that the proposed control method is an effective way to handle with the problems of actuator saturation and faults, full state constraints, and unknown system uncertainties, while simultaneously simplifying the backstepping design and avoiding the issue of explosion of complexity. The asymptotic stability of the closed-loop system is guaranteed and the Zeno behavior can be effectively removed. We present an application example of a linear motor scenario to illustrate the effectiveness of the method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Since state constraints, actuator saturation and faults, unknown mechanism model, and limited bandwidths exist extensively in practical engineering systems, which constantly degrade the operation performance of the plant. To handle these disadvantages, this paper is focus on providing simple but effective ESFC methods to ensure the asymptotic stability and enhance reliability. Compared to existing results, the presented method only uses the state signals of system without using system dynamic functions under mild conditions, which provides a theoretical basis, and has the advantages of low-complexity design, and easy implementation in practical engineering. Preliminary physical experimental comparisons demonstrate that this method is applicable to practical liner-motor platform, and achieves satisfactory control performance.

Combining hybrid metaheuristic algorithms and reinforcement learning to improve the optimal control of nonlinear continuous-time systems with input constraints

Active estimation is becoming a more important issue in control theory and its application, especially in the nonlinear control of uncertain systems, such as robots and unmanned vehicles where time-varying parameters and uncertainties exist extensively in the dynamics and working environment. Among the available techniques for active modeling, Neural Networks (NN) and NN-based self learning have been proposed as one of the most effective approaches in 1990s (Pesonen et al., 2004). However the problems involved in NN, such as training data selection, online guaranteed convergence, robustness, reliability and real-time implementation, still remain open and limit its application in real systems, especially those requiring high reliable control. Most recently, the encouraging achievements in sequential estimation makes it becoming an important direction for online modeling and model-reference control (Napolitano, et al., 2000). Among stochastic estimations, the most popular one for nonlinear system is the Extended Kalman Filter (EKF). Although widely used, EKF suffers from the deficiencies including the requirement of sufficient differentiability of the state dynamics, the susceptibility to bias and divergence during the estimation. Unscented Kalman Filter (UKF) (Julier et al., 1995; Wan & Van der Merwe, 2000) provides a derivative-free way to the state parameter estimation of nonlinear systems by introducing the so called ‘unscented transformation’, while achieving the second-order accuracy (the accuracy of EKF is first order) with the same computational complexity as that of EKF. Although the nonlinear state dynamics are used without linearization and the calculations on Jacobians or Hessians are not involved, UKF still falls into the framework of Kalman-type filters, which can only achieve good performance under a priori assumptions (Jazwinski, 1970), which includes: 1) accurate reference models, 2) complete information of the noise distribution, and 3) proper initial conditions. However, such a priori knowledge is often not accurate, or even not available in practice. The normal UKF will suffer from performance degradation or even instability due to the mismatch between the a priori assumptions and the real ones within the system to be controlled. One of the approaches solving this problem is to introduce adaptive mechanism into a normal filter, i.e., the adaptive law automatically tunes the filter parameters to match the O pe n A cc es s D at ab as e w w w .in te ch w eb .o rg

Sliding Mode Control

Special issue on PID control in the information age: Theoretical advances and applications

The problem of designing nonlinear control systems by the algebraic polynomial-matrix method using quasilinear models is considered. The quasilinear models of nonlinear plants are easily created on the basis of their nonlinear equations in the Cauchy form. To create these models only the differentiability of the plants nonlinearities is required. The solution to the design problem of the nonlinear Hurwitz control systems using the algebraic polynomial-matrix method is available if the quasilinear model of the plant is controllable. The design with application of this method consists of creating the quasilinear model of the nonlinear plant, generating several polynomials, composing and solving a system of linear algebraic equations. The theorem about the global stability of the equilibrium of the nonlinear systems, represented in the quasilinear model, is proved by the method of Lyapunov functions. The numerical examples of the design of nonlinear Hurwitz control systems are given. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article is concerned with the creation of stable nonlinear control systems with nonlinear elements since the linear systems can’t fulfill the quality requirements demanded from modern control systems. Additionally, the known design methods of nonlinear systems, such as the input-state feedback linearization, backstepping, passivity and others, require the transformation of the original nonlinear equations of the plant into some special form. These transformations are often very difficult to find and to execute. A new algebraic polynomial-matrix design method of the nonlinear control systems using the quasilinear models of nonlinear plants is proposed in the article. This method can be applied if the nonlinearities of the plant are differentiable, and the quasilinear model of the plant is controllable. The theorem about global stability of the equilibrium is proved for the systems designed with this approach. The quasilinear models are easily created on the basis of the original equations in the Cauchy form for a given nonlinear plant. The algebraic polynomial-matrix design method is very simple: the quasilinear model is created; several polynomials are calculated with the use of this model and the linear algebraic equations system is composed. The solution of this system allows us to write down the expression which defines the control law as a nonlinear function of the plant’s state variables. This system will be globally or locally stable if the conditions of the theorem or the corollaries, proved in this article, are satisfied. The numerical examples illustrate the application of the suggested approach to the design of nonlinear Hurwitz control systems for the nonlinear plants. The main advantages of this approach: the quasilinear models are created quite easily; the nonlinear control law is found as a solution to the system of linear equations. The results can be applied to the creation of nonlinear control systems of nonlinear plants in many industries: shipbuilding, aircraft construction, automobile construction, agriculture and many others.

This paper presents a new tool for feedback control design of nonlinear systems in the presence of non-smooth measurement errors. We introduce a small-gain design approach to robust control of nonlinear uncertain systems with disturbed measurement. As a design ingredient, a modified gain assignment technique for measurement feedback control of nonlinear uncertain systems is proposed. Through a recursive control design approach, the closed-loop system is transformed into a network of input-to-state stable (ISS) systems and the influences of the measurement errors are represented by ISS gains. The feedback control objective is achieved by applying the cyclic-small-gain theorem to the closed-loop system. Moreover, event-triggered control of nonlinear systems is studied in a unified framework of measurement feedback control.

In this article, a nonlinear control algorithm has been presented, in order to reduce vibrational movements of a flexible beam cantilevered in a cart supported by nonlinear stiffness, actuated by a hardly constrained second-order dynamic system. In the presented control algorithm, the interactive model of the solid body and a flexible beam has been extracted and utilized to design an algorithm, based on which the nonlinear vibrations of the tip point of the beam whose function is smooth and nonoscillatory tracking of the predefined desired trajectory are diminished. To design a nonlinear vibration control system of the beam, it has been assumed that the feedback system includes three modules: a vibrational beam cantilevered on a base, a base affected by nonlinear stiffness and actuator’s control force, and a force imposing system with constraints of bandwidth frequency limitation and actuation saturation boundary. In order to design this control system, the generalized tracking error function has been defined to nonlinearly amplify the vibrationally induced error and its rate, which by properly adjusting them, a new quantity can be extracted that satisfies the control system design constraints. To design a tracking control system for a nonlinear vibrating beam for the aforementioned three-modulus system, first, the generalized tracking error for the three modules is separately defined and parametrized, and then, by simultaneously adjusting all the defined parameters systematically, the predominant system presence in Lyapunov stability conditions is guaranteed. To illustrate the multimodule imitative (MMI) controller design algorithm, a moving support connected to a nonlinear spring and damper is considered, which carries a flexible cantilevered beam. The applied actuation system has second-order linear dynamics with the presence of command control saturation boundaries. For each of the abovementioned modules, a generalized tracking error is defined, and then, it is explained to how simultaneously adjust the parameters based on the stability and actuation constraints. The MMI controller is applied to the mentioned mechanical system modeled in the ANSYS® Mechanical APDL environment, and then, the necessary conclusions are discussed about the performance of the control system in eliminating the vibrations of the flexible arm, considering the actuation constraints while possessing the dominant Lyapunov stability.

Fuzzy finite-frequency output feedback control for nonlinear active suspension systems with time delay and output constraints

Matrix pseudoinverses producing necessary and sufficient conditions for positive and nonnegative definiteness

This paper addresses the problem of robust controller design for holonomic constrained robotic systems which guarantees global asymptotic and exponential like stability of joints' position and velocity tracking error. It is well known that the presence of the constraints makes the controller design more complex as compared to the unconstrained robots such as serial manipulators. Control algorithms should be developed to satisfy both the system dynamics as well as kinematic constraints without explicit computation of the inverse kinematics. The paper develops a new robust control algorithm which can be applied in trajectory tracking control for both parallel and constrained serial manipulators. The method considers the constraint forces in the system dynamics to improve the system stability and tracking performance. The controller is designed through the direct Lyapunov approach and ensures asymptotic and exponential like stability in the position and velocity tracking errors. In order to verify the validity of the proposed control algorithm the algorithm is applied on two different illustrative examples.

This dissertation investigates three principal areas regarding the dynamics and control of nonlinear systems: averaging theory, controllability of mechanical systems, and control of underactuated nonlinear systems. The most effective stabilizing controllers for underactuated nonlinear systems are time-periodic, which leads to the study of averaging theory for understanding the nonlinear effect generated by resonant oscillatory inputs. The research on averaging theory generalizes averaging theory to arbitrary order by synthesizing series expansion methods for nonlinear time-varying vector fields and their flows with nonlinear Floquet theory. It is shown that classical averaging theory is the application of perturbation methods in conjunction with nonlinear Floquet theory. Many known properties and consequences of averaging theory are placed within a single framework. The generalized averaging theory is merged with controllability analysis of underactuated nonlinear systems to derive exponentially stabilizing controllers. Although small-time local controllability (STLC) is easily demonstrated for driftless systems via the Lie algebra rank condition, STLC for systems with drift is more complicated. Furthermore, there exists a variety of techniques and canonical forms for determining STLC. This thesis exploits notions of geometric homogeneity to show that STLC results for a large class of mechanical systems with drift can be recovered by considering a class of nonlinear dynamical systems satisfying certain homogeneity conditions. These theorems generalize the controllability results for simple mechanical control systems found in Lewis and Murray [85]. Most nonlinear controllability results for classes of mechanical systems may be obtained using these methods. The stabilizing controllers derived using the generalized averaging theory and STLC analysis can be used to stabilize both systems with and without drift. Furthermore, they result in a set of tunable gains and oscillatory parameters for modification and improvement of the feedback strategy. The procedure can not only derive known controllers from the literature, but can also be used to improve them. Examples demonstrate the diversity of controllers constructed using the generalized averaging theory. This dissertation concludes with a chapter devoted to biomimetic and biomechanical locomotive control systems that have been stabilized using the generalized averaging theory and the controller construction procedure. The locomotive control systems roll, wriggle, swim, and walk, demonstrating the universal nature of the control strategy proposed.